Broschu re HBE kor 3:Newsletter 3d - Annex49 · PREFACE The first time I encountered with an example of exer-gy analysis on the built environment dates back to the year of 1994 when

reportECBCS Annex 49

Low Exergy Systems for High-PerformanceBuildings and Communities

Working report of IEA ECBCS Annex 49

“Human-Body Exergy Balance and Thermal Comfort“

By Masanori Shukuya1) and his co-workers: Masaya Saito2); Koichi Isawa3); Toshiya Iwamatsu4); and Hideo Asada5)

reportECBCS Annex 49 IM PRINT

1) Masanori Shukuya is a professor at GraduateSchool of Environmental and Information Studies,Tokyo City University (former Musashi Institute ofTechnology until March 2009)

2) Masaya Saito is an assistant professor at theSchool of Design, Sapporo City University. Hewas involved in developing the 1st version ofhuman-body exergy calculation model made in1996 to 2001, while he was a Ph.D. candidateat Musashi Institute of Technology.

3) Koichi Isawa is a research engineer at the Institu-te of Technology, Shimizu Cooperation. He wasinvolved in developing the 2nd version of human-body exergy calculation model in 1999 to 2004,while he was a Ph.D. candidate at Musashi Insti-tute of Technology. He focused on winter cases inparticular.

4) Toshiya Iwamatsu was a research assistant and aPh.D. student at Graduate School of Environmen-tal and Information Studies, Musashi Institute ofTechnology. He has also been involved in develo-ping the 2nd version of human-body exergy cal-culation model since 2005. He has been focusingon summer cases in particular. Since April 2009,he is a research associate at Tokyo MetropolitanUniversity.

5) Hideo Asada is a consulting engineer at Archi-tech Consulting Co., Ltd. He has been involved inthe development of an Excel-sheet software forhuman-body exergy balance calculation togetherwith a simple evaluation tool for radiant heatingand cooling systems. He also studied at the gra-duate school of Musashi Institute of Technologyand was conferred Ph.D. in 2001.

∗ This report was prepared for the activities at theAnnex 49, a project within the International Ener-gy Agency Energy Conservation in Buildings andCommunity Systems Programme (IEA ECBCS),main focus of which is on “Low-Exergy Systemsfor High Performance Buildings and Communi-ties”; it is also for COSTeXergy (COST C24)action, which is one of the European programsfor the CO-operation of Science and Technologydevelopment (COST).

∗ Much of this text was originally prepared andpublished in 2004 for a Japanese textbook edi-ted and written by M. Shukuya together with hisformer Ph.D. students, “Theory of Exergy andEnvironment” from Hokuto-Shuppan Publisher.

∗ M. Shukuya wrote this report as the principalresearcher on the development of human-bodyexergy calculation model with the help of his for-mer Ph.D. students for the period of 1995 to2008. He spent three months as an Otto-MønstedVisiting Professor at the International Center forIndoor Environment and Energy, Technical Uni-versity of Denmark (ICIEE/DTU) in the period of2008 to 2009 and, thanks to this visiting profes-sorship proposed and realized by Prof. Dr. Bjar-ne W. Olesen, he could devote himself much tothe preparation of this report.

PREFACE

The first time I encountered with an example of exer-gy analysis on the built environment dates back tothe year of 1994 when Prof. Masanori Shukuyapresented his finding at one of the sessions, which Ichaired, of Healthy Building conference held inBudapest. It was already common among the scien-tists and engineers to use the concept of energy, notexergy, for heating and cooling load calculationsand also for indoor thermal environment calcula-tions in relation to thermal comfort. Therefore, Iasked him whether such an exergy analysis helps ushave a better understanding of built environment oropen a new way for designing rational heating andcooling systems in buildings, now called low-exergysystems. He replied that he had the same feeling inthe very beginning and such an attempt should beworthwhile doing. I agreed that it might be so.

Since then over the last ten years, the application ofexergy concept to built environment has becomewell recognized by the scientists and engineersinvolved in building thermal science, especiallythrough the international activity of IEA ECBCSAnnex 49 and its predecessor Annex 37, which wasstarted in 1999. Exergy analysis helps us under-stand further the indoor thermal environment and itsassociated heating and cooling systems in order tomeet the requirements of sustainable buildingdesign.

The indoor environment is for people residing inbuildings. Therefore, such an exergy approachshould be extended to the analysis of human-bodythermal process. The theoretical development ofhuman-body exergy balance model was initiated byProf. Masanori Shukuya and his former studentsabout ten years ago and it has grown to the presentstatus described in this report.

I believe that this report is useful for those interestedin indoor thermal environmental science and itsassociated building system design from the viewpo-int of exergy to have a basic understanding ofhuman thermal process and also to have a look atwhat should be challenged in the coming years forsustainable building planning and design for humanthermal comfort and well being.

Prof. Dr. Bjarne W. OlesenHead of the International Centre for Indoor Environment and Energy, Technical University of Denmark

reportECBCS Annex 49PREFACE

reportECBCS Annex 49 SUMMARY

SUMMARY

This report describes how the human-body exergybalance equation is set up in detail and also discus-ses some results of its numerical calculation.

Research on the built environment with the exergeticviewpoint has been grown to the present since early1990s. In due course, the exergy concept itself wasdeveloped and sharpened to a large extent, in orderto make it possible to apply in particular to the fieldof building physics and its related areas such asindoor thermal environmental science. Exergy ana-lysis of the built environment equipped with spaceheating and cooling systems articulates how muchand where exergy is consumed in the whole processfrom its supply and consumption to the resultant ent-ropy generation and disposal. Space heating andcooling systems themselves are physical systems attheir own right, but their purpose is to control thebuilt environmental condition within a certain rangethat allows the occupants to be healthy and com -fortable with rational ways of exergy consumption.

Physics with respect to the built environment and itstechnology must be in harmony with human physio-logy and psychology. In this sense, it is of vitalimportance to have a better understanding of thehuman body as a thermodynamic system at dyna-mic state from exergetic viewpoint; this is to deepenour understanding of the built environment, especi-ally with respect to heating and cooling and therebydevelop rational heating and cooling systems for thebuilt environment in the future.

First, this report reviews the fundamentals of the con-cepts of energy and entropy looking at an imagina-ry heat engine together with the concept of environ-mental temperature, then describes the essence of itsexergy balance and thereby points out that a wor-king system performs its purpose as “exergy-entropyprocess” to maintain its state at dynamic equilibrium.

Then, the precise description of respective terms ofenergy, entropy, and exergy balance equations aregiven followed by the procedure of numerical calcu-lation. The terms developed for the human-bodyexergy balance equation are not necessarily self-evident so that some of their characteristics aregiven and discussed to some extent. They are wetexergy associated with the sweat as liquid water,warm/cool radiant exergies coming into and goingout from the human body, and warm/cool exergyflow by convection around the human body. Then, acouple of numerical examples of the whole human-body exergy balance are given for typical winterand summer conditions and their characteristics arediscussed.

Finally, the human-body exergy consumption ratesfor winter and summer conditions are given: the for-mer is shown as a function of mean radiant tempe-rature and air temperature and the latter as a func-tion of mean radiant temperature and air move-ment. It was found from a series of analyses havingdone so far that there are the minimum values ofhuman-body exergy consumption rate both in win-ter and in summer. These findings suggest that thedevelopment of so-called low-exergy systems forheating and cooling are on the right track.

KEYWORDS: Human body, Heating, Cooling, Exer-gy, Environment, Thermal comfort

reportECBCS Annex 49CONTENTS

CONTENTS

1 INTRODUCTION 7

2 GENERAL CHARACTERISITICS OF EXERGY CONCEPT 7

2.1 Energy and Entropy 7

2.2 Environmental Temperature and Exergy 8

2.3 Exergy-Entropy Process 9

3 SETTING UP THE HUMAN-BODY MODEL 9

3.1 Water Balance 9

3.2 Energy and Entropy Balances 11

3.3 Thermal Exergy Balance 14

4 SOME NUMERICAL EXAMPLES AND THEIR DISCUSSION 19

4.1 Wet Exergy Consumption by Evaporation of Water as Sweat 19

4.2 Warm/Cool Radiant Exergies Coming in and Going out 19

4.3 Warm/Cool Exergy Transfer by Convection 21

4.4 Exergy Balance under Typical Conditions 21

4.5 Human-body Exergy Consumption Rate in Winter and Summer 24

5 CONCLUDING REMARK 27

REFERENCES 27

APPENDICES 29

A.1 Wet/Dry Exergy Contained by Moist Air 29

A.2 Wet Exergy Contained by Liquid Water 31

A.3 Exergy Balance at the Boundary Surface of Moist Air and Liquid Water 32

A.4 Thermal Radiant Exergy 34

A.5 Warm/Cool Exergy Transfer by Convection 36

reportECBCS Annex 49PAGE 7

1 INTRODUCTION

All macroscopic natural phenomena happeningaround us involve the dispersion of energy and mat-ter, which in due course change their forms from oneto another, but the total amount of energy and mat-ter involved is never consumed but necessarily con-served. This is stated clearly by the first law of ther-modynamics: i.e., the total amount of energy is con-served even though forms of energy may changefrom one to another. Nevertheless, such expressionsas “energy consumption”, “energy saving”, andeven “energy conservation” are used very mucheven in scientific discussion these days. In fact, it isconfusing to use one of the most well-establishedscientific terms, energy, to mean “to be conserved”,while at the same time “to be consumed”. Some maysay that it is all right to use these expressions, sinceit is known that they refer implicitly to “energy” asintense energy available from fossil fuels or fromcondensed uranium. This may be true in a sense, butit may also be true that we have forgotten to take acareful look at something that we should do, becau-se of having been so accustomed by the use of theword, “energy”, with the above-mentioned implicitmeaning. It is, I believe, of vital importance to exa-mine our ways of thinking in order to renew themand hence we step forward to be able to havesustainable and better solutions for the future builtenvironment to be developed.

This is why we need to use exergy, one of the thermo-dynamic concepts, to articulate how a system inquestion including human body works. In thermodyna-mic consideration with the exergy concept in its centertogether with the entropy concept, the following is tobe analyzed and to be understood: how much exergyis supplied to a system in question, where and how itis consumed, and then how the generated entropy dueto exergy consumption is discarded into the environ-mental space for the system. Such analysis could leadto a better understanding of lighting, heating, cool ing,and ventilating systems, and thereby allow us to comeup with better solutions for sustainable built-environ-ment systems for the future. With respect to heatingand cooling in particular, it must be interesting andalso important for us to take a careful look at humanbody in relation to thermal comfort from the exergeticviewpoint.

Here in this report, we describe the human-bodyexergy balance model in details and then its calcu-lation procedure after reviewing briefly the essenceof exergy concept in parallel to energy and entropyconcepts and finally we discuss some of the impor-tant findings obtained from our exergy researchdone in the period of 2000 to 2008.

2 GENERAL CHARACTERISTICS OF EXERGYCONCEPT

For exergy analysis, it is necessary to set up exergybalance equations for each of the sub-system com-ponents in a system in question. Some may considerthat it is all right to multiply simply the values of so-called Carnot efficiency and the correspondingenergy values to have exergy values, but it couldoften mislead to a fault answer, or lead only to aninsufficient answer that cannot enable us to have awhole image of the “exergy-entropy process” to bedescribed below.

Therefore we need to start with energy balanceequation together with its corresponding entropybalance equation and thereby to set up exergybalance equations of respective sub-systems of built-environment system. By doing so, it would becomepossible to have a rational picture of a series offunction, that is, the function from exergy supply toentropy disposal. In other words, such thermodyna-mic description enables us to have a holistic andrational picture of the built-environment system. Thesame applies to the human body as a biologicalsystem to be described from the viewpoint of ther-modynamics.

2.1 Energy and EntropyLet us take an example of one sub-system as a sim-ple imaginary heat engine working under a steady-state condition as schematically shown on the left-hand side of Figure 2.1. We first set up its energybalance equation according to the “energy conser-vation law”; i.e., the inflow of energy equals the sumof the outflows of energy. If the sub-system is wor-king under an unsteady-state condition, the changein its energy state must be added to the sum of theoutflows of energy.

The heat engine works in the dispersing flow ofenergy, namely “heat”, from the heat source to thecold source and thereby it extracts non-dispersingflow of energy, namely “work”. Whenever the heatengine produces the useful work, some positivevalue of entropy is necessarily generated. With thisin mind, we can set up the entropy balance equationto be consistent with the energy balance equation.

The limit condition of the heat engine that does notgenerate even a scant amount of entropy is when itis operated with the infinitely-slow motion. The heatengine under such condition is not useful at all, sincethe rate of work extracted is infinitely small. There -fore, any useful heat engines in reality generatesome amount of entropy.

reportECBCS Annex 49 PAGE 8

The unique feature in the entropy balance equationis that there exists a term of “entropy generation” incomparison with energy balance equation. The sumof the inflowing entropy to the system and the gene-rated entropy within it equals the entropy flowingout from it under the steady-state condition. Thisimplies that all of the generated entropy is discardedout of the sub-system in question. If an unsteady-state condition is assumed, the change in its entropystate must be added to the sum of the outflows ofentropy.

The concept of entropy can be regarded to be ameasure to quantify in what degree an amount ofenergy or matter is dispersed or how much thedispersion occurs. “Heat” is one way of energytransfer by dispersion due to conduction, convectionor radiation, sometimes together with mass diffu-sion, namely evaporation of water in the built-envi-ronmental systems. On the other hand, “work” is theother way of energy transfer not by dispersion; it is,in other words, performed by a directional (parallel)movement of molecules composing of a substancethat has a certain shape as solid1).

Energy transfer by heat necessarily accompanieswith entropy transfer and entropy generation, whileon the other hand, energy transfer by work itselfalone accompanies with no entropy transfer. In rea-lity, there are more or less inevitable causes resultingin a decrease in the amount of work to be transfer-red, such as friction, electric resistance and so on.All of them turn into “heat”. It is very important tokeep these facts in mind whenever we set up bothenergy and entropy balance equations.

So far described is focused on the systems operatedunder steady-state conditions, but the same descrip-tion applies to the systems under unsteady-state con-ditions.

2.2 Environmental Temperature and ExergyThe environmental space for a system in question tobe described is filled with dispersed energy. In thecase of a system such as a heat engine as shown inFigure 2.1, the cold source can be regarded as theenvironmental space for the heat source and for theheat engine. Since the concept of entropy is, asmentioned above, a measure to quantify the degreeof dispersion and its unit is J/K (=Onnesa)) (W/K(=Onnes/s) for the rate), the dispersed energy levelof the heat source surrounded by the environmentalspace can be expressed as the product of entropycontained by the heat source and its environmentaltemperature in Kelvin scale, the temperature of thecold source. The product of entropy and environ-mental temperature is called “anergy”, whichimplies dispersed energy; the unit of both energyand anergy is J (W for the rate).

Environmental temperature is sometimes called ‘refe-rence temperature’. Historically speaking, the term‘reference temperature’ must have originated fromthe quantification of temperature by measurementwith the use of a substance such as water “referring”to particular temperatures, namely freezing and boil -ing temperatures2). With this meaning of “reference”in mind, environmental temperature should not beconfused with reference temperature.

Generally speaking, an amount of energy containedby a certain body consists of two portions of energy:one is not-yet dispersed and the other already disper-sed; the latter is the energy fully in equilibrium with thatin the environmental space whose temperature isexactly the “environmental temperature”. In otherwords, a portion of energy to be expressed as the dif-ference between total energy and its dispersed por-tion, anergy, is the amount of energy, which has anability to bring about dispersion of energy and matter.This is exactly the concept of “exergy”. Exergy balan-ce equation is therefore obtained from the two balan-ce equations in terms of energy and entropy togetherwith the concept of “environmental temperature”.

