CHAPTER 5
CHAPTER 4HYGROTHERMAL COMFORT IN BUILDINGS4.1 General
issuesHaving an enclosed indoor space, in the form of a building,
means more than to be dry. It includes most basic ideas of comfort,
well- being and security.
An essential function of civil buildings (i. e. of those
buildings whose main users are people) consists in creating an
indoor climate adapted to human needs, whose global characteristic
can be described as comfortable.
In a broad sense, the term comfort has the meaning of a state of
satisfaction expressed by people with respect to environment. The
comfort offered by building indoor spaces takes into consideration
a great number of agents acting simultaneously on people who use
these spaces; hygrothermal, acoustical, visual, and
olfactory/respiratory agents must be accounted for in the first
place.
Hygrothermal comfort is but a component of
comfort in indoor spaces.
Since it is necessary a certain amount of energy to be consumed
in order to achieve hygrothermal comfort, a very special attention
is being given lately to this component.
Owing to their dual character, objective and subjective, it is
quite difficult to identify the performance exigencies of indoor
spaces related to hygrothermal exigencies of building users. The
human body normal internal temperature of about 37o C is obviously
an objective matter; on the other hand each person has his own
metabolism, his own thermo-regulator system, his own sensitiveness
to the action of external stimuli etc, which are, of course,
subjective elements.
It is in thermal performance that the
building enclosure still has its most urgent need of improvement
by far. Earlier the 20th century, enclosures lightened, windows
became larger and central heating and cooling systems improved.
Energy was still cheap and there came a tendency to under-emphasise
enclosures thermal role and rely on climate services to put things
right. Not very long ago, people became aware of what had come to
be called the energy crisis. Insulation standards and requirements
have risen sharply in many countries but there are also other
things crucial to thermal performance that must be accounted
for.4.1.2. Scale Influence on Thermal Performance
In case of small buildings, the current thermal concern is to
reduce heat loss, with overheating really becoming a problem only
in hot climates. Passing from small to large buildings, the
so-called scale effect must be emphasised in connection with
thermal performance.
Buildings have metabolic or free heat, produced in proportion to
their volume and indoor activities. Artificial lighting, electrical
machinery, various equipment and, of course, people produce heat.
By the scale effect argument, it follows that large buildings are
more able to keep themselves warm in winter, requiring less heat
input than a scaled-up increase in the needs of small buildings
would seem to indicate (Fig4.1).
Fig. 4.1. Scale Effect on Thermal Performance
The size brings a thermal shift, automatically moving large
buildings a few degrees up the temperature scale in comparison with
small buildings and potentially this is a significant bonus.4.2.
Climate Influence on Thermal Performance
Good thermal protection provided by the enclosure means grater
comfort for building users and, increasingly more important, less
energy consumption in heating and cooling.
Thermal performance has mainly to do with reducing heat
transmission (outwards or inwards) through the enclosure. Where
there is a temperature difference between two places, heat tends to
flow from the higher temperature to the lower nature always trying
to correct imbalances and the transmission can occur in three ways,
namely conduction, convection and radiation.
Conduction is encountered when heat passes through a solid, e.
g. a wall. If one of its faces is heated, the vibrations of the
atomic particles on the surface will intensify, pass their added
excitement to the particles behind them and so on as a jostling
chain-reaction through the wall. The energy moves but the matter
does not.
In convection, the matter does move since it is heat
transmission by the flow of a liquid or gas at the interface with a
solid. Air currents, generated by local temperature differences,
collect heat from warmer surfaces and impart it to cooler ones.
This is natural convection, as opposed to forced convection by
mechanical fans.Radiation involves no matter at all in the commonly
accepted sense, being energy transfer by electromagnetic waves.
This phenomenon is characteristic to gaseous or liquid environment,
as being the only cases in which energy transfer as electromagnetic
wave is possible.
In fig. 4.2. is illustrated, in a suggestive manner, heat
transmission by conduction, convection and radiation.
Fig. 4.2. Heat Transmission/Loss by Conduction, Convection and
Radiation
Obviously, heat transmission through building enclosure varies
with the temperature difference across it, so that the first
determinant factor is climate.
The influence of site location represents a starting point,
especially in case of small buildings.
In the extremely unlikely situation of there being a free
choice, and assuming the climate is temperate so that cold stresses
in winter count more than hot stresses in summer, the site located
half-way up the sun-facing slope of a hill is advantageous (Fig.
