Bahman Zohuri Compact Heat Exchangers Selection, Application, Design and Evaluation
Bahman Zohuri
Compact Heat ExchangersSelection, Application, Design and Evaluation
Compact Heat Exchangers
Bahman Zohuri
Compact Heat Exchangers
Selection, Application, Design and Evaluation
Bahman ZohuriGalaxy Advanced Engineering, Inc.Albuquerque, NM, USA
ISBN 978-3-319-29834-4 ISBN 978-3-319-29835-1 (eBook)DOI 10.1007/978-3-319-29835-1
Library of Congress Control Number: 2016953367
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This Springer imprint is published by Springer NatureThe registered company is Springer International Publishing AG Switzerland
This book is dedicated to my daughterDr. Natasha Zohuri MDShe always encouraged me with mypublications
Bahman Zohuri
Preface
Today’s global energy market, places many demands on power generation tech-
nology including high thermal efficiency, low cost, rapid installation, reliability,
environmental compliance, and operation flexibility.
The demand for clean, non-fossil based electricity is growing; therefore, the
world needs to develop new nuclear reactors with higher thermal efficiency in order
to increase electricity generation and decrease the detrimental effects on the
environment. The current fleet of nuclear power plants is classified as Generation
III or less. However, these models are not as energy efficient as they should be
because the operating temperatures are relatively low. Currently, groups of coun-
tries have initiated an international collaboration to develop the next generation of
nuclear reactors called Generation IV. The ultimate goal of developing such
reactors is to increase the thermal efficiency from what currently is in the range
of 30–35% to 45–50%. This increase in thermal efficiency would result in a higher
production of electricity compared to current Pressurized Water Reactor (PWR) or
Boiling Water Reactor (BWR) technologies.
A number of technologies are being investigated for the Next Generation
Nuclear Plant that will produce heated fluids at significantly higher temperatures
than current generation power plants. The higher temperatures offer the opportunity
to significantly improve the thermodynamic efficiency of the energy conversion
cycle. One of the concepts currently under study is the Molten Salt Reactor. The
coolant from the Molten Salt Reactor may be available at temperatures as high as
800–1000 �C. At these temperatures, an open Brayton cycle combined with and
Rankine bottoming cycle appears to have some strong advantages.
Combined-cycle thermal efficiency increases as gas turbine specific power
increases. The gas turbine firing temperature is the primary determinant of specific
power.
Gas turbine engines, both aircraft and industrial power generation, represent one
of the most aggressive applications for structural materials. With ever growing
demands for increasing performance and efficiencies, all classes of materials are
being pushed to higher temperature capabilities. These materials must also satisfy
vii
stringent durability and reliability criteria. As materials are developed to meet these
demanding requirements, the processing of these materials often becomes very
complicated and expensive. As a result, the cost of materials and processes has
become a much larger consideration in the design and application of high perfor-
mance materials. Both the aircraft engine and power generation industries are
highly cost competitive, and market advantage today relies on reducing cost as
well as increasing performance and efficiency.
The distributed power generation market and renewing attention to renewable
source of energy puts some interesting demand on a new aspect of heat exchangers
and their compactness going forward with better efficiency of power plant whether
it is gas driven, fossil fuel or a new generation of nuclear planet.
For the nuclear power plant, in particular new generation and small modular
reactors (SMRs), one of the most economical solutions today is to generate power
through small gas turbine systems in the form of Brayton cycle combined with these
reactors. These gas turbines arbitrarily can be categorized as micro-turbines with
output of (5–200 kW) and mini-turbines with output of (200–500 kW). The thermal
efficiency of such micro-turbines is about 20% or less if no recuperator is used in
the system. Using a recuperator (regenerator can also be considered but has a
number of problems) operating at 87% effectiveness, the efficiency of the gas
turbine system increases to about 30%, a substantial performance improvement.
However, cost of the recuperator is about 25–30% of the total power plant,
therefore total cost of ownership and return on investments are not very well
justified. This necessitates the use of all prime surface heat exchangers with no
brazing. Thus the quest for a novel design of new generation compact heat
exchangers in support of such combined cycle is there and understanding of such
innovative approach among engineers and scientist in the field is rising rapidly.
In order to achieve the above described situation and usage of technology an
approach such as combined cycle driven efficiency of power plants either nuclear or
otherwise demands a better and more compact heat exchanger utilizing Brayton,
Rankine cycle or a combination of them as bottoming or toping configuration.
This book, after providing the necessary concise information on all aspects of
this innovative approach such as combined cycle and associated turbines such as
micro-turbines combined, moves on to the discussion on various types of compact
heat exchanger surfaces and novel designs that can be considered for the cost
effective heat exchangers and packaging in the system.