Figure 2.1: An imaginary heat engine representinga portion of the built-environment systems. It workswith the heat source whose temperature is constantat and with the cold source (heat sink) whosetemperature is constant at . The engine extractsan amount of work, , which is not yet dispersed,through the two dispersing flows of thermal energy,

and , together with their corresponding ent-ropy flows, and , from the heatsource to the cold source.

THTL

W

QLQ TH H/ Q TL L/

QH

Heat Engine

Cold Source

Heat Source

HQ

LQ

HT

LT

W

Energy and Mass Conservation

Environmental Temperature

Entropy Generation

Exergy Consumption Theorem

a) “Onnes” comes from H. Kammerlingh-Onnes, a Dutch scientist, who first succeeded in liquefaction of helium and reaching 4.1 K in due course14).

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2.3 Exergy-Entropy ProcessThe unique feature of the exergy balance equation isthat there exists a term of “exergy consumption”,which implies that a portion of exergy supplied fromthe heat source flowing into the system is necessari-ly consumed and thereby an amount of work, whichis exergy itself, is extracted.

In order to remain the state of the imaginary engineshown in Figure 2.1 unchanged so as to keep gene-rating an amount of work at a certain rate, it is neces-sary for the engine to keep disposing of the genera-ted entropy. Even at the limit condition that no entro-py is generated within the engine, while at the sametime no rate of work is obtained, there needs to be anamount of entropy flowing out of the engine andthrown away into the cold source, which is exactly thesame amount to that flowing into the engine.

We call such a series of process, from exergy supplyvia exergy consumption and then entropy generationto entropy disposal, “exergy-entropy process” 19).Table 2.1 summarizes the four steps of one cycle ofexergy-entropy process. Any working systems in rea-lity work as “exergy-entropy process” so that theycan sustain their state at dynamic equilibrium.

“Feeding on negative entropy”, which is an expres-sion coined by Schrödinger trying to explain theessence of life3), some sixty years ago corresponds to“exergy supply” and the whole of exergy-entropyprocess with respect to human body corresponds tothe biochemical process that keeps a “dynamic stateof body constituents” clearly shown by Schoenhei-mer some seventy years ago with clear experimen-tal evidence4). Such holistic images together withwhat is summarized in Table 2.1 applying to avariety of the built-environmental systems includinghuman body is, I think, important for us to look intoa better solution to be come up with, though it maysound a little bit philosophical.

Table 2.1: Exergy-Entro-py Process: four funda-mental steps for a systemto continue its work incyclic operation

1. Exergy supply To feed on energy or matter which has an ability todisperse;

2. Exergy consumption To disperse a portion of the supplied energy or mat-ter inside the system to do work;

3. Entropy generation To generate an amount of entropy proportional to theamount of exergy consumed, which is due to thedispersion of the supplied energy or matter;

4. Entropy disposal To dispose of the generated entropy into the environ-mental space from the system to let its temperature,pressure and molar free-energies(chemical potenti-als), namely the intensive quantities of state, at theirdesired values so that the process can return to thefirst step, exergy supply.

3 SETTING UP THE HUMAN-BODYMODEL

Animals including human being live by feeding onorganic matters containing a lot of exergy in chemi-cal forms. They move muscles by consuming it notonly to get their food but also not to be caught asfood by other animals. All of such activity realizedby their body structure and function is made possi-ble by chemical-exergy consumption.

The chemical-exergy consumption brings aboutquite a large amount of “warm” exergy. In fact, thisis the exergy consumed effectively by those animalscalled homeotherms including human being to keeptheir body-core temperature almost constant, atwhich various bio-chemical reactions necessary forlife proceed smoothly at a controlled rate. This tem-perature level, as we know by our own experiencethrough usually unconsciousness, is generally higherthan the environmental temperature.

There are two kinds of animals from the viewpoint ofthermoregulation of their body temperature: homeo-therms (endotherms) as described just above andpoikilotherms (ectotherms). To the former belongthose animals maintaining their body temperature atan approximately constant level regardless of theirenvironmental temperature variations and to the lat-ter those animals whose body temperature fluctuatesin accordance with their environmental temperaturevariations.

Either homeotherms or poikilotherms generate a cer-tain amount of entropy in proportion to the exergyconsumption inside their bodies in due course of lifeand they must excrete the generated entropy intotheir environmental space, as summarized in Table2.1, by long-wavelength(LW) radiation, convection,conduction, and evaporation.

It is vitally important for the homeotherms to be ableto get rid of the generated entropy immediately andsmoothly to be alive because of their relatively largerate of exergy consumption. We humans are noexception.

In what follows, we discuss the exergy balance ofhuman body as a system of homeotherms and then itsrelation to thermal comfort in the built environment.

3.1 Water BalanceWe drink water several times a day and also excretewater with waste, namely urinate, several times a day.The urination is the primary way of discharging thewater from our body, but there are two other ways:

Inhaled air

Exhaled air

Shell

Core

Blood Circulation

Core

Blood Circulation

Shell

reportECBCS Annex 49 PAGE 1 0

one is by breathing and the other by secreting sweat.The former is originated from the secretion and eva-poration of water inside the internal space of the lungand the latter takes place at our skin surface.

The primary purpose for us to drink water is tomaintain the concentration of various cations,anions and organic compounds necessary for all ofroughly 60 trillion living cells within our body, whileat the same time to dispose of the used blocks ofamino-acids and others by dispersing them into thewater and excrete as urination, and the second pur-pose, equally important as the primary one, is tomaintain the body-core temperature at an almostconstant level regardless of the fluctuations of sur-rounding temperature.

In order for keeping the dynamic equilibrium4) ofhuman body, the disposal of generated entropy dueto chemical-exergy consumption is of vital importan-ce. The thermal-exergy consumption within thehuman body is, in other words, for such inevitableentropy disposal.

Table 3.1 summarizes the approximate amounts ofwater taken in and given off by an average personfor one day5). The water supplied to the body bydrinking and by eating food amounts to 86% andthe rest is generated by biochemical reactions insidethe body.

The chemical compounds contained by most of thefoodstuffs are composed of carbon and hydrogenatoms in addition to nitrogen in proteins so that theirdecomposition under the condition at body tempera-ture with a help of various enzymes and with the exi-stence of much oxygen molecules brought by brea-thing results in the production of carbon-dioxide andwater molecules as by-products of the primary pro-duction of building blocks and a variety of proteinsmade of amino-acids as building blocks for our bodycells and ATP, adenosine tri-phosphate, as fuel.

Table 3.1 Water balance of a human body for one day

In short, the hydrogen atoms contained by variousorganic matters such as glucose, proteins, and fattyacids react with the oxygen atoms supplied by bre-athing and thereby the water molecules are genera-ted. This implies that the “wet” exergy of water isproduced by the consumption of chemical exergyoriginally contained by food.

Figure 3.1: Modeling ofa human body consistingof two subsystems: thecore and the shell. Thecore is the central por-tion of the body whosetemperature is keptalmost constant at 37°Cindependent of the vari-ations of surroundingtemperature and humidi-ty. The shell is the peri-pheral portion, whosetemperature is depen-dent much on the varia-tions of surrounding tem-perature and humidityand on the level of meta-bolism.

The output of water amounts to 2500 ml/day, whichis the same as the input. The 60% of water output isdue to urination and a half of the rest, 20%, is dueto breathing and the other half is due to sweat secre-tion by 80%, namely 16% of the total output, and theexcretion with waste matter by 20%, namely 4% ofthe total.

Both drinking and urinating are the intermittentbehaviors so that our body weight changes fromtime to time, but if we take a look at our averagebody weight at one-day intervals, there is no chan-ge due to water inflow and outflow. Therefore wecan set up a water-balance equation for the humanbody at a steady-state condition. The water inputequals the water output.

An interesting estimation with respect to the waterbalance of human body is such that all of water con-tained by the body is replaced within twenty days orso assuming that the 70% of the body weight of a 70kg person is comprised of water.

Input Output

2500 ml (100)* 2500 ml (100)

Drinking 1000 (40) Urination 1500 (60)

Eating food 1150 (46) Breathing 500 (20)

Metabolism 350 (14) Sweat secretion 400 (16)

Excretion withwaste matter

100 (4)

* The figures in the brackets are relative amounts to the input or the output in percentage

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[The inhaled humid air] +[The liquid water generated by metabolism in the core] +

[The blood flowing into the core from the shell]= [The exhaled humid air] +

[The blood flowing out of the core to the shell]. (3.1)

At the “shell” subsystem,

[The liquid water generated by metabolism in the shell] +[The blood flowing into the shell from the core]

= [The liquid water secreted as sweat at the skin surface] +[The blood flowing out of the shell to the core]. (3.2)

[The inhaled humid air] + [The liquid water generated by metabolism in the core]

+ [The liquid water generated by metabolism in the shell]= [The exhaled humid air]

+ [The liquid water secreted as sweat at the skin surface]. (3.3)

3.2 Energy and Entropy BalancesAccording to our daily experience, chemical exergycontained within the foodstuffs may seem to be cons-umed mostly for the production of work, but we mustnot forget that it is also consumed for maintaining avariety of body structure and function in order4). Fromthe thermodynamic viewpoint, the human body is atypical dissipative structure, which self-organizes itsform by running the “exergy-entropy” process, thechain of exergy supply, its consumption and the resul-tant entropy generation, and the entropy disposal. Theproduction of work is never realized without chemical-exergy consumption for the body structure and itsassociated function.

If the liquid water contained by foodstuffs is squeezed,then they would burn very well. Although it is only withan imagination, the same would be true for the humanbody. As described in 3.1, there is always the waterinflow and outflow through the human body. The 65 to70 % of our body weight is always filled with liquidwater so that a sudden rise of body temperature is notlikely to happen; if it happened, it could cause an irre-versible fatal damage of a complex body structure andfunction. We can say that the structure and the func-tion of our body are formed by a moderate rate ofburning foodstuffs in a special manner with the abun-dance of water. In due course, a large amount of ther-mal energy and entropy is produced necessarily.

The thermal energy has to be dumped into the envi-ronmental space, because it is accompanied with alot of entropy generated within the human body forthe complex bio-chemical reactions. Otherwise thehuman body could malfunction as described above.

Let us assume that a human-body system as shown inFigure 3.2 resides in a room space. The temperaturesof the human-body, room air, and outdoor air areassumed to be higher in this order. Thermal energyoutgoing across the body surface first enters the roomspace and then flows out into the outdoor environ-mental space. The liquid water secreted from thesweat glands forms a thin water film over the skin sur-face and then it evaporates into the room space unlessthe moisture contained by the room air is saturated. Aportion of the room air having the water vapor origi-nating from the human body has to be ventilated sothat the room air can always allow the moisturedischarged from the human body to disperse.

As described in the beginning of this section, humanbeing is one kind of homeotherms, but the tempera-ture of the peripheral part of the body such as handsand foots in particular varies with the surrounding-temperature variations. Therefore, let us assume thatthe human body consists of two subsystems for ther-modynamic modeling: the core and the shell asshown in Figure 3.1.

The core is one subsystem whose temperature ismaintained nearly constant at 37°C almost inde-pendently from the variations of surrounding tempe-rature and humidity variations; while on the otherhand, the shell is the subsystem whose temperatureis rather dependent much on their variations. Bet-ween these two systems, there is a circulation ofblood, whose rate is variable dependent on externaland internal conditions of the body.

The steady-state mass balances of these two subsy-stems with respect to humid air and liquid water canbe described in the form of input being equal to out-put as follows. At the “core” subsystem,

In these equations, all terms of the left-hand side ofthe equal sign are input and those of the right-handside are output. The generated liquid water, whichappears in each of the above two equations, inclu-des an amount of water absorbed in the course ofdrinking water and eating food in addition to thatgenerated in the course of metabolism.

Combining the two equations yields the waterbalance equation for the whole human body.

The exhaled humid air is more humid than the inha-led humid air, since it contains the water vapor origi-

nating from the liquid water generated in the core.The liquid water to be secreted as sweat at the skinsurface is assumed to originate from the liquid watergenerated in the shell that is expressed at the lefthand side of eg. (3.3).

Inhaled air

Exhaled air

Radiation

Blood Circulation

Cloth

Evaporation

Tr , pvr , par

To , pvopao

Tcl , pvcl Tsk , pvs(Tsk)


Most portions of the outside surface of the body-shellare covered by cloth, but the rest is naked; the head,the face, and the hands are exposed usually to theenvironmental space. The whole shape of humanbody is complex because of the head, the arms, andthe legs hanging on the body center. Theoreticallyspeaking, it should be possible to set up energy, ent-ropy, and exergy balance equations taking suchcomplexity and non-uniformity into consideration,but the more complicated the equations are, themore unknown variables we have to assume foractual calculation. This could result in little improve-ment of the accuracy, especially when looking intothe exergy balance, and could even bring aboutsuch results that are hard to understand. Therefore,we had better make a moderate model with reason-ably accurate exergy calculation by compromisingtwo rather opposite requirements, the precision andthe simplicity.

Here we start with a two-node energy-balancemodel of the human body, since it has been usedquite extensively by building-science researchersand engineers in the field of heating and cooling inbuildings6)~9). This model was given as the energybalance equation, in which the metabolic energyemission rate as input equals the sum of thermalenergy stored within the body and the net thermalenergy transfer into the surrounding space by respi-ration, evaporation, convection and radiation. Thereis also conduction in reality, but it is neglected andimplicitly considered in a portion of convection.

This model has a form convenient for the calculationof body-core, body-shell, and clothing tempera -tures, but not for that of warm/cool exergy andwet/dry exergy. Therefore, it is necessary to make alittle bit of modification of the model.

One modification is to change the net thermal ener-gy transfer due to the humid-air transport by brea-thing and the evaporation of sweat into five explicitforms of the enthalpy values: those of inhaled and

Figure 3.2: Modeling of a humanbody consisting of two subsys tems:the core and the shell. The core isthe central portion of the bodywhose temperature is kept almostconstant at 37°C independentlyfrom the variations of surroundingtemperature and humidity. Theshell is the peripheral portion,whose temperature is dependentmuch on the variations of surround - ing temperature and humidity andon the level of metabolism.

[Thermal energy emerged by metabolism]+ [Enthalpy of the inhaled humid air]

+ [Enthalpy of the liquid water generated in the core by metabolism]+ [Enthalpy of the liquid water generated in the shell by metabolism]

+ [Radiant energy absorbed by the whole of skin and clothing surface]= [Thermal energy stored in the core and the shell]

+ [Enthalpy of the exhaled humid air]+ [Enthalpy of the water vapor originated from the sweat secreted]

+ [Radiant energy emitted by the whole of skin and clothing surfaces]+ [Thermal energy transferred by convection from the whole of skin

and clothing surfaces into the surrounding air]. (3.4)

exhaled humid air, those of liquid water producedby metabolism in the body-core and in the body-shell, and that of water vapor discharged from theskin surface by evaporation.

One other modification is to make the net radiantenergy transfer between the human body andhis/her surrounding into the explicit forms of radiantenergy: one absorbed by the whole of skin and clo-thing surfaces and the other emitted from the wholeof skin and clothing surface.

The modified energy-balance model, the form ofwhich is consistent with the water balance equation(3.3), is expressed as follows.

Metabolic thermal-energy generation as input on theleft-hand side and thermal energy stored within thehuman-body on the right-hand side are the characte-ristic difference in the energy balance equation fromthe water balance equation (3.3). This energy balan-ce equation is set up with an assumption of unsteady-state condition, while on the other hand, the waterbalance equation with steady-state condition.