5.3.). It avoids the valley floor, where cool dense air tends to
collect and hence hold the temperature several degrees below the
prevailing average. Similarly, it avoids the wind-prone hill crest,
where heat lost by convection increases sharply with the velocity
of the surrounding air stream. There could be around 30 % heat-loss
difference between exposed and sheltered locations.
Fig. 5.3. Influence of Site Location on Thermal Performance
Conversely, in hot climates, the criteria may reverse, with
buildings sited specifically for shade or for catching whatever
cooling breeze is going.
The influence of climate on building shape is an accepted fact.
A buildings heat loss or gain increases with the area of surfaces
it exposes to the air outside. Nature adapts form to climate and so
does tradition in small buildings practice all
around the world, as illustrated Fig. 4.4. Form Adaptation to
Climate There is an influence of solar radiation on optimum plan
shape and orientation which, especially in temperate climates,
tends to offset the compactness argument. It would obviously be a
good thing if a building could be shaped to collect as much solar
heat as possible in winter, and yet avoid collecting to much in
summer; interestingly, it is possible to obtain such a result.
For instance, in the northern hemisphere, during the winter most
of the suns heating effect occurs in the middle of the day, since
in the morning and afternoon the sun is low on the horizon and its
effect is weak. So, if the building is elongated on the east-west
axis, thus presenting a relatively longer southern wall, it will be
exposing a larger collecting surface to available sun radiation.
But what may appear, at first, surprising is that this plan shape
and orientation is also one of the best suited for avoiding
excessive summer heat gain. The long south wall is not so
vulnerable then, simply because the summer sun is so much higher in
the sky. This means that the radiation on this wall is very oblique
and, hence, diluted. In summer, the vulnerable times during the day
are fairly early morning and late afternoon, when the sun is lower
in the sky, and thus its rays arrive at an angle closer to normal
to the walls. This is exactly why the elongated east-west plan
behaves favourable again, because it presents its shorter east and
west elevations to the sun at those times of the day. This
situation is illustrated in Fig. 4.5. Fig. 4.5. Influence of Solar
Radiation on Building Configuration and Orientation The effect of
window sizing on different wall elevations is also present in the
balancing act between reducing heat transmission and yet capturing
solar radiation; the overriding influence is more urgently between
providing adequate day-lighting while satisfying thermal needs as a
whole. Even double glazing has less than half of the insulating
value of a good block/brick cavity wall and is at least 20 times
more admissive to radiation, so thermal questions arise
sharply.
The extend to which daylighting and thermal requirement align or
conflict depends on climate. In the hot, dry climate they are
convergent, since the very bright hot conditions favour relatively
small windows. In moderately warm climates, the windows can be
larger, and the southerly oriented ones may useful add solar gain
in winter time. In the temperate, cool climate, daylight and
thermal needs tend to conflict. Basically, the windows should be as
small as daylighting needs allow; however, a larger southerly
window will have the merit of allowing solar gain in winter. Of
course, large southern windows increase conductive losses to the
outside air, which may persist even when radiation gain occurs;
hence, they are prime candidates for multiple glazing.4.3.
Exigencies Related to Hygrothermal Indoor Microclimate4.3.1.
Man-Indoor Space Heat Exchange The study of hygrothermal comfort
and of the possibilities to achieve it requires, as a first step,
the investigation of human body perception and reaction to
temperature variations of the indoor environment.
Due to metabolic processes, there is a permanent heat production
inside the human body, which must be partially eliminated in order
to keep its internal temperature within normal limits (i.e. around
37o C). A certain amount of heat is received by the human body,
through various specific mechanisms, from its environment.
Theoretically, bodys thermal balance should equal zero, but
actually a relation of the form (5.1) operates: Q = Qinternal +
Qreceived Qeliminated(5.1)where: Q = residual heat (no matter the
sign);
Qinternal = amount of heat produced by the human body during a
given interval of time;
Qreceived , Qeliminated = amount of heat received, respectively
eliminated, by the human body during the same interval of time.
Due to a kind of brain-controlled thermal regulator system, the
human body can momentarily adapt itself to slightly unfavourable
indoor thermal conditions, that is it can take over a limited
amount of residual heat Q. If this amount becomes significant, a
feeling of thermal discomfort appears. Building indoor spaces,
which act as environment for their users, must create conditions
for ensuring properly balanced heat exchanges, thus avoiding
overstressing of human thermal regulator system.