The simple Brayton cycle is modified to include recuperators or compact heat
exchangers (which will transfer heat from the turbine exhaust to preheat com-
pressed high pressure air before going to the combustion chamber), it will require
less fuel to obtain the desired turbine inlet temperature of compressed air and also
the optimum pressure ratio (either for compressor or turbine) is reduced to typically
3–4. This improves the thermal efficiency of the cycle. Alternatively, a regenerator
can also be used replacing a recuperator.
Development of high temperature/high strength materials, corrosion resistant
coatings, and improved cooling technology have led to increases in gas turbine
firing temperatures. This increase in firing temperature is the primary development
viii Preface
that has led to increases in Combined Cycle Gas Turbine (CCGT) thermal efficien-
cies. The improvements in combined-cycle thermal efficiencies and the commercial
development of combined-cycle power plants have proceeded in parallel with
advances in gas turbine technologies.
Compact heat-exchangers, filters, turbines, and other components in integrated
Next Generation Nuclear Power Plant combined cycle systems must withstand
demanding conditions of high temperatures and pressure differentials. Under the
highly sulfiding conditions of the high temperature such as inlet hot steam or other
related environmental effects, the performance of components degrade significantly
with time unless expensive high alloy materials are used. Deposition of a suitable
coating on a low cost alloy may improve its resistance to such sulfidation attack and
decrease capital and operating costs. A review of the literature indicates that the
corrosion reaction is the competition between oxidation and sulfidation reactions.
The Fe- and Ni-based high-temperature alloys are susceptible to sulfidation attack
unless they are fortified with high levels of Cr, Al, and Si. To impart corrosion
resistance, these elements need not be in the bulk of the alloy and need only be
present at the surface layers.
Those that practice the art of Nuclear or Mechanical Engineering must have a
physical and intuitive understanding of the mechanisms and balances of forces,
which control the transport of heat and mass in all physical systems. This under-
standing starts at the molecular level, with intermolecular forces and the motion of
molecules, and continues to the macroscopic level where gradients of velocity,
temperature, and concentration drive the diffusion of momentum, heat, and mass,
and the forces of pressure, inertia, and buoyancy balance to drive convection of
fluids.
This text covers the fundamentals of combined cycle that is required to under-
stand electrical power generation systems and driven efficiency of combined cycle.
It then covers the application of these principles to nuclear reactor power systems. It
is a general approach to Brayton combined cycle text, and aimed at explaining the
fundamentals of combined cycle with these compact heat exchangers in the loop
and applying them to the challenges facing actual nuclear power systems. It is
written at an undergraduate level, but should also be useful to practicing engineers
and scientists as well.
Chapter 1 provides the basic definitions and principles behind the basic and old
science of thermodynamics that one needs to understand the study of energy,
energy transformations, and its relation to matter, where we need to use the analysis
of thermal system or thermal hydraulic through the application of the governing
conservation equations, namely Conservation of Mass, Conservation of Energy
(first law of thermodynamics), the second law of thermodynamics, and the property
relations. Energy can be viewed as the ability to cause changes. This chapter allows
us to have a better understanding of Compact Heat Exchangers (CHEs) and their
designs for a typical power plant layout and the scope of thermodynamics behind it
as part of CHEs applications.
Chapter 2 covers the general aspect of heat exchanges and what types there are
as well as general rules of their designs, before we launch to specifics about
Preface ix
compact heat exchangers in the rest of the book. Then we are going to look at, cost,
design, performance and their application in appropriate industry, where these
CHEs are going to be used.
Chapters 3 and 4 deal with thermal hydraulic and heat transfer of heat exchanger
in order for the reader to have a fair idea of how the designed heat exchanger would
perform when installed in the power plant and One-Dimensional analysis modeling
is presented using MATLAB software while Three-Dimensional modeling study of
the heat exchanger is undertaken with the use of the COMSOL Metaphysics
software. Specifically speaking Chap. 4 walks the reader through design process
and computer modeling, simulation and selection of a Compact Heat Exchanger
(CHE) for its application in a Solar Gas Turbine Power Plant and is heavily written
around the work that was done by Noah Yakah and his Master of Science thesis
under supervision of Dr. James Spelling at KTH School of Industrial Engineering
and Managements in Stockholm Sweden and his MATLAB (1-D) and COMSOL
(3-D) simulations approach (i.e., Heat Exchanger Design for a Solar Gas-Turbine
Power Plant) for the selection of CHE.