This energy balance equation assumes that the thermalconduction from the foot to the floor or from the back tothe chair is implicitly included in the portion of convec tive


energy transfer. It is also assumed that the output of workis neglected; in other words, this energy balance equa-tion can be applied to the human body at the posture ofstanding or seating with up to light office work.

All of five terms of the enthalpy values in equation(3.4) must be expressed as the enthalpy differencesfrom the humid air outdoors. This is in order for theactual numerical calculation of exergy balance. Thismathematical operation is done by adding the same

[Thermal entropy given to the body by metabolism]+ [Entropy of the inhaled humid air]

+ [Entropy of the liquid water generated in the core by metabolism]+ [Entropy of the liquid water generated in the shell by metabolism]

+ [Radiant entropy absorbed by the whole of skin and clothing surfaces]+ [Entropy generation]

= [Thermal entropy stored in the core and the shell]+ [Entropy of the exhaled humid air]

+ [Entropy of the water vapor originated from the sweat secreted and dispersing into the surrounding space]

+ [Radiant entropy discharged from the whole of skin and clothing surfaces]+ [Thermal entropy given off by convection from the whole of skin and clothing surfaces].

(3.5)

enthalpy values of outdoor humid air, whoseamounts are consistent with water balance equation,if converted into their corresponding mass values, toboth sides of the energy balance equation.

It is also necessary to make the two terms of radiantenergy be those of radiant energy difference mea-sured from the radiant energy emitted by an imagi-nary surface at the outdoor air temperature; this isdone by adding the same radiant-energy values,which could be emitted from the imaginary surfaceat outdoor air temperature, to both sides of the ener-gy balance equation.

Such operations applied to the terms of enthalpy andradiant energy are not necessary for other threeterms: thermal energy emerged by metabolism, ther-mal energy stored in the body-core and the body-shell, and thermal energy transfer by convection.

The sum of the enthalpies of inhaled humid air andthe liquid water generated by metabolism in thebody-core, which appear on the second and thirdterms on the left-hand side of equation (3.4) relatesto the enthalpy of the exhaled humid air on theright-hand side of the equation. Their difference isthe thermal energy discharged by respiration.

The enthalpy value of the liquid water generated inthe body-shell by metabolism, which appears on the

fourth term of the left-hand side of the energy balan-ce equation relates to the enthalpy of the water vapororiginated from the sweat secreted and dispersinginto the surrounding space, which appears on thethird term of the right-hand side of the energy-balan-ce equation. Their difference is the thermal energydissipated by evaporation at the skin temperature.

The entropy balance equation, which is consistentwith equation (3.4) can be written as follows10)~13).

The first term in the left-hand side of this equation,the entropy given to the body by metabolism, is theentropy generated by all of bio-chemical reactionsin order to keep the body structure and function.

The term of “entropy generation” appeared in theend of the left-hand side of the above equation,which is unique in entropy balance equation beingdistinct from the energy balance equation, is due notonly to thermal energy dispersion caused by tempe-rature difference between the body-core and thebody-shell, but also due to the dispersion of watermolecules into the surrounding moist air. The pres -sure difference in water vapor between the wet skinsurface and the surrounding space of the body playsa key role in the latter case.

Mathematical operations similar to the energybalance equation are also necessary for the entropybalance equation to be applied to develop the exer-gy balance equation. There are three such opera-tions in the case of entropy balance equation.

The first two of them are exactly the same as thoseapplied to the energy balance equation. One of themis to make the five terms of entropy associated withthe inhaled and exhaled humid air, the liquid watergenerated by metabolism in the body-core and in thebody-shell, and the water vapor discharged from theskin by evaporation, into the respective five terms of


3.3 Thermal Exergy Balance12)13)

Thermal exergy balance of human body can bederived by combining the energy balance equationand the entropy balance equation, both of whichare the resultant equations of the mathematical ope-rations described above, together with the environ-mental temperature for exergy calculation, which isoutdoor air temperature.

One may wonder if the environmental temperatureis room air temperature or operative temperature,but it is neither of them, except a case that thehuman body is assumed to be outdoors, for whichthe surrounding air temperature of the human bodyturns again to be exactly the outdoor air (or opera-tive) temperature. If an overall investigation of thehuman-body exergy balance is made together withspace-heating or –cooling system’s exergy balance,the environmental temperature to be taken must bethe same for both human body and space heating orcooling system.

[Warm exergy generated by metabolism]+ [Warm/cool and wet/dry exergies of the inhaled humid air]

+ [Warm and wet exergies of the liquid water generated in the core by metabolism]+ [Warm/cool and wet/dry exergies of the sum of liquid water generated in the shell by

metabolism and dry air to let the liquid water disperse]+ [Warm/cool radiant exergy absorbed by the whole of skin and clothing surfaces]

- [Exergy consumption]= [Warm exergy stored in the core and the shell]

+ [Warm and wet exergies of the exhaled humid air]+ [Warm/cool exergy of the water vapor originating from the sweat and wet/dry exergy of the

humid air containing the evaporated water from the sweat]+ [Warm/cool radiant exergy discharged from the whole of skin and clothing surfaces]

+ [Warm/cool exergy transferred by convection from the whole of skin and clothing surfaces into the surrounding air].

(3.6)

[Chemical exergy supply] – [Exergy consumption]

= [Exergy supply for body function] + [Warm exergy generated]

(3.7)

entropy differences measured from the enthalpy valueof the humid air outdoors. The other is to make thetwo terms of radiant entropy be those of radiant ent-ropy measured from the radiant entropy emitted froman imaginary surface at the outdoor air temperature.

The third of the mathematical operations required is uni-que in entropy balance equation. Let us look at the thirdterm of the right-hand side of the entropy balance equa-tion (3.5). The dispersion of water vapor takes place inthe surrounding space, where there is room air. In otherwords, the water vapor does not disperse into a spaceof vacuum. Therefore, we need to assume a correspon-ding amount of dry air, which is to disperse mutuallywith water vapor to become a portion of room air witha certain value of humidity. Its entropy value is added toboth sides of equation (3.5) to be applied for develo-ping the exergy equation. The idea of this operation isagain exactly the same as that to be done for entropyvalues relating to mass transport by respiration andsweat secretion and also for radiant entropy values.

The first term of eq.(3.6) is the warm exergy produ-ced as the result of chemical exergy consumption fora variety of cellar activities, mainly for the contrac-tion of muscle tissues, the composition of proteins,and the sustenance of the relative concentrations ofvarious minerals in the body cells. The metabolicexergy balance can be expressed as follows:


Tables 3.2-a), b) and c) summarize the details of allterms of eq.(3.6) to make numerical calculation.Those interested in the derivation of mathematicalformulae in Table 3.2-a) are welcome to go throughAppendices from A.1 to A.3.

The procedure of calculation is as follows:1) Assume six variables: metabolic energy genera-

tion rate; amount of clothing in clo unit; surround -ing air temperature; surrounding air relative

The chemical exergy supplied to the human body byeating food is the exergy trapped by the specialcompositions of carbon, hydrogen, oxygen, nitro-gen and other miscellaneous atoms, which origina-tes from the short-wavelength radiant exergy provi-ded by solar radiation. The hydrogen atoms in theliquid water generated by metabolism originatefrom the hydrogen atoms contained within the liquidwater molecules absorbed by the roots of plants forphotosynthesis. All of the warm and wet exergiesgenerated within the human body come from thematters brought by other living creatures. This is theimportant fact that we should keep in mind. Thesecond term of the right-hand side of eq.(3.7) isexactly the warm exergy appeared in the first termof eq.(3.6).

The exergy-consumption appeared in the last termof the left-hand side of eq.(3.6) is due to two kindsof dispersion: one is thermal dispersion caused bythe temperature difference between the body core,whose temperature is almost constant at 37°C, andthe body shell, namely the skin, whose temperaturerange from 30 to 35°C, and the clothing surface,whose temperature range from 20 to 35°C; theother is dispersion of liquid water into water vapor,in other words, free expansion of water moleculesinto their surrounding space.

The chemical exergy consumption appeared ineq.(3.7) usually amounts to more than 95% of che-mical exergy supply. It implies that the amount ofentropy generated in due course is very large, sincethe amount of entropy generation is exactly propor-tional to that of exergy consumption.

All terms in the right-hand side of eq.(3.6) exceptthe first term, exergy storage, play important rolesrespectively in disposing of the generated entropydue to chemical exergy consumption within thehuman body, while at the same time disposing of thegenerated entropy due to thermal exergy consump-tion appeared in eq.(3.6). These processes of outgo-ing exergy flow together with exergy consumptioninfluence very much on human well-being: healthand comfort.

humidity; mean radiant temperature; air current.2) Calculate the body-core temperature, the body-

shell (skin) temperature, the clothing-surface tem-perature, and the skin-wettedness. These valuescan be determined by following the proceduregiven by Gagge et al.6)~8).

3) Calculate the sweat-secretion rate using the skinwettedness.

4) Substitute the results of three calculated tempera-tures and the sweat-secretion rate into the termsgiven in Table 3.2-a) and calculate their valuesexcept the term of exergy consumption.

5) Substitute the values of exergy obtained from theabove calculation into eq.(3.6) and then calcu -late the value of exergy consumption.

The infinitesimal time interval, , given in Table3.2-a) is replaced to be the finite increment of time,

, e.g. 300 seconds, for actual numerical calcula-tion. The same applies to the values of and

. For example, The infinitesimal temperaturechange, , is replaced to be a finite difference intemperature between time and time , sothat the skin temperature at time is calculatedfrom that at time .

If the average rate of exergy input, consumption,storage and output are to be calculated, then thevalues obtained from the calculation above are div -ided by the assumed finite increment of time, .

dTcr

dTsk

dt

Δt

dTcr

nn

Δt

n−1

n−1

Table 3.2-a): The mathematical formulae of the respective terms in eq.(3.6)


Warm exergy generatedby metabolism

MT

Tdto

cr

( )1−

Warm/cool and wet/dryexergies of the inhaledhumid air

V

cRT

P p cRT

p

in

para

vr pvra

vr( )( ) ( ) (M Ma w− +

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪TT T T

T

T

T

TP p

P p

ra o ora

o

o

ravr

v

− −⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

+ −−

) ln

( )ln rr

vovr

vr

voP p

pp

p

dt

−+

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

ln

Warm and wet exergies ofthe liquid water generatedin the core by metabolism

V

c T T TT

T

RT

w core w

pw cr o ocr

o

o

−

− −⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

+

ρ

( ) ln

lMw

nn( )p T

p

dtvs o

vo

⎡

⎣

⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥

Warm/cool and wet/dryexergies of the sum ofliquid water generated inthe shell by metabolismand dry air to let the liquidwater disperse

V

c T T TT

T

RT

w shell w

pw sk o osk

o

o

−

− −⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

+

ρ

( ) ln

Mw

lln( )

lnp T

p

P p

p

P p

P pvs o

vo

vr

vr

vr

vo

+− −

−

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

dt

Warm/cool radiant exergyabsorbed by the whole ofskin and clothing surfaces

f f a hT T

T Tdt

eff cl pj cl rb

j o

j oj

N

ε( )

( )

−

+=

∑2

1

Exergy consumption rate,which is only for thermore-gulation

δS Tg o

Warm exergy stored in thecore and the shell

QT

TdT Q

T

TdT

coreo

crcr shell

o

sksk

( ) ( )1 1− + −

Warm and wet exergies ofthe exhaled humid air

V

cRT

P p T cRT

p T

out

pacr

vs cr pvcr

vs cr( )( ( )) ( ) ( )M Ma w− +

⎧⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪− −

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

+

( ) ln

(

T T TT

T

T

TP

cr o ocr

o

o

cr

−−−

−+p T

P p T

P pp T

p Tvs cr

vs cr

vovs cr

vs cr( ))ln( )

( )ln( )

pp

dt

vo

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

⎡

⎣

⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

Warm/cool exergy of thewater vapor originatingfrom the sweat andwet/dry exergy of thehumid air containing theevaporated sweat

V

c T T TT

T

RT

w shell w

pv cl o ocl

o

o

−

− −⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

+

ρ

( ) ln

Mw

lln lnp

p

P p

p

P p

P pvr

vo

vr

vr

vr

vo

+− −

−

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

⎡

⎣

⎢⎢⎢⎢⎢⎢⎢

⎤

⎦

⎥⎥⎥⎥⎥⎥

dt

Warm/cool radiant exergydischarged from the wholeof skin and clothing surfa-ces

f f hT T

T Tdt

eff cl cl rbcl o

cl o

ε( )

( )

−

+

2

Warm/cool exergy trans-ferred by convection fromthe whole of skin and clo-thing surfaces into the sur-rounding air

f h T TT

Tdt

cl ccl cl rao

cl

( )( )− −1


Table 3.2-b): The mathematical symbols used in Table 3.2-a)

Every term in Table 3.2-a) is expressed for the infinitesimal period of time, and for one squared-meter ofhuman-body surface. The symbols used in the formulae from the top to the bottom denote as follows.

M metabolic energy generation rate [W/m2]

To

outdoor air temperature as environmental temperature for exergy calculation [K]

Tcr

body-core temperature [K]

t time [s] and is its infinitesimal incrementdt

Vin

volumetric rate of inhaled air [(m3/s)/ m2]

cpa specific heat capacity of dry air [J/(kg K)] (=1005)

Ma

molar mass of dry air [g/mol] (=28.97)

R gas constant [J/(mol K)] (=8.314)

Tra

room air temperature [K]

P atmospheric air pressure [Pa] (=101325)

pvr water-vapor pressure in the room space [Pa]

cpv specific heat capacity of water vapor [J/kg K] (=1846)

Mw

molar mass of water molecules [g/mol] (=18.05)

pvo water-vapor pressure of the outdoor air [Pa]

Vw core−

volumetric rate of liquid water generated in the body core, which turns into water vapor andis exhaled through the nose and the mouth [(m3/s)/ m2]

ρw density of liquid water [kg/m3] (=1000)

cpw specific heat capacity of liquid water [J/(kg K)] (=4186)

p Tvs o( ) saturated water-vapor pressure at outdoor air temperature [Pa]

Vw shell−

the volumetric rate of liquid water generated in the body shell as sweat [(m3/s)/ m2]

Tsk

skin temperature [K]

feff

the ratio of the effective area of human body for radiant-heat exchange to the surface area ofthe human body with clothing (=0.696~0.725)

fcl

the ratio of human body area with clothing to the naked human body area (=1.05~1.5)

apj

absorption coefficient between the human body surface and a surrounding surface denotedby [dimensionless] (it can be assumed to be equal to configuration factor, the ratio of inco-ming diffuse radiation to the human body to the diffuse radiation emitted from surface inmost cases);

j

j

εcl emittance of clothing surface [dimensionless](its value is usually higher than 0.9)

hrb

radiative heat-transfer coefficient of a black surface [W/(m2K)] (=5.7~6.3)

Tj

temperature of surface [K]j

δSg

amount of entropy generation during the infinitesimal period of time [(Onnes/s)/m2] (“Onnes” isthe unit of entropy, exactly equal to J/K. “Onnes” comes from H. Kammerlingh-Onnes, a Dutchscientist , who first succeeded in liquefaction of helium and reaching 4.1 K in due course14).)

Qcore heat capacity of body core [J/(m2K)]

dTcr

infinitesimal increment of body-core temperature [K]

Qshell

heat capacity of body shell [J/(m2K)]

dTsk

infinitesimal increment of skin temperature [K]

Vout

volumetric rate of exhaled air [(m3/s)/ m2]

p Tvs cr( ) saturated water-vapor pressure at body-core temperature [K]

Tcl

clothing surface temperature [K]

hccl

average convective heat-transfer coefficient over clothed body-surface [W/(m2K)]


Table 3.2-c): Footnotes for Table 3.2-b)

*1 The value of can be determined from the empirical formula given for human-bodyenergy balance calculation7) as a function of metabolic generation rate. .