The metabolic heat produced by human body is different from one
person to another and depends on the kind of activity performed.
Several average hourly values are given below: lying, at
rest_____________75...90 Wh/h
sitting, still______________90...105 Wh/h
standing, still____________95...120 Wh/h
slow walking (3 km/h) ____175...230 Wh/h
fast walking (8 km/h) _____230...460 Wh/h
light activities, sitting______120...140 Wh/h
light activities, standing____150...200 Wh/h
heavy activities___________500...700 Wh/hIf these values are
associated to the skin area of human body (1.7...1.8 m2), the
resulting densities of internal thermal flow qinternal (W/m2) are
those presented in Table 5.1. This table also includes values
expressed in met, which represents a reference unit corresponding
to a hourly metabolic heat production of about 58 W/m2 (healthy
adult person, sitting, still).Table 5.1. Metabolic Heat Values
Kind of activityMetabolic Energy
W/m2met
Lying, at rest44...520.75...0.90
Sitting, still52...600.90...1.05
Standing, still56...701.00...1.20
Slow walking100...1301.70...2.25
Fast walking140...2602.40...4.50
Light activities, sitting70...801.20...1.40
Light activities, standing90...1151.55...2.00
Heavy activities280...4004.80...6.90
Heat exchanges that occur in both senses between the human body
and its environment are mainly performed by convection, radiation
and evaporation. Thermal conduction operates in a special manner,
through contact between bodys skin and clothing items; these later
convey then the heat to environment by convection and radiation.
4.3.2. Global Assessment of Thermal Quality of Indoor Spaces
Based on comprehensive investigation carried out on all terms
included in eq. (5.1), the conclusion has been reached that the
value of residual heat Q is dependent on six parameters.
Four of them represent thermo-physical characteristics of indoor
spaces. They are:
ti= average indoor air temperature;
sm = average surface temperature of all elements enclosing the
respective indoor space, also termed average radiant
temperature;
vi= average velocity of indoor air movement;
i= relative humidity of indoor air.
The other two parameters are related to users characteristics,
namely:
M= metabolic energy depending on the kind of activity carried
out;
R= thermal resistance of clothing.
Obviously, for given values of M and R, the feeling of thermal
comfort or discomfort is the result of simultaneous effect produced
by the action of ti, sm,, vi, i . The dependence of thermal comfort
on each of these parameters has been ascertained on experimental
basis by drawing certain relationships (sm= f1(ti), vi= f2(ti) i=
f3(ti), as illustrated in Figs. 5.7, 5.8 and 5.9 respectively.
Fig. 4.7. Dependence of Thermal Comfort on Average Indoor
Temperature
and Relative Humidity of Indoor Air
In order to ensure proper conditions of thermal comfort, a
certain difference between indoor air temperature and average
surface temperature of elements enclosing the indoor space is
required. Optimum values of the difference ti - (sm correspond to
the so-called thermal neutrality (the hatched zone in Fig. 5.7),
meaning that human organism needs no effort to adapt itself to
environment thermal conditions.
If the velocity of indoor air movement vi remains below 0.1 m/s
(for air temperature between +16 and +22o C), it does not influence
the amount of internal heat eliminated by normally dressed people.
The optimum range of thermal comfort in relation to the average
velocity of indoor air movement corresponds to the hatched zone in
Fig. 5.8.
Fig. 4.8. Dependence of Thermal Comfort on Average Indoor
Temperature and Average Velocity of Indoor Air Movement
From the physiological viewpoint, thermal comfort can be
obtained when the relative humidity on indoor air ranges between 30
and 50 percent. If the average indoor air temperature is situated
between +16 and +22, the variation of relative humidity of indoor
air between 30 and 70 percent does not have any relevant influence
on the quantity of internal heat eliminated by a normally dressed
person performing a light-type activity. Significant thermal
discomfort appears - in the form of humid heat exhaustion when
increased air temperature is associated with increased air relative
humidity, a sensation of sultriness occurs, as shown by the hatched
zone in Fig. 4.9).