Vin

V x Min≈ −1 2 10 6.

*2 The value of can be determined from the empirical formula as a function of meta-bolic energy generation rate and water-vapor pressure in the room space.

Vw core−

V x M x pw core vr−

− −≈ ⋅ −1 2 10 0 029 0 049 106 4. ( . . )

*3 The value of is given as the product of the skin wettedness, [dimensionless],and the maximum evaporative potential from the skin surface to the surrounding roomspace, [W/m2], divided by the latent-heat value of evaporation of liquid water at 30°C (=2450 J/g). .

The value of is determined by the calculation procedure given for effective temperaturebased on human-body energy balance by Gagge et al. 6)~8). The value of can bedetermined as the product of evaporative heat-transfer coefficient, which is proportional toconvective heat-transfer coefficient via a Lewis-relation constant, and the difference inwater-vapor pressure between liquid water at skin-surface temperature and room air.

Vw shell w−

ρ w

Emax

V w Ew shell w−

≈ ⋅ρmax

/ 2450

wE

max

*4 The values of and are given by the following formulae9).and , where

is the fractional skin mass depending on the blood flow rate to the body shell (skin);is the ratio of body mass to body-surface area [kg/m2]; and is speci-

fic heat capacity of human body that is 3490 J/(kg K).

Qcore

Qshell

Q m A ccore sk body body body

= − ⋅( )( / )1 α Q m A cshell sk body body body

= ⋅α ( / ) αsk

m Abody body

/ cbody

*5 The value of is assumed to be equal to that of .Vout

Vin

*6 We assume that the boundary-surface temperature of human-body system is representedby the average clothing temperature. Therefore, thermal exergy outflow by radiation andconvection from the human body includes the clothing temperature(see the last two columnsof Table 3.2-a).) The water vapor pressure for the calculation of wet/dry exergy of humidair coming out from the human-body system should also, strictly speaking, be based on thevalue at the clothing surface. But, in reality, much dispersion of water vapor takes placesdirectly at the skin surface such as forehead, neck, arms and so on. For this reason toget-her with the avoidance of unnecessarily complicated calculation, we use water vapor pres-sure in the room space for the calculation of wet/dry exergy of the humid air containingthe evaporated sweat (see the third row from the bottom of Table 3.2-a).).

*7 The value of can be determined by one of the empirical formulae of convective heat-transfer coefficient of the human body as a whole, which is given for human-body energybalance calculation8).

hccl


4 SOME NUMERICAL EXAMPLES ANDTHEIR DISCUSSION

Here in this section, we first show some numericalexamples of wet exergy given by sweat, warm/coolexergy in relation to radiation and convection, awhole exergy balance under typical outdoor/indoorconditions in winter and in summer, and therebydiscuss their essential characteristics. Finally someresults of the sensitivity analysis of exergy consump-tion rates with respect to mean radiant temperatureand room air temperature in winter conditions andthose with respect to mean radiant temperature andair movement in summer conditions are given anddiscussed.

4.1 Wet Exergy Consumption by Evaporation ofWater as SweatWet exergy contained by liquid water as sweat ori-ginating from the skin surface is consumed more orless until it reaches the surrounding humid air. Thisrelates much to the effectiveness of human-body ent-ropy disposal.

Figure 4.1-a) shows the wet exergy contained by thesum of liquid water generated in the body shell assweat and dry air to let this liquid water disperse,while on the other hand -b) shows the wet/dry exer-gy of humid air containing the water vapor origina-ted from the sweat. Each line of respective graphsrepresents equi-exergy flow rate of wet exergy ordry exergy for 1 m2 of body surface area with theoutdoor air humidity on the horizontal axis and withthe indoor air humidity on the vertical axis. In thesegraphs, the outdoor air temperature is assumed tobe 30°C and equal to the indoor air temperatureand mean radiant temperature. The sweat secretionrate is assumed to be 0.013 g/(s m2), which is givenby the calculation of skin wettedness6~8). For exam-ple, wet-exergy flow rate of 0.13 W/m2 corre-sponds to the liquid water containing 10 J/g

Figure 4.1: Rates of wetexergy contained by thesum of sweat and itsassociated dry air, a),and wet/dry exergy ofthe humid air after theevaporation of sweat, b).All of the lines in thesegraphs represent theequi-exergy flow rate inthe unit of W/m2.

100

90

80

70

60

50

40

30

Ind

oo

r Re

lativ

e H

um

idity

[%]

10090807060504030

Outdoor Relative Humidity[%]

wet

dry

100

90

80

70

60

50

40

30

Ind

oo

r Re

lativ

e H

um

idity

[%]

10090807060504030

Outdoor Relative Humidity[%]

a) Wet exergy contained by the sum of sweat and its associated dry air

b) Wet/dry exergy of the humid air after the evaporation of sweat

(=0.13/0.013) of wet exergy coming out from theskin surface each second.

The wet exergy values indicated just on the diagonalline in the left-hand side graph are those for the con-dition of outdoor air humidity being equal to indoorair humidity, which are the smallest for a variety ofoutdoor air humidity values.

As can be seen in the right-hand side graph, thereis “wet” exergy in the cases of indoor air humidityhigher than outdoors and “dry” exergy in the oppo-site cases. “Dry” exergy contained by a certainamount of resultant humid air even after sweat eva-poration implies that this volume of humid air stillholds a capacity to let disperse the water vapor con-tained by outdoor air. Their values are, whether theyare wet exergy or dry exergy, much smaller than thewet exergy values to be found in the left-hand sidegraph, the sum of sweat and dry air. Their differen-ce is the exergy consumption due to sweat evapora-tion.

For example, in the case of indoor air humidity of70% at the condition of outdoor air humidity of 60%,the sum of liquid water as sweat and its associateddry air flows out at the rate of 0.65 W/m2 of wetexergy, while on the other hand, the correspondinghumid air after evaporation flows at the rate of0.05W/m2 into the surrounding humid air. Their dif-ference, 0.6 W/m2 is the exergy consumption ratedue to the evaporation of sweat.

4.2 Warm/Cool Radiant Exergies Coming in andGoing OutThermal radiative exergy exchange between thehuman body and his/her surrounding surfacesinfluences very much on thermal comfort so that it isimportant not only to understand its qualitativeaspect, but also to grasp the orders of thermal exer-gy values available indoors.

Figure 4.2-a) and -b) show the radiant exergy inci-dent upon human body and that emitted from thehuman body, respectively. These two graphs aredrawn with an assumption of mean radiant tempe-rature equal to room air temperature. The horizon-tal axis represents outdoor air temperature as envi-ronmental temperature for exergy calculation andthe vertical axis the mean radiant temperature.

Radiant exergy incident upon the human-body sur-face becomes null if the outdoor air temperatureequals the mean radiant temperature. The diagonalline in Figure 4.2-a) represents such a case. The left-hand side of this diagonal line represents the cases


Figure 4.2: Warm/coolradiant exergy rates inci-dent upon and emittedfrom the human-bodysurface area of 1 m2.The former is shown onyour left and the latterright. In either of thesegraphs, there is the lineindicating the case ofexergy rate at null,which split warm exergyside in its left and coolexergy in its right.

that “warm” radiant exergy is incident upon thewhole of human body and the right-hand side thecases that “cool” radiant exergy is incident upon thehuman-body surface.

In Figure 4.2-b), the line with neither warm nor coolexergy emission, namely 0 W/m2, corresponds tothe condition that the clothing temperature is justequal to the outdoor air temperature. The left-handside of this line is the cases that warm radiant exer-gy is emitted from the whole of human-body becau-se of the clothing temperature higher than the out-door air temperature. The right-hand side of this lineis the cases that “cool” radiant exergy is emittedbecause of the clothing temperature lower than theoutdoor air temperature.

For example, under a winter condition of outdoorair temperature of 5°C, if the mean radiant tempe-rature is controlled at 20°C, “warm” radiant exergyof 1.5 W/m2 is available at the body surface. Onthe other hand, emitted by the human body is warmradiant exergy of 3.6W/m2. Under such winter con-dition, net warm radiant exergy transfer from thehuman body to the surrounding surfaces turns out tobe 2.1 (=3.6-1.5) W/m2.

If the mean radiant temperature is lower than 20°C,say 15°C, the warm radiant exergy received redu-ces to 0.8 W/m2 from 1.5 W/m2, while on the otherhand, the warm radiant exergy emitted reduces to2.4 W/m2 from 3.6 W/m2. Radiant exergy values inthe case of 15°C of mean radiant temperature aresmaller than those in the case of 20°C and the netwarm radiant exergy transfer turns out to be 1.6(=2.4-0.8) W/m2, which is also smaller than that inthe case of 20°C of mean radiant temperature.

Radiant-exergy exchange between the human-bodysurface and the surrounding surfaces at a highertemperature level must relate much to the thermalcomfort in winter with less cognition of draught.Such a condition is usually more comfortable thanconventional forced convective heating that hasbeen used much in the room spaces with low meanradiant temperature due to poor thermal insulationfor building envelopes.

An appropriate use of heat capacity of the wallstogether with the external insulation and of thermal-ly-well insulating glass windows and sashes enableus to have higher interior surface temperatures,which fluctuate less for the whole period of one day.Such an indoor condition lets the warm radiantexergy available in the room space be at a favorab-ly high level and thereby let the cognition of warmthemerge15)16). Actual examples of this kind of condi-

tion are the well-designed passive solar houses orthose buildings with thermally activated floors orwalls together with appropriate thermal insulationfor the windows and the walls.

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a) Warm/cool radiant exergy rate incident on one squared-meter of body surface

b) Warm/cool radiant exergy rate emitted from one squared-meter of body surface

Let us discuss a summer case with a similar view -point to the winter case described above. Under asummer condition of outdoor air temperature of30°C, if the mean radiant temperature is 25°C,“cool” radiant exergy of about 0.3 to 0.4 W/m2

(=300 to 400 mW/m2) is available. If the meanradiant temperature rises to 28°C, there is still asmall rate of cool radiant exergy available from thesurrounding surfaces, around 0.02 to 0.06 W/m2

(=20 to 60 mW/m2) . Such amounts of rather smallradiant exergy rate seems to play a key role inproviding the occupants with adaptive thermal com-fort with natural ventilation17)18).

“Cool” radiant exergy available from the sky on ahorizontal surface ranges from 0.5 to 1 W/m2,namely from 500 to 1000 mW/m2 19)20). A radiantcooling system, which makes the ceiling or wall sur-face temperature a little lower than outdoor air tem-perature, let those surfaces emit about 0.02 W/m2

(20 mW/m2) of cool radiant exergy quite easily. Thisis even possible by nocturnal ventilation, if the roomspace is equipped with an appropriate level of heatcapacity together with external shading and insula-tion as well as the internal heat generation is mini-mized18). The fact that the rate of radiant exergy tobe available indoors necessary for having coolnessis very small, say 20 mW/m2 or so, and it is onlyone-fiftieth of cool radiant exergy rate from the sky,is worthwhile keeping in mind. This kind of exerge-tic consideration let us recognize the importance ofnatural exergy to be found in our immediate out-door environment1).


Figure 4.3: Warm/cool exergy flow rate by con-vection between the human body and the surround -ing air. The exergy values are indicated with theunit of W/m2. The left-hand side of the line indica-ting the warm/cool exergy flow rate of zero repre-sents the cases that warm exergy is going out fromthe human body, and the right-hand side the casesthat cool exergy is coming into the human-body.

4.4 Exergy Balance under Typical ConditionsFollowing the discussion from 4.1 to 4.3 on the cha-racteristics of the respective terms appeared in thehuman-body exergy balance equation, let us moveonto the discussion on the whole exergy balance ofa human body under some typical summer and win-ter conditions.

The general form of exergy balance equation for asystem is expressed as follows.

4.3 Warm/Cool Exergy Transfer by ConvectionConvection due to air movement affects very muchon thermal comfort levels as well as radiation. Thisis the well-known fact by our own daily experience.Discussed here are some pieces of findings fromhuman-body exergy analyses focusing on thermal-exergy transfer by convection.

Figure 4.3 shows the relationship between room airtemperature and “warm/cool” exergy transferredby convection between the whole of human bodyand the room air. Air movement is assumed to be0.1 m/s for the whole of Figure 4.3. The horizontalaxis represents outdoor air temperature and the ver-tical axis room air temperature, which is assumed toequal the mean radiant temperature. Under a con-dition that the clothing temperature is equal to out-door air temperature, there is neither warm nor coolexergy transferred by convection. This is indicatedby the bold line going upward from around themiddle of horizontal axis to the upper right corner ofthe graph. The left-hand side of this line correspondsto the cases that warm exergy is flowing out from thehuman-body surface into the room air and the right-hand side of this line the cases that cool exergy isflowing onto the human-body surface from the roomair by convection.

Under a winter condition of outdoor air tempera tureof 5°C, if the room air temperature is controlled at20°C, about 1.7 W/m2 of “warm” exergy flows outby convection from the human body. Even if theroom air temperature is raised up to 30°C, there isstill 0.9 W/m2 of warm exergy flowing out by con-vection. This confirms that the purpose of space hea-ting is not to provide a human body with a certainamount of “warm” exergy, but to let him/her dissi-pate warm exergy at an appropriate rate by convec-tionb).

Under a summer condition of outdoor air tempera-ture of 30°C, if the room space is naturally ventila-ted with a sufficient number of air change and there -by the room air temperature is about the same asoutdoor air temperature, 0.1 to 0.2 W/m2 of“warm” exergy flows out from the human body byconvection. On the other hand, if the room air tem-perature is controlled at 24°C or lower, the humanbody does necessarily receive about 0.1 W/m2 of“cool” exergy by convection. Symptoms of so-calledspace-cooling syndrome, “reibo-byo” in Japanese,which is one of the combination of dullness, fatigue,and/or stiffness felt around shoulders and legs,and/or dried eyes usually emerge in such a roomcondition of low air temperature and humidity.“Cool” exergy, probably together with “dry” exergy,given by convection could be its primary cause21)22).If this is so, the purpose of space cooling is not toprovide a human body with “cool” exergy by con-vection.

According to the above discussion so far, the pur -pose of space heating and cooling seems to be neit-her to provide the human body with “warm” exergynor “cool” exergy, but to make the human bodydischarge “warm” exergy at an appropriate rate,that is exactly for entropy disposal.

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[Exergy input] – [Exergy consumption]= [Exergy stored] + [Exergy output]

(4.1)

b) If convective exergy flow rate calculated from the term given in Table 3.2-a) turns out to be positive, it implies “outgo-ing warm exergy”. If the calculated result is negative, it implies “incoming cool exergy”18). More about convective ther-mal exergy calculation is described in Appendix A.5.


What we described in 3.3 was to give all terms ofthe above equation in detail, specific to the humanbody residing in a room space. Equation (4.1) maybe rewritten as follows.

All of the twin-bar graphs shown in Figures 4.4.1 tobe discussed below are consistent with the expressiongiven in equation (4.2). Let us explain this furthertaking a look at Figure 4.4.1, which shows threenumerical examples of the whole human-body exer-gy balance in a winter condition, outdoor air tempe-rature and relative humidity of 0°C and 40%, respec-tively. The indoor operative temperature in thesethree examples is assumed to be 22°C equal to eachother, but the combination of mean radiant tempera-ture and surrounding air temperature are differentfrom each other: they are, from the top to the bottom,22°C; 22°C, 19°C; 25°C, and 25°C; 19°C.

The left-hand-side bars shows the exergy input andthe right-hand-side bars the sum of exergy con-sumption, exergy stored, and exergy outputs. Theexergy input consists of five components: 1) metabolic thermal exergy, which is given by che-

mical-exergy consumption within all of thehuman-body cells;

2) the sum of the exergy contained by the inhaledhumid air;

3) the exergy contained by liquid water generatedin the body core;

4) the exergy contained by the sum of liquid wateras sweat together with dry air for mutual disper-sion; and

5) warm radiant exergy.

In Figure 4.4.1, three components associated withthe inhaled humid air and liquid water emerged inthe body-core and in the body–shell are not so largeas other two components so that they are shown alltogether as one to be “Humid air + Water”. Since theexergy stored is very small compared to the exergyconsumption and other terms of exergy output, it isnot apparent in the bars shown in Figure 4.4.1.

The exergy output consists of four components: 1) the exergy contained by the exhaled humid air;2) the exergy contained by the resultant humid air

containing the evaporated sweat; 3) warm radiant exergy discharged from the whole

of skin and clothing surfaces; and 4) warm exergy transferred by convection from the

whole of skin and clothing surfaces into the sur-rounding air.

[Exergy input] = [Exergy consumption] + [Exergy stored] + [Exergy output]

(4.2)

If the convective exergy transfer to be calculated asone of the outputs turns out to be negative, it impliesthat there is cool-exergy inflow by convection; thisresults in the number of input components being six,while on the other hand, that of output three, alt-hough such a case is not likely to occur in ordinarywinter conditions.

Figure 4.4.1: Three examples of the whole human-body exergy balance under typical winter condi-tion(outdoor air temperature and relative humidity:0°C and 40%). Exergy stored is negligibly small sothat it is not shown in these graphs.

0 20 40 60 80 100

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rgy

Rate

[W

/m2 ]

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MRT = 19 C, ta = 25 C

Meta.(7.6W/m2)

Humid air + Water Humid air

Warmrad.

Con-sump.(3.14)

Warmrad.

Convection

Relative Rate [%]

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rgy

Rate

[W

/m2 ]

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Meta.(7.6W/m2)

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Warmrad.

Con-sump.(2.95)

Warmrad.

Con-vec.

Relative Rate [%]

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Con-vec.

Relative Rate [%]

Input Consumption + Output


The height of each bar indicates the value of inputexergy rate, which is exactly the same as the sum ofexergy consumption rate, exergy stored rate, and theoutput exergy rate. The relative magnitudes of thecomponents explained above are indicated by theircorresponding widths in the horizontal direction.

The input exergy rates are different from each other,though the operative temperature of the three casesis the same. The smallest is given in the case of themean radiant temperature lower than the surroun-ding air temperature, while on the other hand, thelargest in the case of the mean radiant temperaturehigher than the surrounding air temperature.

More than 60% of the input exergy rate is the meta-bolic exergy of 7.6 W/m2 for all three cases, 5 to 15%, the warm/wet exergy contained by the inhaled

humid air and the liquid water to be dischargedmostly from the lung cells, and the rest, 25 to 35 %the warm radiant exergy absorption.

The exergy-consumption rate amounts to 20 to 30 %of the input exergy rate and they are different fromeach other in three cases, among which the smallestis in the case of the mean radiant temperature higherthan the surrounding air temperature, while on theother hand, the largest in the case of the mean radi-ant temperature lower than the surrounding air tem-perature. In general, the smaller the difference in tem-perature between the core and the shell of the humanbody, the smaller also the exergy consumption rate is.

Relative rates of warm radiant exergy emission andconvective warm exergy transfer are very large inthe case of the mean radiant temperature higherthan the surrounding air temperature, compared tothose in the case of the mean radiant temperaturelower than the surrounding air temperature.

In winter, it is very important to make both theabsorption and emission of warm radiant exergy byraising the interior surface temperature so that theaverage temperature of the skin and clothing surfa-ces becomes sufficiently high and thereby the occu-pants do feel comfortable. The fact that the relativerate of warm exergy transfer by convection becomeslarger in the case of higher mean radiant tempera-ture than the surrounding air temperature is due tosuch skin and clothing surface temperature rise. Thisresults in the above-mentioned consequence of asmaller exergy consumption rate.

Figure 4.4.2 shows two examples of the wholehuman-body exergy balance under a typical sum-mer condition in hot and humid regions, outdoor airtemperature and relative humidity of 33°C an 60%,respectively. How to read these twin-bar graphs are exactly the same as Figure 4.4.1. The twin-bargraph at the top shows a case of radiant coolingtogether with natural ventilation and that at the bot-tom a case of mechanical air cooling. For the for-mer, the surrounding air temperature, humidity andair movement are assumed to be 30°C; 65% and0.3 m/s, respectively, and for the latter, 26°C; 50 %,and 0.1 m/s, respectively. For both cases, the meanradiant temperature is assumed to be 27°C.

The profiles of exergy balance in summer cases arequite different from those in winter cases. There arefour apparent differences. One is that the absolutevalues of exergy input rate in summer are muchsmaller than those in winter; this is because of asmall temperature difference between indoors andoutdoors in summer. The second is that the relative

Figure 4.4.2: Two examples of the whole human-body exergy balance under typical summer condi-tion(outdoor air temperature and relative humidi-ty:33°C and 60%). Exergy stored and exergy con-tained by the inhaled air is negligibly small so thatthey are not shown in these graphs.

0 20 40 60 80 100

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rgy

Rate

[W

/m2 ]

0 20 40 60 80 100

Convective cooling(MRT=27 ºC, ta = 26 ºC, 50%rh, 0.1 m/s)

Meta.(0.79W/m2)

Humid air+ Water

Coolradiation

Consumption (2.49)

Exhaled humid air

Coolconvection

Relative Rate [%]

Humid air(sweat)Cool radiation

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[W

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Meta.(0.79W/m2)

Coolradiation

Consumption (2)

Exhaled humid air + Humid air(sweat) +

Cool radiation Coolconvection

Relative Rate [%]

Humid air+ Water

Input Consumption + Output


rates of wet exergy contained by liquid water, espe-cially in the body-shell rather than in the body-core,are much larger than those in winter. The third is thatthere is cool exergy provided by convection in addi-tion to radiation, though its relative magnitude issmaller than that of cool radiant exergy. The fourthis that the relative rates of exergy consumption arevery large compared to the output exergy rate.

The metabolic exergy rate is warm exergy giveninside the human body. With this fact in mind, all ofthe wet exergy of liquid water given inside thehuman body and the cool radiant exergy comingonto the human body in addition to cool exergytransferred by convection is to let this inevitablemetabolic “warm” exergy be consumed in order tomaintain the human body within a desirable ther-mally-well-being state.

The relative magnitude of the output exergy ratesare small as mentioned above, but it does not implythat they are less important; they are essential indisposing of the generated entropy inside the humanbody due to exergy consumption of “warm” and“wet”/”cool” exergies. In other words, the outputexergy rates are small, since they contain a lot ofentropy to be discarded into the environmentalspace for the human body.

4.5 Human-body Exergy Consumption Rate inWinter and in SummerAs described in 3.3, the values of exergy consump-tion can only be obtained from the exergy balanceequation, once all other terms of exergy inputs, sto-rage and output are calculated. The exergy con-sumption rate is the function of the difference in tem-perature and also water-vapor pressure between thecore of the human body and its surrounding space,so that it must relate much to the conditions of ther-mal comfort. Here, we show three numerical exam-ples of the exergy consumption rate in relation tomean radiant temperature and air temperature inwinter cases and mean radiant temperature and airmovement in summer cases.

Figure 4.5.1 shows an example for winter condi-tion12)13). The horizontal axis represents air tempera-ture and the vertical axis mean radiant temperaturesurrounding a human body. Mean radiant tempera-ture is the average of internal surface temperaturesof building windows, walls, floor, and ceiling. Finelines with numbers are equi-exergy-consumption-rate lines within the human body. The metabolic con-dition is assumed to be for sedentary work, clothingfor winter and room air is still, air velocity lowerthan 0.1 m/s.

The bold line drawn from upper-left down to lower-right corresponds to the state of human body whosemetabolic energy emission rate equals the energy out-flow due to radiation, convection, evaporation, andconduction. According to the previous knowledge ofhuman thermal physiology, such a condition in whichoverall energy outflow from the human-body surfaceequals the metabolic energy emission rate providesthe human body with thermal comfort. In other words,any sets of room air temperature and mean radianttemperature on the bold line in Figure 4.5.1 must givea comfortable indoor thermal condition.

There is a set of room air temperature (18 to 20 ºC)and mean radiant temperature (23 to 25 ºC) whichprovides him/her with the lowest exergy consump-tion rate. According to experienced architects andengineers concerned about designing comfortablebuilt environment, a set of relatively high mean radi-ant temperature and relatively low air temperaturebrings about a better indoor thermal quality in win-ter season. This sounds consistent with such anindoor condition that brings about the lowest exergyconsumption rate within the human body as shownin Figure 4.5.1. It suggests that the human body asa biological system has evolved over long yearssince the birth of life on the earth so that humans canfeel the most comfortable with the lower exergy con-sumption rate, at least in winter conditions.

The relationship given in Figure 4.5.1 is yet furtherto be investigated in relation to the preference ofoccupants by experiments in-vitro, laboratory tests,and in-vivo, field surveys.

We can make a similar chart to Figure 4.5.1 as wechange the outdoor environmental condition forsummer season. The values obtained are different,

Figure 4.5.1: Relations-hips between human-body exergy consump-tion rate, whose unit isW/m2 (body surface),and his/her environmen-tal temperature under awinter condition (0ºC;40%rh). There is a set ofroom air temperature (18to 20 ºC) and mean radi-ant temperature (23 to25 ºC) which provideshim/her with the lowestexergy consumption rate.This relationship was firstfound by Isawa and Shu-kuya (2002, 2003).

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but such a relationship that a combination of highermean radiant temperature and lower air temperatu-re gives the lowest exergy consumption rate beco-mes almost the same. This seems consistent withwhat has been so far aimed at in the case of con-ventional convective cooling.

A good combination of nocturnal natural ventilationtogether both with external solar shading and withan appropriate amount of internal thermal mass pro-vides us with an indoor condition of a little lowermean radiant temperature than air temperatureduring daytime, which is comfortable enough espe-cially in residential buildings. Figure 4.5.2 shows anexperimental example of the relationship betweenthe percentage of comfort votes and warm/cool radi-ant exergies available in a naturally ventilated roomwhere the subjects perceived no air current becauseof little outdoor wind, though the windows for crossventilation were open. This result was obtained froman in-situ experiment made in two small woodenbuildings with natural ventilation in summer18).

The closed circles “●” denote the cases that coolradiant exergy is available and the open circles “○”denote warm radiant exergy. As the warm radiantexergy rate grows, the percentage of subjects votingfor comfort decreases. The warm radiant exergyflow rate reaching 20 mW/m2 results in the condi-tion that no subjects vote for comfort. On the otherhand, the same rate of “cool” radiant exergy resultsin a totally opposite condition in which most of thesubjects vote for comfort. An amount of cool radiantexergy rate at 20mW/m2 is available provided thatthe mean radiant temperature is lowered slightlycompared to the outdoor air temperature. As can beseen in Figure 4.5.3, interior surfaces whose tempe-rature is 31 ºC emit about 40 mW/m2 of cool radi-ant exergy in the case of outdoor air temperature of33 ºC.

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Figure 4.5.2: The percentage of comfort votesunder the condition of no perceived air current asa function of radiant exergy emitted from interiorwall surfaces.

These results confirm that the use of external solarshading is the first priority in order to make a com-fortable built environmental condition in summerwith natural ventilation. The use of external solarshading devices together with nocturnal ventilationand the use of moderate thermal mass of floors andwalls realize the production of cool radiant exergyduring the daytime in summer.

There are a lot of existing buildings having no exter-nal but internal solar shading, at least in Japan. Thebuilt environment in those buildings in summer isequivalent to being heated by internal solar shadingdevices as radiant heating panels. This in turn requi-res lower air temperature and humidity to be reali-zed by high-exergy supply.

Figure 4.5.3: Radiant exergy available from theinterior surfaces of building envelopes in a summercondition. Here in this example, the outdoor airtemperature as the environmental temperature forexergy calculation is assumed to be 303 K(=33ºC).The amount of “warm” and “cool” radiant exergyrate ranges from 0 to 250 mW/m2.

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Recent study by Iwamatsu and Shukuya (2008)shows that there seems to be a set of mean radianttemperature and air-current velocity giving thelowest human-body exergy consumption rate23).What follows discusses briefly this result.

Figure 4.5.4 shows a relationship between thehuman-body exergy consumption rate, whose unit isW/m2 (body surface), and the combination of meanradiant temperature and air movement under a sum-mer condition (33ºC;60%rh) in the case of mechani-cal convective cooling. Room air temperature andrelative humidity are assumed to be 26 ºC; 50%rh.The lowest exergy-consumption rate of 2.3 W/m2 orless can be found for the range of 0.3 to 0.4 m/s ofair movement with mean radiant temperature ofabout 26 ºC. But, such a rather high air velocity


Figure 4.5.4 Relationships between human-bodyexergy consumption rate, whose unit is W/m2 (bodysurface), and the combination of mean radiant tem-perature and air movement under a summer condi-tion (33ºC;60%rh) in the case of convective cooling.Room air temperature and relative humidity areassumed to be 26 ºC; 50%rh. This relationship wasfirst found by Iwamatsu and Shukuya (2008).

around the human body in a mechanically air-con-ditioned space must result in discomfort. This is usu-ally due to the fact that the air current coming outfrom the outlet sweep the body surface directly orindirectly and thereby causes the draught or uncom-fortable mechanical patterns of air movement, espe-cially at the hands and foots. This may also causedried eyes, sore throat and others. Therefore, the aircurrent for mechanical cooling mainly by the useconvection should be reduced to the air movementof 0.15 m/s at the highest.

If the air movement is assumed to be 0.1 m/s for thisreason, the lowest exergy consumption rate ofaround 2.4 W/m2 can be found with the mean radi-ant temperature of 24 ºC, which is 2 ºC lower thanthe room air temperature assumed for this cal -culation. This is an indoor environmental conditionthat is rather difficult to realize by a convective coo-ling system alone, whose task is not to cool the wallsurfaces, but the room air. In addition, there are usu-ally some radiant heat sources such as glass win-dows absorbing more or less the incident solar radi-ation and electric-lighting fixtures mounted on theceiling, computer screens and so on.

Therefore, the mean radiant temperature is usuallymuch higher than 24 ºC, say 29 to 30 ºC. There aresome cases that it reaches even higher, almost 31 ºC.If this is the case, we can see from Figure 4.5.4 that thehuman-body exergy consumption rate becomes evenslightly larger and reaches around 2.5 to 2.7 W/m2.

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Figure 4.5.5: Relations-hips between human-body exergy consump-tion rate, whose unit isW/m2 (body surface),and the combination ofmean radiant tempera -ture and air movementunder a summer condi-tion (33ºC;60%rh). Roomair temperature andrelative humidity areassumed to be 30 ºC;65%rh for the indoor aircondition by natural ven-tilation. This relationshipwas first found by Iwa-matsu and Shukuya(2008).

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2.1

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S W 0.25

3.2 3.0

2.3

2.2

Figure 4.5.5 shows the same relationships as Figure4.5.4, but assuming that room air temperature andrelative humidity are different; here they are 30 ºCand 65%. Such a room air condition during daytimeat outdoor air temperature and relative humidity of33 ºC and 60% can be realized by natural ventilationtogether with radiative cooling wall or ceiling panels,thermally-activated building-envelope system, or withthe cool storage by floor, walls and ceiling due to noc-turnal ventilation by either an active system or a pas-sive system made during the previous days24)25).