Fig.5.9. Dependence of Thermal Comfort on Average Indoor
Temperature
and Relative Humidity of Indoor Air
In order to get a global assessment of the thermal quality of a
given environment, in relation to an average user dressed in a
conventional manner, the so-called Predicted Mean Vote (PMV)
indicator is being currently used. It takes into consideration all
six parameters to determine the value of residual heat Q and can be
calculated by the relation: PMV= (0.303.e-0.036.M +
0.028)Q(5.2)
When Q= 0, meaning that the human body eliminates exactly the
internal heat it produces, PMV= 0 and, theoretically, every person
should feel comfortably. However, it has been experimentally found
that is practically impossible to build an environment able to
offer simultaneously same degree of thermal comfort to everybody;
even when Q= 0 (and subsequently PMV= 0), about 5 percent of people
may declare a slight feeling of discomfort. Another indicator,
expressing the probable percentage of declarations of thermal
discomfort has been worked out based on statistical processing of
experimental data. Known as Predicted Percentage of Dissatisfaction
(PPD), In case of residential buildings, for instance, the
following values are required:
In winter time:
average operational temperature of indoor air, +20o C for most
of the rooms;
average velocity of indoor air, max. 0.15 m/s;
relative humidity of indoor air, max. 70 percent, with
recommended
values 50...60 percent;
temperature of flooring surfaces, min. +18o C;
difference between indoor air temperature ti and average value
of surface temperature (si of any enclosure element to be kept as
small as possible. Maximum accepted values for this difference are
4o C for exterior walls and 3o C for terrace floor.
In summer time:
average temperature of indoor air, max. +26o C;
average velocity of indoor air, max. 0.30 m/s;
4.4. Main Phenomena,
Characteristics and Parameters in Hygrothermics of
Buildings4.4.1 Heat, Temperature, Thermal Flow, Density of Thermal
Flow Heat is a special form of energy, whose presence is detected
by the human body which can make the difference between warm and
cold.
The quantity of heat held by a body is expressed by means of its
absolute temperature (T), measured in degrees Kelvin (K). This is
related to the temperature (t or ), measured in degrees Celsius (o
C) by:
T= t + 273(5.4)
Currently, the notation t is used for air temperature, whereas
is used for the temperature of solid bodies.
In case of two bodies with different temperatures that are in
direct or indirect contact, heat passes naturally from the warmer
to the cooler body. This thermal exchange, which stops only when
the temperatures of the two bodies become equal is generally
expressed in terms of quantities of heat, i. e. in quantities of
thermal energy.
The unit for measuring heat quantity is watt-hour [Wh], that has
replaced Kilocalorie [Kcal]; however, this later is sometimes still
in use. Their relationship is given by:
1Kcal= 1.16 Wh(5.5)
The thermal flow () represents the quantity of heat
exchanged
during a time-unit (an hour), measured in watts (W).
The density of thermal flow (q) represents the thermal flow
passingthrough a unit area ( 1 m2) whose points have the same
temperature; it is measured in W/m2.4.4.2. Mass Heat, Thermal
Conductivity, Thermal Diffusivity, Thermal Absorption
The mass heat (c) of a material represents the quantity of heat
required by a mass-unit (1 kg) to increase its temperature by 1o C
(or 1 K); accordingly, the mass heat is measured in Wh/KgoC.
However, there is still a common engineering practice to use the
so-called technical values of mass heat (given in handbooks tables)
expressed in KJ/KgoC. The conversion is based on the relation:
1[Wh/KgoC]= 0.278[KJ/KgoC](5.6)
The thermal conductivity of a material expresses its aptitude to
transmit heat through its mass, from one particle to another. This
aptitude is quantified by means of a coefficient of thermal
conductivity (), whose physical significance is density of thermal
flow passing through a plane element 1 m thick, when a difference
of 1o C exists between the temperature on its two faces;
accordingly, the coefficient of thermal conductivity whose value is
determined on experimental basis for any material is measured in
W/moC.
The thermal conductivity of a material is mainly dependent on
its apparent density, type and structure of pores, humidity and
temperature. Materials with low apparent density (i. e. with high
porosity) have small thermal conductivity (due to the air contained
by pores, which has very small value) and are conveniently used for
thermal insulation. When getting wet and having pores filled with
water, thermal insulating materials diminish drastically their
efficiency (water is about 25 times greater than air).
The design values of for various materials are conventional
values accounting for the probable humidity under service
conditions, as well as for influence of other unfavourable factors
(e. g. increase of apparent density due to settlement of the
material).
A layer of immobile air, 3...5 mm thick, has the lowest known
value of the coefficient of thermal conductivity (= 0.024 W/moC)
among current materials. Highly efficient thermal insulating
materials (such as cellular polystyrene, polyurethane, mineral wool
et al) exhibit extremely small values for (0.020...0.050 W/moC).