A combination of mean radiant temperature control-led lower than 30 ºC, say in the range of 28 to 29ºC, and air movement exceeding 0.2 m/s providesthe human body with his/her lowest exergy con-sumption rate. The lowest exergy-consumption rateturns out to be about 2 W/m2 for the air movementsmaller than 0.2 m/s and even a little less than 2W/m2 for the air movement over 0.2 m/s.

In a naturally ventilated room space, almost randomnatural fluctuation of soft air movement, namely bree-ze, brings about pleasant coolness, which is called“Suzushisa” in Japanese; this is rather a dynamiccondition different from static neutrality of neither hotnor cold. It is interesting that the human-body lowestexergy consumption rate given by convective-coolingconditions is larger than that by natural ventilationwith some “cool” radiant exergy to be available fromthe interior wall surfaces in the room space.

This suggests that passive strategies for indoor ther-mal environment control such as solar control byexternal shading device over glass windows andnatural ventilation should come to the first priorityand then there need to be an active cooling system,which can well suit them. The development of low-exergy cooling systems is to be made on this direc-tion, which is consistent with that of low-exergy hea-ting systems24)25).


5. CONCLUDING REMARK

This report has described an application of one ofthe core concepts of thermodynamics, “exergy”, tothe human-body thermoregulatory system in orderto have a better understanding of thermal comfort inthe built environment. In due course, we believe thatwe could demonstrate such a thermodynamicapproach to be fruitful in strengthening our thoughton the development of sustainable future technologywith the rational scientific basis.

The science of thermodynamics has been usuallyconsidered to be one of the completed classicalsciences and to have no room for a further develop-ment, but it is not necessarily true as demonstratedthrough our discussion in this report.

The important points described in this report are asfollows:

1. The concept of exergy can quantify what is cons-umed for a system to work. It is derived by com-bining the concept of energy necessarily to con-serve, that of entropy necessarily to generate,and that of environmental temperature for thesystem in question.

2. Any thermodynamic systems work as “exergy-entropy” process, in which exergy is supplied,consumed and thereby entropy is generated andthe resultant entropy is discarded into the envi-ronmental space for a system in question.

3. With the image of “exergy-entropy” process inmind, we can set up the human-body exergybalance equation with the basis of water-, ener-gy-, and entropy-balance equations with theenvironmental temperature for exergy calcula-tion.

4. In winter, “warm” radiant exergy supplied to thehuman-body surface from the surrounding surfa-ces such as the ceiling, the floor, the walls and thewindows plays a key role in providing the humanbody with a lower exergy consumption rate.Thermal insulation of building envelope such aswalls and windows is usually considered for thepurpose of reducing the overall heat loss and the-reby decreasing the thermal energy requirement,but its role for the purpose of raising the interiorsurface temperature should be highlighted sinceit is equivalent to install a passive type of radiantheating panels. In this sense, thermally-activatedbuilding envelope systems should be recognizedto be attractive as rational low-exergy heatingsystems.

5. In summer especially in hot and humid regions, itis of vital importance to decrease “warm” radiantexergy available from windows and walls inorder to bring about a lower human-body exer-gy consumption rate. The installation of exteriorshading devices over glass windows is essential,while at the same time the role of daylightingshould be re-evaluated since the reduction of theinternal heat generation caused by electric ligh-ting is also essential. The installation of radiantcooling panels as an active system to provide“cool” radiant exergy indoors is in harmony withthe passive strategy for decreasing the “warm”radiant exergy. Therefore, thermally-activatedenvelope systems are considered to be on theright track. The reduction of “warm” radiantexergy together with providing with a smallamount of “cool” radiant exergy makes naturalventilation very effective and attractive.

6. Exergetic research on human-body thermoregu-latory system in relations to space heating andcooling confirmed not only what the rational typeof built-environmental conditioning for humanthermal comfort is, but also the usefulness of theexergy concept itself.

REFERENCES

1) M. Shukuya, “The Exergy Concept and Its Rela-tion to Passive/Active Technologies and Re -newable/Non-renewable Energy Sources”,IEA–ECBCS -Annex 49: Low-Exergy Systemsfor High Performance Buildings and Communi-ty Systems, Newsletter No.2 September 2007,pp.5-7.

2) J.C. Maxwell, “Theory of Heat”, originallypublished by Longmans, Green and Co., in1888, Dover Edition with the notes given by J.Strutt(Rayleigh) in 1891 and with an introduc-tion by P. Pesic in 2001, p.3.

3) E. Schrödinger, “What is life?”, Cambridge,1945, reprinted version in 1967 by Doverbooks.

4) K. Y. Guggenheim, “Rudolf Schoenheimer andthe Concept of the Dynamic State of Body Con-stituents”, The Journal of American Institute ofNutrition, No.121, 1991, pp.1701-1704.

5) M. Fujimoto, “Metabolism of water” in theNew Dictionary of Contemporary Medicine,Ishiyaku-Shuppan Publishers, 1996, p.1383(inJapanese).

6) A. P. Gagge, Y. Nishi, and R. R. Gonzalez,“Standard Effective Temperature – A Single


17) K. Isawa, I. Takahashi, M. Saito and M. Shu-kuya, “Comparison of Human-Body ExergyBalance in Two Rooms Conditioned by ‘Sairei’and by Mechanical Air-Conditioning”, Trans-actions of Architectural Institute of Japan-thesection of Environmental Engineering-,No.556, June 2002, pp.31-38 (in Japanese).

18) M. Shukuya, K. Tokunaga, M. Nishiuchi, T.Iwamatsu, and H. Yamada, Thermal RadiantExergy in Naturally-Ventilated Room Spaceand Its Role on Thermal Comfort、Proceedingsof Healthy Buildings 2006 (Lisboa, Portugal),4-8 June 2006, pp.257-262.

19) M. Shukuya ed., “Theory on Exergy and Envi-ronment”, Hokuto Shuppan Publishers Ltd.,2004 (in Japanese).

20) M. Shukuya, “Exergy Concept and Its Applica-tion to the Built Environment”, Building andEnvironment, Vol.44, Issue 7, July 2009,pp.1545-1550.

21) H. Egashira, R. Sayama, M. Saito, and M.Shukuya, “Study on Fatigue Sensation due toComing in and out Mechanically Air-Conditio-ned Space (Part 1. Field Measurement)”, Pro-ceedings of Annual Meeting, Building ScienceSection, Architectural Institute of Japan, Sep-tember 2001, pp.441-442 (in Japanese).

22) R. Sayama, H. Egashira, M. Saito, and M.Shukuya, “Study on Fatigue Sensation due toComing in and out Mechanically Air-Conditio-ned Space (Part 2. Subjective Experiment)”,Proceedings of Annual Meeting, BuildingScience Section, Architectural Institute ofJapan, September 2001, pp.443-444 (inJapanese).

23) T. Iwamatsu, S. Nagasawa, K. Hayashi, E.Kataoka, N. Kitamura and M. Shukuya, “Studyon the Possibility of SAIREI -A Way of the Radi-ative Cooling- in Apartment Building (Part 3.Comparison of Human-Body Exergy Balancebetween Radiative Cooling with Natural Venti-lation and Conventional Convective Cooling)”,Proceedings of Annual Meeting, BuildingScience Section, Architectural Institute ofJapan, September 2008, pp.529-530 (inJapanese).

24) T. Iwamatsu, Y. Hoshino, E. Kataoka, and M.Shukuya, “An Experimental Study on the Feasi-bility of SAIREI-A Way of Radiative Cooling- inNaturally Ventilated Room Space, Journal ofEnvironmental Engineering, Architectural Insti-tute of Japan, No.618, August 2007, pp.45-52.

25) M. Shukuya, “Radiant Exergy and its Impor-tance for Thermal Comfort in the Built Environ-ment”, IEA/ECBCS/Annex 49 NewsletterNo.3, 2008, pp.5-7.

Temperature Index of Temperature Sensationand Thermal Discomfort”, Proceedings of theCIB Commission W45 Symposium, London1972, HMSO, 1973, pp.229-250.

7) A. P. Gagge, J. Stolwijk and Y. Nishi, “AnEffective Temperature Scale Based on a SimpleModel of Human Physiological RegulatoryResponse”, ASHRAE Transactions 77(1),1971, pp.247-262.

8) A. P. Gagge, A. P. Fobelets, and L. G. Ber-glund, “A Standard Predictive Index of HumanResponse to the Thermal Environment”, ASH-RAE Transactions 92(2B), 1986, pp.709-731.

9) ASHRAE Handbook of Fundamentals 2005,Chapter 8 “Thermal Comfort”, pp.8.1-8.8.

10) M. Saito, M. Shukuya, and T. Shinohara,“Human-Body Exergy Balance and ThermalComfort”, Transactions of Architectural Instituteof Japan-the section of Architectural Planningand Environmental Engineering-, No.534,August 2000, pp.17-23(in Japanese).

11) M. Saito and M. Shukuya, “The Human BodyConsumes Exergy for Thermal Comfort”, Inter-national Energy Agency(IEA) Energy Conser-vation in Buildings and Community Systems(ECBCS)-Annex 37, Low-Ex News No.2, Janu-ary 2001, pp.5-6.

12) K. Isawa, T. Komizo, and M. Shukuya,“Human-Body Exergy Consumption and Ther-mal Comfort ”, International EnergyAgency(IEA) Energy Conservation in Buildingsand Community Systems(ECBCS)-Annex 37,Low-Ex News No.5, June 2002, pp.5-6.

13) K. Isawa, T. Komizo, and M. Shukuya, “TheRelationship Between Human-Body ExergyConsumption Rate and A Combination ofIndoor Air Temperature and Mean RadiantTemperature”, Transactions of ArchitecturalInstitute of Japan-the section of EnvironmentalEngineering-, No.570, August 2003, pp.29-35 (in Japanese).

14) M. Zemansky and R. Dittman, “Heat and Ther-modynamics” Six Ed., McGraw-Hill, 1981,p.519.

15) M. Shukuya, “Exergetic Way of Thinking andSymbiotic Architecture”, Proceedings of the32nd Symposium on Heat Transfer Problems inBuildings, Architectural Institute of Japan,November 2002, pp.51-57.

16) H. Egashira, T. Naoi, K. Isawa, M. Shukuya,M. Ikushima, and M. Ishikawa, “Study on ‘Ata-takasa’ Perception – Comparison of ‘Saion’and ‘Saidan’ (Part 2. Thermal sensation andhuman-body exergy consumption rate)”, Pro-ceedings of Annual Meeting, Building ScienceSection, Architectural Institute of Japan, Sep-tember 2003, pp.601-602 (in Japanese).


APPENDICES

Described here is the concise, but still detailed, deri-vation of mathematical formulae necessary for thenumerical calculation of thermal exergy. Those inter-ested in the fundamentals of thermodynamics andheat transfer and their applications to exergy calcu-lation are welcome to go through what followsbelow. In due course, the equations given in Table3.2 for wet/dry exergies, warm/cool radiant exer-gies and warm/cool exergy transfer by convectionare explained thoroughly.

The first three sections below deal with moist air andliquid water. Then, the following two sections descri-be how to deal with radiation and convection.

A.1 Wet/Dry Exergy Contained by Moist AirSuppose that there is an amount of liquid water,whose upper surface bounds up with an amount ofmoist air above as shown in Figure A.1.1. We assu-me two tiny systems sharing the boundary surfaceeach other: one is the liquid water below the boun-dary surface of liquid water and moist air the mostair and the other the most air above. This sharedboundary surface is open to the heat transfer andalso to the trans portation of water molecules fromliquid to vapor phase or vice versa. Therefore, bothsystems are typic al open systems, but we can simpli-fy the systems to be closed, namely those systems notallowing mass transfer but heat transfer alone. Thismakes easier the derivation of wet/dry exergy formulae.

Figure A.1.1: Two tiny systems near the liquidwater surface: one consists of moist air above thesurface and the other of liquid water below thesurface. They are surrounded by huge spacesabove (moist air) and below (liquid water), whichare the environment for them. Although the systemsize is very small relative to the environment, theystill have enormous number of molecules. See alsothe footnote a) in the last page 38.

The reason for enabling us to assume two closedsystems is that, although there is always the constantsupply of water molecules into the moist-air systemthrough the shared boundary surface from theliquid-water system below, there is also the corre-sponding constant release of exactly the sameamount of water molecules as vapor phase into thesurrounding moist-air space across the upper round-shaped boundary surface. While on the other hand,the same amount of liquid-water molecules as that ofevaporated is also always constantly supplied fromthe surrounding liquid water across the lower round-shaped boundary surface into the liquid-watersystem.

In short, the input and output of water molecules areconstant so that it is equivalent to assume that thereis neither input nor output of water molecules to eit-her of the two systems. These two closed systems aretinya) so that we consider that they are in equilibrium.For this condition, the amounts of internal energyand entropy and also the number of molecules areconstant for either system.

Infinitesimal energy balance equations for the twosystems are first expressed with the quantities ofstate alone, namely temperature, pressure, entropyand volume and then they are combined with theconditional equations representing the equilibriumin which the sum of infinitesimal increase in entropyof both systems is null.

These series of mathematical operation yields theexact condition of three system variables for theequilibrium: temperature, pressure, and molecularfree-energy (chemical potential). They are related tothermal equilibrium, mechanical equilibrium, andchemical equilibrium, respectively. For the thermallyequilibrium condition, the temperature of bothsystems has to be equal to each other. The same istrue for pressure to have the mechanically equili-brium condition. The last is unique with respect tophase change from liquid water to water vapor orvice versa. The molar free energy of the two systemsis equal to each other for the chemically equilibriumcondition.

The next step starting with this last condition is tocombine an infinitesimal energy change of bothsystems with an infinitesimal change in molar free-energy. Once these infinitesimal changes areexpressed as two mathematical equations, we canthen reduce them into one equation having infinite-simal changes of temperature and pressure, entropyand volume of liquid water and those of watervapor, namely all together six variables. This opera-tion finally brings us a differential equation indica-

Moist air

Liquid water

Dry airWatervapor

Moist air

vV aV v aV V V= +

ting that the rate of an infinitesimal change in satu-rated vapor pressure with respect to that change intemperature is exactly expressed as the ratio of thedifference in entropy between the tiny systems to thatin volume: this important relationship is called Cla-peyron-Clausiusb) equation.

Combining the Clapeyron-Clausius equation to -gether with the ideal gas equation based on Boyle-Gay-Lussacc) theorem and the thermal energy neces-sary for vaporization, the specific latent heat valueof water vapor as a constant of 2450 kJ/kgd), in therange of 0 to 40 ˚C yields the saturated water-vaporpressure, in the unit of Pascal, as a function oftemperature, in the unit of Kelvin, in the form of

If the values of relative humidity and temperature ofa certain moist-air system is given, then its vaporpressure can be calculated as the product ofeq.(A.1.1) and the value of relative humidity in per-centage divided by 100.

Eq.(A.1.1) is useful in numerical calculation ofwet/dry exergy of moist-air systems and also of wetexergy of liquid water. The Clapeyron-Clausiusequation is used again to derive the exergy balanceequation for a liquid-water surface to be discussedin A.3. What has been so far described is the pre-paration for deriving the exergy formula withrespect to moist air. Let us move into the core of thisderivation.