For comparison, for several other construction materials are given
below:
solid brick masonry.......................0.80
cellular concrete block masonry....0.27...0.34
mortar..........................................0.70...0.93
reinforcedconcrete.........................1.62..1.74 The
thermal diffusivity (a) of a material expresses its aptitude to
spread heat, i. e. to equalise its temperature. Its value is
computed with the relation:
a=/c [m2/h](5.7)
where:
= coefficient of thermal conductivity [W/moC]
= apparent density [kg/m3]
c= mass heat [Wh/KgoC]
Current values of a range from 0.0016 m2/h for cellular concrete
and gypsum plates to 0.049 m2/h for cellular polystyrene. The
thermal absorption (or assimilation) of a material represents its
capacity to absorb (to assimilate) heat through the surface in
contact with a warmer (solid or fluid) medium. This capacity is
quantified by means of a coefficient of thermal absorption (s),
whose physical significance is ratio between the variation
amplitude of density of heat flow acting on the plane surface of a
material and the variation amplitude of temperature on the
respective surface.5.4.3. Heat Transmission by Conduction
Conduction is the phenomenon of heat transmission (or transfer)
inside a solid or between two solid bodies in contact. Conductive
heat transmission is carried out from one molecule to another; the
energy moves but the matter does not.
In case of building enclosure elements, the conductive thermal
transfer is caused by differences in temperature existing between
their inner and outer faces.
If interior and exterior temperatures of the air (ti and te,
respectively) have negligible variations in time, the conductive
heat flow between any two points of the element has constant value
with respect to time and the thermal conduction is termed
stationary.
If at least one of the temperatures ti or te presents
significant variation in time, the conductive heat flow between any
two points of the element has variable values with respect to time
and the thermal conduction is then termed non-stationary.
5.4.4. Heat Exchanges by Convection and Radiation Between
Surfaces of Enclosure Elements and Adjacent Media
The main phenomena related to heat exchange between interior and
exterior environment that are analysed by the hygrothermics of
buildings take place between: interior and exterior surfaces of
enclosure elements;
surfaces of enclosure elements and the air in their immediate
vicinity ; interior surface of enclosure elements and surfaces of
partitions locatedin their immediate vicinity;In the first case,
heat exchange is carried out by conduction, in the second case by
convection and in the third case by radiation. This complex
phenomenon involving all three elementary types of thermal exchange
is schematically illustrated in Fig. 5.11. Fig.5.11. Schematical
Representation of Elementary Thermal Exchanges Through Enclosure
Elements, if Indoor Temperature is Larger than Out Door Temperature
(ti>te) Convection is the phenomenon of heat exchange between
the surface of a solid body and a fluid in direct contact with
it.
In case of building enclosure elements, thermal convective
exchange occurs on both their surfaces, the fluid being interior
and exterior air, respectively. Generally speaking, air currents
collect heat from warmer surfaces and impart it to cooler ones. In
fact, it is the local temperature differences that cause the
currents; thus, air getting warmer expands, becomes less dense and
starts to float upwards over cooler, denser air flowing in to
replace it.
A typical situation is that of vertical elements of the
enclosure, i.e. exterior walls. In winter time, the temperature of
their outer surface is higher than that of exterior air; the latter
absorbs heat, gets warmer and moves slightly upwards. At the same
time, the temperature of walls inner surfaces is lower than that of
interior air, which looses heat, gets cooler and moves slightly
downwards (Fig. 4.12)
Fig. 4.12. Influence of Convective Thermal Exchanges Upon Air
Temperature in the Vicinity of an Exterior Wall Surface, if Indoor
Temperature is Larger than Out Door Temperature (ti>te)
Radiation is the phenomenon of heat exchange between the
surfaces of two far apart bodies, the energy being transferred by
electromagnetic waves.
Since thermal exchanges by convection and by radiation occur
simultaneously on a given surface of the enclosure element the
outer one in contact with exterior air and the inner one in contact
with interior air for practical purposes a complex thermal exchange
is considered. A schematically representation of such a
convective-radiant thermal exchange is shown in Fig. 4.13, which
could be looked upon as a simplified variant of Fig. 4.11.