Based upon the fact that a moist-air system, whosepressure within the atmospheric pressure value canbe characterized very well by the ideal-gas equationaccording to the Boyle-Gay-Lussac theorem, weassume that this is also true for each of either satu-rated water vapor or dry air system since their par-tial pressure values are smaller than the atmosphericpressure value. As shown in Figure A.1.2, let us sup-pose a system of water-vapor alone with the volumeof and also another system of dry air alone withthe volume of . If they are mutually dispersed intothe volume of , which is exactly equal to the sumof and , then this brings about the entropyincrease of both systems and their total is just equalto their sum. This is based on Gibbse) theorem claim -ing that neither work nor heat needs for either mutu-al dispersion or separation due to a careful thoughtexperiment with a schematic drawing as shown inFigure A.1.3.

pvsT

VvVaV

Vv Va


p evsT=

−( . )25 895319

(A.1.1) Figure A.1.2: Mutual dispersion of water vaporand dry air to bring about moist air. The entropyof the moist air is larger than the sum of respectivevalues of entropy with respect to each of watervapor and dry air alone. Their difference is exactlythe summation of the entropy increase in watervapor and dry air due to free expansion, namelythe increase in respective volumes.

Figure A.1.3: Two compartments, A and B, are inthe positions as overlapped in the beginning asshown on your left. The right partition of A allowsthe air molecules to transmit freely, while on thehand, the left partition of B allows the water vaporto transmit freely. Since neither work nor heat isrequired to separate the air and the water vapormolecules, the entropy of the moist-air system isexactly equal to the sum of the entropy values ofthe independent systems of water vapor and dryair as shown on your right,. This is called Gibbstheorem.

A B

A B

,v vp P p−

vp vP p−

,vo vop P p−

system

environment

,v vp P p−

,vo vop P p−

If the relative size of the environment is hugeenough, then the vapor pressure of the environmentremains unchanged even after the moist-air systemhas dispersed. In this particular case, the wholechange in the entropy contained by the system andthe environment between before and after the moist-air system dispersing into the environment, , canbe reduced to the following equation with a little bitof mathematical operation.

ΔS


What we are aiming at here in this discussion is toderive a formula for wet or dry exergy contained byan amount of moist air whose relative humidity is dif-ferent from its surrounding moist air. For this purpose,the discussion so far has to be extended as follows.

As can be seen in Figure A.1.4, suppose that thereare a system and the environment: the former haswater-vapor pressure of and dry-air pressure of

, where is the atmospheric pressure; thelatter has and .The sum of the entropycontained by the system and the environment can beexpressed by following exactly what was describedabove, based upon Gibbs theorem.

P pv−pv

Ppvo P pvo−

Figure A.1.4: A moist-air system whose vaporpressure, , is different from that of its environ-ment, . The atmospheric pressure is and thepressure denoted by in the system is thedry-air pressure. The same applies to the dry-airpressure in the environment. We assume that therelative size of the environment to the system islarge so that the dispersion of moist air containedby the system into the environment causes littlechange in the environmental vapor pressure, .The moist air system contains “wet” exergy, if ishigher than , while on the other hand, it con-tains “dry” exergy, if is lower than .

pvpvo P

P pv−

pvopv

pvopv pvo

ΔS nRP pP

P pP

pP

pp

v v v v

vo

=− −

+⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪ln ln , (A.1.2)

where is the whole number of water and dry-airmolecules in the unit of mol and is gas constant,which is equal to 8.314 J/(mol·K). An importantfeature of this equation is that is always greaterthan null for both cases of and .

nR

ΔSp pvo v< p pv vo<

According to the “exergy-consumption” theorem,we can express the general form of exergy balanceequation as follows.

X S Tg o− = 0 . (A.1.3)

X nRTP pP

P pP

pP

ppo

v v v v

vo

=− −

+⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪ln ln . (A.1.4)

xTT

P pP pP

ppp

ov

vv

v

vo

= −−

+⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪( ) ln ln , (A.1.5)

Let us suppose that is an amount of exergy con-tained by the moist-air system shown in the left ofFigure A.1.4, and then the entropy generation, ,corresponds exactly to the entropy increasemention ed above. The product of the entropy gene-ration, , and the environmental temperature, ,is the exergy consumption. Therefore, the exergycontained by the moist-air system can be expressedas follows.

X

Sg

Sg To

It is convenient to express the moist-air exergy as avolumetric intensive value as follows.

where is the temperature of the moist-air system.

Equation (A.1.5) can also be obtained from thegeneral formula of chemical exergy to be containedby an open system, which is expressed as the sum-mation of the respective products of the difference inmolar free-energy (chemical potential) of molecularcomponents between the system and the environ-ment and the number of molecules in the unit of mol.We reach exactly the same result as eq.(A.1.5).

T

A.2 Wet Exergy Contained by Liquid WaterAn amount of liquid water as an open system, whosetemperature is equal to the environmental tempera -ture, , still has an amount of exergy called “wet”exergy, since it can disperse into its environment bymass diffusion. What follows describes how to deri-ve the formula of wet-exergy for liquid water.

First, suppose that there is an amount of moist airwhich contains mol of water molecules and theirpressure is in the unit of Pascal. These moleculescan be separated in accordance with Gibbs theo-rem, as shown in Fig. A.1.3.

Let us regard this water-vapor system separated tobe a closed system consisting of water molecules

To

nvpvo

Water vapor

Liquid water

,vo op TWater vapor

aloneHeat

Work

,vs op T

Heat

Liquid water

, oP T( ),( )

v v o

ov v

o

n M L TL Tn MT

( )ln vs ov

o vo

p TW n RT p

=

alone. Starting with this condition, we may considera thought experiment, a series of ‘work’ to compressthe system from vapor phase until saturated isother-mally, namely with outgoing ‘heat’ whose amountexactly equals that of work given, and then ‘cool’ byextracting heat to condense further the saturatedwater vapor into the liquid phase. During these pro-cesses, we assume that the temperature of the systemremains unchanged at . The whole thought expe-riment is schematically shown in Figure A.2.1.

The differences in energy (enthalpy), , and ent-ropy, , contained by the closed system beforeand after becoming liquid phase, are expressed as

To

ΔHlΔSl

For example, turns out to be 96.8MJ/m3 for =303.15K(=30˚C) and =50%.

This is huge if comparing with the order of wet/dryexergy, 50 to 200 J/m3 to be calculated fromeq.(A.1.5). The volumetric wet-exergy values ofliquid water are one-million time larger than thoseof moist air. This fact that liquid water is very rich inwet exergy suggests that its consumption plays veryimportant role in thermo-regulation of human bodyespecially under hot and humid conditions.

xw Toϕo

report

Figure A.2.1: A series of thought experiment tobring a water-vapor system into the liquid-watersystem. In the course of isothermal compression, inwhich the temperature of the system is kept constant,

of entropy is given

off and in the course of cooling, of

energy and of entropy are given off.

n Rp Tpvvs o

vo

ln( )

n M L Tv v o( )

n ML TTv vo

o

( )

ECBCS Annex 49 PAGE 3 2

ΔH n M L Tl v v o= − ( ) , (A.2.1)

ΔS n Rp Tp

n ML TTl v

vs o

vov v

o

o

= − −ln( ) ( )

. (A.2.2)

where is the molar mass of water molecules(18.05 g/mol), is specific latent-heat value atthe environmental temperature, , whose unit isJ/g and is saturated water vapor pressure atthe environmental temperature, , to be calculatedby eq.(A.1.1). Eq.(A.2.1) indicates that the thermalenergy, namely latent heat, is given off in the cour-se of condensation and eq.(A.2.2) the sum of entro-py given off in the course both of isothermal com-pression and of condensation.

Substitution of eqs.(A.2.1) and (A.2.2) into thegeneral form of exergy formula yields the followingequation.

Mv

L To( )

Top Tvs o( )

To

Since is equal to , where is the densityof liquid water and its volume and also the relati-ve humidity, , in percentage value is equal to theratio of to multiplied by 100, we canexpress the volumetric wet exergy of liquid water as

n Mv v ρwV ρwV

ϕopvo p Tvs o( )

Substituting the values of (=1000kg/m3), (=8.314J/(mol·K)), and (=18.05g/mol), isexpressed simply as

ρw RMv xw

X H T Sw l o l= − ⋅Δ Δ

= n RTp Tpv ovs o

vo

ln( )

. (A.2.3)

xR

MTw

w

vo

o

=ρ

ϕln

100. (A.2.4)

x Tw oo

= 460609100

lnϕ

(A.2.5)

A.3 Exergy Balance at the Boundary Surface ofMoist Air and Liquid WaterLet us suppose a liquid-water surface, whose tempe-rature is , surrounded by moist air, as shown inFigure A.3.1.

T

Figure A.3.1: Liquid water surface where evapora-tion is taking place. In due course, water vaporcarries away an amount of entropy in addition toenergy.

where and are specific heat capacity ofwater vapor (=1846J/(kg·K)) and liquid water(=4186J/(kg·K)), respectively. Substituting intoeq.(A.3.2), we get the following equation:

cpv cpw

To

The second term of the left-hand side of eq.(A.3.5)is necessarily greater than zero, since

, , , , ,

, where is relative humidi-

ty in percentage of the surrounding moist air at itstemperature of g).

This confirms that the evaporation of water, a typicalmass-diffusion phenomenon, is exactly accompa-nied by entropy generation quantified by the secondterm of eq.(A.3.5). We may regard eq.(A.3.5) to bean entropy balance equation as ,where is entropy generation to be expressed bythe second term of eq.(A.3.5).

The water vapor does not exist itself alone after itsevaporation, but it disperses spontaneously with themoist air nearby. Assuming that the evaporatedwater molecules of mol does not change thewater-vapor pressure in the surrounding moist air,

, in other words, the relative-humidity value ofthe surrounding air is given to be constant, then thenumber of dry-air molecules in the unit of mol canbe expressed as follows by applying the ideal-gasequation based on Boyle-Gay-Lussac theorem.

0 < nv 0 < Mv 0 < L T( ) 0 < T 0 < R

0100

< =ln( )

lnp Tpvs

vr ϕϕ

T

pvr

Δ ΔS S Sl g v+ =Sg

nv


Δ ΔH n M L T Hl v v v+ =( ) . (A.3.1)

We assume that an amount of liquid water, whosemolecular number is mol, has the energy (enthal-py) level of , which is exactly the difference inenergy at the liquid-water surface temperature, ,and at the environmental temperature, . If thisliquid water evaporates, namely all of the moleculesturn into the vapor phase, then the energy levelbecomes , which is greater than , by anamount of latent heat, . Namely,

nvΔHl

TTo

ΔHv ΔHln M L Tv v ( )

L T L c c Tpv pw( ) ( . ) ( )( . )= + − −273 15 273 15 , (A.3.2)

The specific latent-heat, , which is in the unit ofJ/kg, at an arbitrary value of temperature, , can beapproximated very well by the following equation:

L T( )

T

Subtraction of eq.(A.3.3) from eq.(A.3.2) and multi-plication of over the whole resultant equationyields,

n Mv v

L T L c c To pv pw o( ) ( . ) ( )( . )= + − −273 15 273 15 . (A.3.3)

n M L T c T T n M L T n M c T Tv v o pw o v v v v pv o− + −{ } + = −( ) ( ) ( ) ( ) . (A.3.4)

The first term of the left-hand side of eq.(A.3.4) isexactly and the right-hand side is . Thefact that and can be expressed by therespective corresponding terms is that theenergy(enthalpy) contained by water vapor andliquid water is a quantity of state.

The equation with respect to entropy, which is parallelto eq.(A.3.4) for energy, can be derived starting fromthe Clapeyron-Clausius equation described in A.1, towhich we substitute the relationship of eq.(A.3.3) inste-ad of substituting a constant value to derive eq.(A.1.1)for saturated water-vapor pressuref).

The result is as follows:

ΔHl ΔHvΔHl ΔHv

Δ ΔS n M L TT

Rp Tp

Sl v vvs

vrv+ +

⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪=

( )ln

( ), (A.3.5)

where ΔS n Rp Tp

n ML TT

c TTl v

vs o

vov v

o

opw

o

= − − −⎧⎨⎪

⎩⎪

⎫ln

( ) ( )ln ⎬⎬

⎪

⎭⎪, (A.3.6)

ΔS n Rpp

n M c TTv v

vr

vov v pv

o

= − +ln ln . (A.3.7)

nP pp

navr

vrv=

−(A.3.8)

( ln )

(

Δ

Δ

SP pp

n RP pP p

S

SP pp

n

lvr

vrv

vr

vog

vvr

vr

−− −

−+

= −−

vvvr

vo

RP pP p

ln )−

−

. (A.3.9)

For the reason that the evaporated water moleculescannot exist themselves alone, we add the entropyvalue of dry air for the number of molecules to begiven by eq.(A.3.8) to both sides of eq.(A.3.5); it isactually the addition of negative value of dry-air ent-ropy to be measured from the entropy state corre-sponding to the environmental condition, since thedry air which also cannot exist alone has lower ent-ropy value than the dry air as a portion of the envi-ronment. This operation yields the following equa-tion. Namely,

Using appeared in eq.(A.3.1), which was final-ly expressed by the first term of eq.(A.3.4), and

expressed by eq.(A.3.6) together with the termattached to it as indicated in the first term ofeq.(A.3.9), and the environmental temperature,

, the molar exergy of liquid water, , can beexpressed by

ΔHl

ΔSl

To xl

The first term of the right-hand side of eq.(A.3.10) isthermal exergy, which is either warm or cool, andthe rest is wet exergy contained by liquid water andits associated dry air. The latter, the sum of wet exer-gy contained by liquid water and its associated dryair, was drawn as a numerical example in Figure4.1-a). See p. 19.

The same procedure as for eq.(A.3.10) brings us themolar exergy of moist air expressed as follows:

report

Figure A.4.1: A roomwith an external wall,whose interior surfacetemperature is ,assum ed for theoreticalconsideration of radiantexergy calculation. Theroom is surrounded bythe environmental spacewhose temperature is .

T1

To


x M c T T T TT

RTp Tp

l v pw o oo

ovs o

v

= − −⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

+

( ) ln

ln( )

ooo

vr

vr

vr

vo

RTP pp

P pP p

+− −

−ln

. (A.3.10)

x M c T T T TT

RTpp

RT

v v pv o oo

ovr

vo

= − −⎧⎨⎪

⎩⎪

⎫⎬⎪

⎭⎪

+ +

( ) ln

ln oovr

vr

vr

vo

P pp

P pP p

− −

−ln

. (A.3.11)

The sum of the second and the third terms of theright-hand side of eq.(A.3.11) is wet or dry exergyof moist air, which was drawn as the other numeri-cal example of Figure 4.1-b).

Let us confirm how the exergy balance equation foran amount of liquid water with mol can beexpressed for a special case that the water tempera-ture, , is equal to the environmental temperature,

,

nv

TTo

Substituting eqs.(A.3.10) and (A.3.11) toeq.(A.3.12) yields,

Eq.(A.3.13) indicates that “wet” exergy containedby liquid water is consumed by evaporation even ifthe liquid-water temperature is exactly equal to theenvironmental temperature unless the relative humi-dity in the environment is 100%.

n x S T n xv l g o v v− = . (A.3.12)

S T n RTg o v oo

= ln100

ϕ. (A.3.13)

A.4 Thermal Radiant ExergySuppose that there is a room as shown in FigureA.4.1. Environmental temperature for this room is

in the unit of Kelvin. There is one external walland its interior surface temperature is , again inthe unit of Kelvin. The rate of radiant energy emittedfrom 1m2 of this surface towards the interior spacecan be expressed as

ToT

1

q Tr = εσ1

4 . (A.4.1)

where is the emittance of the surface, which is usu-ally very close to unity, say 0.9 to 0.95 in the cases ofordinary building walls, and is Stephan-Boltzmannconstant, which is equal to W/(m2·K4)h).

The 4th power equation given by eq.(A.4.1) can bederived by performing a series of algebraic opera-tion for the energy balance equation of a closedsystem filled only with electromagnetic wave whosepressure against the interior surface of the walls ofthe system is exactly one-third of the volumetricinternal energy value.