Fig. 4.13. Schematical Representation of Convective Radiant
Thermal Exchanges Through Enclosure Elements, if Indoor Temperature
is Larger than Out Door Temperature (ti>te)
4.4.5. Main Characteristics of the Humid Air
The atmospheric air always contains water vapours. No matter the
temperature, there is a certain amount of water in vapour form. The
effective humidity is currently termed absolute humidity (). Its
physical significance is quantity of water in vapour form contained
in a unit volume of air and is measured in g/m3.
The effective humidity of the air cannot exceed a limit value
known as saturation humidity (s), beyond which water vapours pass
into liquid phase. The value of s increases with air temperature
(Fig. 4.14); in other words, the warmer the air, the larger is the
quantity of water vapours it can contain.
Fig. 4.14. Relationship Between Saturation Humidity and Air
Temperature At a given moment, the ratio between the effective
humidity of the air and its saturation humidity corresponding to
air temperature at that moment, defines the relative humidity ()
expressed in percentage.
The temperature at which a volume of air must be cooled to reach
saturation level of humidity is called dew temperature (d). It
depends on air temperature and air relative humidity
(Table4.3).
If a mass of air having the dew temperature d has contact with a
cold surface whose temperature s is smaller than d, part of the
water vapours it contains will condense on that surface. This
phenomenon is called superficial condensation and is accompanied by
emanation of heat (0.7 Wh/g).
The partial pressure of water vapours contained in a certain
volume of air, representing their pressure should vapours occupy
the entire volume, is termed effective pressure of water vapours
(p). If the air is saturated with water vapours, the corresponding
pressure value is called saturation pressure of water vapours (ps).
Both values are measured in pascals [Pa].
As in case of saturation humidity (s), the value of ps increases
with air temperature (Fig. 4.15); in other words, the warmer the
air, the grater is the saturation pressure of water vapours it
contains.4.5. Modelling Thermal Behaviour of Enclosure
Elements4.5.1 General Issues
The special complexity of problems related to achieving correct
and efficient hygrothermal layout of buildings strongly requires in
the first place to set up a systemic framework for analysis. As it
is well known, the simplest scheme of a functional system is
represented like a physical entity (of the black box type) which
transforms an input function into an output function (Fig. 4.16).
In general, the input consists in external actions that generate
perturbations of state of the system frequently of random character
thus triggering its running. The output represents results or
effects of input actions.
Fig. 4.16. Schematical Representation ("Black Box" Type) of a
System
The notion of system is intrinsically related to that of model,
usually having mathematical features. A mathematical model
represents, in mathematical terms, the running of a system and
hence offers the possibility to predict qualitative and
quantitative evolution of its output (response) to various inputs
(external actions).
In case of problems concerning thermal dynamics of the systems,
input and output functions are essentially thermal excitation and
thermal response, respectively. The basic scheme to solve problems
concerning thermal analysis of the systems can be represented as in
Fig. 4.17. According to this scheme, the relevant characteristics
are specified for both thermal excitation and system subjected to
investigation. The scope of this analysis consists in assessing
systems thermal response to variation of thermal excitation.
Fig. 4.17. Basic Scheme of Thermal Analysis of Systems In case
of problems concerning thermal layout of the systems, the basic
scheme is illustrated in Fig. 4.18, where initially specified input
data are those characterising both thermal excitation and thermal
response. The scope of thermal layout of a system consists in
designing it so that its response to a given thermal excitation
(real or conventional) ranges between pre-established values.
Hence, the results of computations should substantiate geometrical
and thermophysical characteristics to be requested from the
system.
Fig. 4.18. Basic scheme for Designing Thermal Layout of
Systems4.5.2. Problems of Defining Enclosure System and Its
Physical- Geometrical Model
For reasons aimed to simplify the design process, in the current
practice both modelling and analysis are performed on enclosure
elements and sub-ensembles. In most situations, thermal exchanges
occur through building elements of wall-type (mainly, exterior
walls) and of floor slab-type; Any enclosure element is physically
and functionally connected to other elements of same kind situated
in its plane, as well as to different other elements situated, as a
rule, in planes orthogonal to its own. The thermal response of an
exterior wall, taken as a whole, is obviously influenced by its
connections to other building elements that introduce more or less
significant thermal effects. A rigorous assessment of its thermal
response should, therefore, be based on 3- dimensional models with
adequate coverage of connection zones (Fig. 4.19).