The emission rate of radiant entropy parallel toeq.(A.4.1) can also be derived in a similar mannerand is expressed as follows:

ε

σ5 67 10 8. × −

s Tr =4

3 1

3εσ (A.4.2)

The theoretical consideration to arrive eqs.(A.4.1)and (A.4.2) was first made by Boltzmann.

εσ εσT T2

4

1

4= . (A.4.3)

oT 1T

In order to have radiant exergy equation, we needto combine both eqs.(A.4.1) and (A.4.2) and theenvironmental temperature. For its simplest descrip-tion, let us suppose a case of two surfaces facingeach other, both surrounded by the environmentalspace in vacuum, as shown in Figure A.4.2. The twosurfaces as a whole are surrounded by their envi-ronmental space whose temperature is . Unlessthe emittance of the surfaces is unity, there is mutualreflection of radiation, but for simplicity of discus-sion here, we neglect it. This is all right as far as theordinary wall surfaces are concernedi).

Assuming that the temperature of these two surfacesis constant and regarding surface 1 to be a system inquestion, its input is and its output is .Energy balance equation for this system is thereforedescribed as follows:

To

εσT1

4εσT2

4

Due to our assumption that the two surface elementsare surrounded by the environmental space at itstemperature of , their portions of radiant energyto irradiate at the environmental temperature, , isalready “dispersed”. Taking this into consideration,eq.(A.4.3) can be rewritten as follows to get theamount of energy that is not yet dispersedj),

ToTo

Take also the temperature difference between surfa-ce 1 and the environment as . Then wecan express two temperatures, and , as follows

ΔT T To= −1

T1

To


Figure A.4.2: Two surfaces emitting radiant ener-gy and entropy each other in accordance respecti-vely with the 4th and 3rd powers of the absolute tem-perature of the two surfaces.

1T 2T

oT

εσ εσ εσ εσT T T To o2

4 4

1

4 4− = − . (A.4.4)

In the calculation of thermal radiant energy, entropyand exergy for built environment, the temperaturelevel that we encounter with ranges from -10 to40˚C. It allows us to use linearized approximation ofeq.(A.4.4).

Let us show this linearization below taking the caseof surface 1 as an example, referring to a schema-tic drawing shown in Figure A.4.3. Take the avera-ge of two temperatures, and , as , namely,T

1To Tm

TT T

mo=

+1

2. (A.4.5)

Figure A.4.3: The relationship between the systemtemperature, , and the environmental tempera-ture, , with their average, , and their diffe-rence, .

T1

To TmΔT

Absolute zero

100

200

400

The range of temperature for building systems and their environment

1T

mT2TΔ

2TΔ

oT

[K]

T T Tm1 2

= +Δ

and T T To m= −

Δ

2. (A.4.6)

Substituting the relationships expressed byeq.(A.4.6) into the right-hand side of eq.(A.4.4) anda little bit of algebraic operation yields the followingequation.

Since , the above equation can be redu-ced to

ΔT Tm

εσ εσ

εσ

T T

T T T To

m m

1

4 4

3 382

82

−

= +⎧⎨⎩

⎫⎬⎭

( ) ( )Δ Δ . (A.4.7)

εσ εσ εσ

ε

T T T T

h T To m

b o

1

4 4 3

1

4− ≈

= −

( )

( )

Δ, (A.4.8)

where equal to is radiative heat-transfercoefficient of a black surface in the unit ofW/(m2·K).

The equation for entropy, which is parallel toeq.(A.4.3) for energy, can be written as follows:

hb 4 3σTm

ε σ ε σ( ) ( )4

3

4

32

3

1

3T s Tg+ = . (A.4.9)

where is entropy generation rate due to theabsorption of the incoming radiation from surface 2to surface 1. We apply the same operation as wedid from eq.(A.4.4) to eq.(A.4.7) and reach the fol-lowing equation,

sg

ε σ ε σ

ε σ

( ) ( )

( )

4

3

4

3

4

36

2

1

3

1

3

2

T T

T Tm

−

= Δ

++⎧⎨⎩

⎫⎬⎭

22

3( )ΔT

. (A.4.10)

Again, since , ΔT Tm

ε σ ε σ

ε σ ε

( ) ( )

( )

4

3

4

3

4

1

3

2

3

2

T T

T T hm

−

= = Δ bbo

m

T TT

1−

. (A.4.11)

Now, we have the radiant energy emission rateexpressed by eq.(A.4.8) and the correspondingradiant entropy emission rate expressed byeq.(A.4.11). The general form of exergy can bewritten with the difference in energy between the

report

Figure A.5.1: The relationship between clothingtemperature and room air temperature togetherwith the environmental temperature. There are sixcases depending on the conditions among the tem-perature values of the clothing, the room air, andthe environment. They are different in whetherexergy is warm or cool and also in whether exergyis outgoing or incoming. See also Table A.5.1 forthe detail of the conditions. The shaded area corre-sponds to an actual example given in Figure 4.3.


x E T Sr o= − ⋅Δ Δ . (A.4.12)

system and its environment, , that in entropy,, and the environmental temperature, , as fol-

lows:

ΔEToΔS

x h T T T hT TT

h T TT

r b o o bo

m

b o

= − −−⎛

⎝⎜

⎞

⎠⎟

= − −

ε ε

ε

( )

( )(

1

1

11 oo

mT)

. (A.4.13)

For , we can substitute eq.(A.4.8) and for ,eq.(A.4.11). Namely,

ΔE ΔS

x hT TT Tr b

o

o

=−

+ε

( )1

2

1

. (A.4.14)

Taking the relation expressed by eq.(A.4.5) into con-sideration, eq.(A.4.13) can finally be expressed bythe following equation.

Due to the fact that , , , and, the radiant exergy is necessarily lar-

ger than zero except a case that the surface tempe-rature equals the environmental temperature. For thecases of , there is “warm” radiant exergy andfor the cases of , there is “cool” radiant exergy.

A.5 Warm/Cool Exergy Transfer by ConvectionThermal energy transfer by convection from 1m2 ofthe human body, , is calculated by,

0 < ε 0 < hb 01

< +T To0

1

2< −( )T To

T To < 1

T To1<

qc

q f h T Tc cl ccl cl ra= −( ) , (A.5.1)

sqT

f h T TTc

c

cl

cl ccl cl ra

cl

= =−( )

. (A.5.2)

x f h T TTTc cl ccl cl rao

cl

= − −( )( )1 . (A.5.3)

where is the ratio of human body area with clo-thing to the naked human body area (=1.05~1.5),

is average convective heat-transfer coefficientover clothed body-surface in the unit of W/(m2·K)),

is clothing surface temperature in the unit of Kel-vin, and is room air temperature in the unit ofKelvin. The entropy transfer, , parallel to the ener-gy transfer expressed by eq.(A.5.1) is given by

fcl

hccl

TclTra

sc

Exergy transfer by convection is therefore expressedas follows, using the environmental temperature of

in the unit of Kelvin:To

The clothing temperature, , varies with the condi-tions of six variables: mean radiant temperature;ambient air temperature; ambient relative humidity;overall average air velocity around the human bodysurface; the thermal resistance of clothing ensembles;and metabolic energy emission rate. If the five vari-ables except room air temperature are assumed tobe constant, then we can regard the clothing tempe-rature to be a function of the single variable of roomair temperature or vice versa. We can get this rela-tionship by solving the energy balance equation setup for the clothing ensembles as a system. FigureA.5.1 shows schematically the general relationshipbetween clothing temperature, , and room airtemperature, ; the higher the clothing temperatu-re is, the higher also the room air temperature is.

With what has been described so far in mind, wemay regard the rate at which thermal exergy trans-ferred by convection to be calculated fromeq.(A.5.3) as a function of two variables: room airtemperature, , and the environmental tempera -ture, , since we now regard the clothing tempera -ture, , as a function of room air temperature, .

If the values of warm- or cool-exergy transfer by con-vection are given for various sets of room air tem -perature, , and the environmental temperature,

, then they could be given as equi-convectiveexergy lines as shown in Figure 4.3. See p.21.

Tcl

TclTra

TraTo

TraTcl

TraTo

ra clT T=

raT

,cl oT T

cl oT T=

III ( )Cool / Out

V ( )Cool / OutI ( )Warm / In

II ( )Warm / Out

VI ( )Cool / In

IV( )Warm / Out

Theoretically speaking, there are six cases depen-ding on the order of three temperature values: theclothing temperature, , room air temperature, ,and the environmental temperature, . These sixcases are different in whether a given exergy valueimplies “warm” or “cool” and also different in whet-her they are outgoing from or incoming onto thehuman body. These six cases correspond to the sixareas denoted by the symbols from I to VI, which arebordered by three lines in Figure A.5.1; the threelines are as follows: one is the line representing therelationship between room air temperature, , andthe clothing temperature, , which also indicatesthe cases of the clothing temperature equal to theenvironmental temperature, ; one other is the hori-zontal line crossing the point where room air tempe-rature equals clothing temperature; and the last is thediagonal line representing room air temperatureequal to the environmental temperature. Table A.5.1summarizes the conditions of the respective caseswith respect to thermal exergy transfer by convection.

TclTo

Tra

TraTcl

To

Whether exergy transfer by convection turns out tobe “warm” or “cool” is determined by the sign ofCarnotk) factor, , and whether it becomes outgoingas defined in eq.(3.6) or incoming is determined bythe sign of the product of temperature difference,

, and Carnot factor, .

In the cases of II and IV, where the clothing tempera-ture is necessarily higher than room air temperature,there is outgoing warm exergy, while on the otherhand, in the case of VI, there is incoming cool exer-gy due to the fact that the room air temperature islower than the clothing temperature and both arelower than the environmental temperature.

β

βα


Table A.5.1: The details of six cases of exergytransfer by convection

Temperature Warm/Cool In/Out

I - + - Warm In

II + + + Warm Out

III - - + Cool Out

IV + + + Warm Out

V - - + Cool Out

VI + - - Cool In

o cl raT T T< <

o ra clT T T< <

cl o raT T T< <

ra o clT T T< <

cl ra oT T T< <

ra cl oT T T< <

α = −cl raT T 1β = − o

cl

TT

α β×

Other three cases of I, III, and V are very extremeand rarely encountered in reality: in case I, there isincoming warm exergy due to the correspondingroom air temperature higher than both the environ-mental temperature and the clothing temperature; incases III and V, there is outgoing cool exergy due tothe clothing temperature lower than room air tempe-rature.

An actual example with numerical values shown inFigure 4.3 corresponds to the shaded area indicatedwithin Figure A.5.1.

Footnotes for Appendices

a) If each of the tiny systems is a cube whose edgeis 0.1 mm, it contains about watermolecules for the liquid-water system and

molecules of oxygen, nitrogen andwater molecules for the moist-air system. Thesenumbers are large enough to assume thermo-dynamic systems.

b) Clapeyron was a French scientist and engineerwho contributed to the establishment of thisrelationship in addition to his re-discovery ofCarnot’s work; and Clausius was a Germanscientist who first conceived and discovered theconcept of entropy. They worked in the mid of19th century. With respect to Carnot, see k).

c) Boyle was a British scientist who did a series ofexperiment, with the help of another Britishscientist Hooke, to clarify the relationship bet-ween the pressure and the volume of gas. Boy-le’s name is famous for his contribution to thispressure volume relationship, but Hooke’s con-tribution should not be disregarded. Hooke isalso famous for his book “Micrographia” andalso his discovery of the proportionality of thespring length to the weight. More than one-hundred years later, Gay-Lussac found thequantitative proportional relationship betweenthe pressure-volume product and the tempera-ture.

d) The actual latent-heat value at 0 C̊ is only 2.1%larger and that at 40 C̊ only 1.8% smaller than2450 kJ/kg.

e) Gibbs was an American scientist in the 2nd halfof 19th century who is very famous for hismemorial work in the foundation of statisticalthermodynamics.

f) If we use the specific latent heat expressed byeq.(A.3.2) instead of a constant value,2450kJ/kg, then we reach the following

equation: , which is

a little more complicated than eq.(A.1.1), but itinduces only 0.1% of error at maximum for therange of 0 to 70 C̊. On the other hand,eq.(A.1.1) induces 1% of error at maximum forthe range of 0 to 40 C̊. Nevertheless,eq.(A.1.1) having a simple form is applicableto most cases in the built environment.

g) Note that the water vapor pressure of a certainmoist air, , is given as the product of thesaturated water vapor, , and the relati-ve humidity, , divided by 100.

h) The name of this constant, , comes from thecommemorating works of the two scientists inthe 2nd half of 19th century. Stephan, a Germanexperimental scientist, found that overall ther-

34 1015×

2 5 1015. ×

p evs

TT=

− −( . . ln.

)59 866 5 08026815 26

pvrp Tvs( )

ϕσ

mal radiant energy emission rate is proportion -al to the fourth power of the absolute tem -perature of radiant sources investigating high-temperature furnaces, while on the other hand,Boltzmann, an Austrian theoretical scientist,derived the 4th power equation of radiant ener-gy from his then unique consideration trying toforge a bridge between the electromagnetic-wave equations and the thermodynamic ener-gy and entropy equations for a closed system.

i) What we should be careful is a case of an alu-minum surface or a low-emissivity glass surfa-ce, but either of them can be treated as anapplication of what is described here.

j) This mathematical operation is similar to thatfor obtaining eq.(A.3.9) from eq.(A.3.5) withrespect to water vapor and dry air.

k) Carnot was a French scientist who was activefor a rather short period of time in early 19thcentury; he passed away at the age of thirtysix. His theoretical considerations were all verymuch related to the fundamentals of thermody-namics. He clarified that there is the upper limitof ‘work’ output to be obtained from an imagi-nary ideal ‘heat’ engine. This implies that it isof vital importance to have ‘cold’ source inaddition to ‘heat’ source. It is worthwhile keep -ing in mind that both ‘heat’ and ‘cold’ sourcesare equally important, since the former is wellrecognized by many of those concerned aboutso-called energy and environmental problems,but the latter has not yet been well recognized.With the latter in mind, it becomes easier tounderstand thermodynamic systems. Althoughimplicitly, it seems that Carnot’s work alreadyincluded the concept of energy to be conser-ved, entropy to be generated, exergy to beconsumed and the environmental temperaturefor a thermodynamic system.


IEA ECBCS ANNEX 49

Annex 49 is a task-shared international research project initiated withinthe framework of the International Energy Agency (IEA) programme onEnergy Conservation in Buildings and Community Systems (ECBCS).

Annex 49 is a three year project. About 22 research institutes, universitiesand private companies from 12 countries are involved.

The main objective of this project is to develop concepts for reducing theexergy demand in the built environment, thus reducing the CO2-emissionsof the building stock and supporting structures for setting up sustainableand secure energy systems for this sector.

Annex 49 is based on an integral approach which includes not only theanalysis and optimisation of the exergy demand in the heating and coo-ling systems but also all other processes where energy/exergy is used wit-hin the building stock. In order to reach this aim, the project works with theunderlying basics, i.e. the exergy analysis methodologies.

These work items are aimed at development, assessment and analysismethodologies, including a tool development for the design and perfor-mance analysis of the regarded systems. With this basis, the work on exer-gy efficient community supply systems focuses on the development of exer-gy distribution, generation and storage system concepts.

For the course of the project, the generation and supply is as interesting asthe use of energy/exergy. As a result, the development of exergy efficientbuilding technology depends on the reduction of exergy demand for theheating, cooling and ventilation of buildings. Finally, all results of Annex49 are to be made public information. The knowledge transfer and disse-mination activities concentrate on the collection and spreading of informa-tion on ongoing and finished work.

www.annex49.com

Broschu re HBE kor 3:Newsletter 3d - Annex49 · PREFACE The first time I encountered with an example of exer-gy analysis on the built environment dates back to the year of 1994 when

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