Fig.4.19. 3D-Model for Thermal Analysis of an Exterior
Wall4.5.3. Problems of Defining Thermal Excitation The enclosure of
a building can be
considered as interface between two environments, having
different thermal characteristics which are inherently variable in
time. Consequently, any enclosure element acts like a filter
performing heat exchanges between two environments of different
temperatures. Fig.4.25. Schematical Representation of Thermal
Actions Exerted on Enclosure simplified representation of an
equivalent thermal convective exchangeeach of the two environments
separated by enclosure elements can be characterised by an unique
parameter of temperature-type. In general, these temperatures
exhibit time-variations, each governed by its own laws, but having
close correlation. As long as the difference ti te, is not 0, there
is a heat exchange between indoor and outdoor environment through
the enclosure, this phenomenon being strongly influenced by its
geometrical and thermophysical characteristics, and by the exterior
conditions.
In general, these data represent hourly average temperatures
recorded during a significant period in winter (or summer) time and
extended over relatively many successive years. In case of
common-type buildings, the current design practice takes into
consideration, instead of a conventional variation of te during the
day (24 hours), just its average value. For example, the parameter
te,conv used for establishing the required characteristics of
heating installations represents the average value of outdoor air
temperature corresponding to a winter conventional day; for
Bucharest this average value is equal to 15.3o C.
Present Romanian technical regulations provide a map of the
territory, defining a number of 4 macro-zones from the viewpoint of
the outdoor air temperature during a winter conventional day, as
shown in Fig. 5.26. Similarly, another map defines 3 macro-zones
from the viewpoint of outdoor air temperature during a summer
conventional day (Fig. 5.27).
Fig.5.26. Winter Climatic Zoning of Romanian Territory
Fig.5.27. Summer Climatic Zoning of Romanian Territory4.6. BASIC
ISSUES RELATED TO THERMAL RESPONSE OF ENCLOSURE
ELEMENTS In case of single-layer elements (withhomogenous
structure in all directions), the differential equation of thermal
conduction takes for a stationary unidirectional thermal regime the
simple form (Fig. 4.31):
d2/dx2= 0 (4.16)
whose integration gives the solution:
(x)= C1x+C2 (4.17)
Fig. 4.31. Convention for the Reference System a) in winter
time; b) in summer time
The two constants are obtained by means of limit conditions,
i.e.:
for winter conditions
(0)= si and (d)= se for summer conditions
(0)= sse and (d)= si
The solution results as follows:
for winter conditions:
(x)= -(si se)x/d + si (4.18)
for summer conditions:
(x)= -( se - si)x/d + se(4.19)
Since the values of si and se are not known, the relations
(4.18) and (4.19) are not operational. In order to get these
values, one should make use of the limit conditions stating that,
in case of stationary thermal regime, the density of thermal
conductive-radiant flow that penetrates one of the elements surface
is conserved during its passage and also when getting out through
the opposite surface. This is expressed by (Fig. 5.32):
qiC-R= qk= qeC-R(5.20)
Fig. 5.32. Conservation of the Density of Thermal Flow in Case
of Stationary
RegimeFor instance, under winter condition, one can write:
qiC-R= (ti-si)/Rsi(5.21)
qk = (si-se)/R (5.22)
qeC-R= (se-te)/Rse (5.23)
Hence, eqs. (5.20) can be written as follows: (ti-si)/Rsi=
(si-se)/R= (se-te)/ Rse= (ti-te)/RT
(5.24.)
where:
Rsi and Rse represent resistance to surface thermal exchange
(for inner and outer surface, respectively)
R= d/ represents resistance to thermal conductive transfer
through elements thickness d, for a material with coefficient of
conductivity . This also termed resistance to thermal
permeability.
In eqs. (4.24), the notation: RT= Rsi+R+Rse has been introduced,
RT having the significance of resistance to thermal transfer (or,
for the sake of simplicity, just thermal resistance) and being
measured in [m2 oC/W].
The inverse value: U= 1/RT, [W/m2 oC] is currently termed
thermal transmittance.
By operating conventional transformations, eqs. (5.24) will
yield to the following relations:
si= ti-Rsi(ti-te)/RT (4.25)
se= te+Rse(ti-te)/RT
(4.26) corresponding to winter conditions.
In a similar manner, the following relations are established for
summer conditions:
si= ti+Rsi(te-ti)/RT(4.27)
se= te-Rse(te-ti)/RT(4.28)
Getting back to eqs. (4.18) and (4.19), and introducing the
expression of si and se from eqs. (4.25)...(4.28), one can write
the following relations:
for winter conditions
(x)= ti-(Rsi+x/)(ti-te)/RT(4.29)
for summer conditions
(x)= te-(Rse+x/)(te-ti)/RT(4.30)
which can be further transformed to:
(x)= [-(ti-te)/RT]x+[ti-Rsi(ti-te)/RT] (4.31)
and
(x)= [-(te-ti)/RT]x+[te-Rse(te-ti)/RT] (4.32)
for winter and for summer conditions, respectively.
A graphical representation of these linear functions of
temperature field is shown in Fig. 4.33. Obviously, their gradient
is inversely proportional to the value for , hence illustrating the
fact that temperature fall increases along with the increase of
thermal insulating characteristics of the material the element is
made of.
Fig. 4.33.Variation of the Function "Temperature Field" Inside
Enclosure Elements a) in winter time; b) in summer time
Any of the diagrams in Fig. 4.33 can be completed to account for
temperature variation occurring in the air layers adjacent to
elements surfaces (Fig. 4.34). The temperature fall ti-si, as well
as se-te can be interpreted as the effect of resistance to thermal
permeability presented through the convection-radiation phenomenon
between air and the solid element.
Fig. 4.34. Variation of the Function "Temperature Field" For
Enclosure Elements, Accounting for Temperature Variation in the Air
Layers Adjacent to Element's Surfaces (Winter Time) In case of
multi-layer elements (with nonhomogenous structure on x axis only)
one should make use of limit condition imposing conservation of the
density of thermal conductive flow when passing from one layer to
another. This is expressed by (Fig.4.35):
qiC-R= q1k= q2k=...= qnk= qeC-R (4.33)
With the notations previously used in case of single-layer
elements eqs. (5.33) can be put in the form:
(ti-si)/Rsi = (si-1)/R1= (1-2)/R2=...=(n-1-se)/Rn= (se-te)/Rse=
(ti-te)/RT (5.34)
where:
RT= Rsi+(R1+ R2+... Rn)+Rse= Rsi+R+Rse
R=jdj/j represents resistance to thermal conductivity transfer
(or, resistance to thermal permeability) of a multi-layer
element.
Fig.4.35.Conservation of the Density of Thermal Conductive Flow
in Case of Multy-Layer Enclosure Elements (Non Homogeneous
Structure in x-Direction Only)
Fig, 4.36. Variation of Winter-Time Temperature inside a
Multy-Layer Enclosure Element, in Case of Stationary Regime Within
the large picture of thermal bridges, the most common are those
created by linear (vertical or horizontal) inclusions of materials
with high thermal conductivity. Another category is represented by
joining and connecting zones of enclosure elements; very
frequently, in these zones are also present highly thermal
conductive materials. From another viewpoint, thermal bridges can
be categorised into: current-field bridges (partially penetrating
into or completely breaking through the element), intersection (or
corner) bridges, complex-type bridges (typically encountered at the
joints of prefabricated large panels used for exterior walls).
Some typical examples of thermal bridges in building enclosure
elements are illustrated in Figs. 4.39 and 4.40.
Fig.4.39. Examples of Thermal Non-Homogeneities (Generating
Thermal Bridges) in Enclosure Elements Horizontal Sections Through
Exterior Walls Fig.4.40. Examples of Thermal Non-Homogeneities
(Generating Thermal Bridges ) in Enclosure Elements-Vertical
Sections Through Exterior Walls4.7.2. Temperature Variation Around
Thermal Bridges
In order to analyse the characteristics of thermal
field associated to a thermal bridge zone in an enclosure
element, one of the simplest case (already considered as classic)
is in the fig.below:
Fig. 4.50. Layout of an Exterior Structural Wall Made of Brick
Masonry With Additional Thermal ProtectionINPUT x ()
(cause)
SYSTEM
OUTPUT y ()
(effect)
THERMAL
EXCITATION
SYSTEM
input data specified initially
output data to be computed
THERMALRESPONSE
THERMALRESPONSE
SYSTEM
THERMAL
EXCITATION
input data specified initially
Output data
0.89
1.06
1.25
1.52
1.81
2.15
4.6
9.4
10.68
12.14
13.66
17.3
15.36
-20
-18
-16
-14
-12
-10
-8
-6
-4
-2
0
2
4
6
8
10
12
14
16
18
20
0
2
4
6
8
10
12
14
16
18
20
s
(g/m
3
)
t (
o
C)
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