Chapter 4 discusses the thermal design compact heat exchanger and it goes
through the concept of this selection process both from modeling, physics, and
thermal hydraulic criteria and shows what is involved in the selection process, both
for fully developed laminar flow and fully developed turbulent and design formu-
lations as well.
Chapter 5 presents analysis of three dimensional modeling of a printed circuit
compact heat exchanger using COMSOL Multiphysics functionality and shows
different screen shots of this software and how the setup of heat transfer modeling
for such exchanger takes place and the work follows as complementary to Chap. 4,
where MATLAB software is used to do similar work using one dimensional
modeling for a similar type of compact heat exchanger.
Since a lot of concerns in recent years have been raised from the use of fossil
fuels such as coal, oil, and natural gas as sources of producing heat energy to
generate electricity and the rise of demand on such source energy in order to layout
the ground for justification and need for new generation nuclear power plants and
other means of renewable energy source, Chaps. 6, 7, and 8 are devoted to different
forms of these power plants and how the heat exchangers are improving their
overall out efficiencies during off and on grid circumstance, while describing in
some more detail how these plants and available options work and goes on to
describe heat exchangers in general and then talks about the compact heat
exchangers as the most efficient and cost effective for their application in such
innovative approaches.
There are also a total of seven appendices added to the book where Appendix A
illustrates some table of physical properties and graphs, Appendix B reflects
information about gas properties and tabulates them for selected gases and air
properties both in SI and British units. Appendix C is a presentation of the
thermodynamic properties for water and Appendix D tabulates the thermodynamic
properties of Carbon Dioxide (CO2), while Appendix E shows similar information
for Sodium. Finally Appendix F captures some mathematical modeling and
x Preface
experimental data from work done by Akash Pandey on his work on Performance
Analysis of a Compact Heat Exchanger in room temperature. Appendix F shows
steps-by-steps of how to use 3-Dimensional analysis using COMSOL Multiphysics
to design a gas-to-gas plate fin compact heat exchanger (PFCHX) based on param-
eters defined for this particular compact heat exchanger as well.
Note that steam tables published in this book were updated by Dr. McDaniel and
this author when they published their book with Springer publishing company
under the title of Thermodynamics In Nuclear Power Plant Systems in 2015 when
they found out some errors in most steam tables recently published by other authors
in their related text books.
The book also concentrates on fundamentals of new applications to energy
conversion technology in Chap. 4 to cover power conversion systems and their
components and how we can take the waste heat from a power plant in order to
recover it and put it into use for driving overall output efficiency higher, so the
owner of these plants will enjoy better revenue for day-to-day operations.
And finally the last few chapters of the book cover current and projected
industrial applications and how the novel design of these compact heat exchangers
from a thermal design perspective in principle are applied to their innovative
designs, operation, and safety analyses.
Detailed appendices cover metric and English system units and conversions,
detailed steam and gas tables, heat transfer properties, and nuclear reactor system
descriptions, as well as a holistic approach to understanding of nuclear power plants
and each generation in general.
Albuquerque, NM Bahman Zohuri
Preface xi
Acknowledgments
I would like to acknowledge all the individuals for their help, encouragement, and
support. I have decided not to name them all, but we hope they can at least read this
acknowledgment wherever they may be.
Last but not least, special thanks to my parents, wife, children, and friends for
providing constant encouragement, without which this book could not have been
written. I especially appreciate their patience with pure frequent absence from
home and long hours in front of the computer during the preparation of this book.
My sincere appreciation goes to Professors and Instructors of Department of
Nuclear Engineering at University of New Mexico Albuquerque, New Mexico,
whom provided me the knowledge that I have now and continue teaching me what I
need to know to go forward.
I am also indebt to another teacher, mentor and now a true friend, Professor
Dimiter N. Petsev of University of New Mexico, Chemical Engineering Depart-
ment, for whom I have a lot of respect as well.
The other true gentleman for whom I have a lot of respect and helped a lot and
pushed me forward is Professor Cassiano R. E de Oliveira of Nuclear Engineering
Department at University of New Mexico.
xiii
Contents
1 Definitions and Basic Principles of Thermodynamics . . . . . . . . . . . . 1
1.1 Thermodynamics and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Scope of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Units and Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.1 Fundamental Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3.2 Thermal Energy Units . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.3.3 Unit Conversion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.4 Classical Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.5 Open and Closed Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.6 System Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.6.1 Density . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6.2 Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
1.6.3 Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.7 Properties of the Atmosphere . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.8 The Laws of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . 17
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2 Heat Exchanger Types and Classifications . . . . . . . . . . . . . . . . . . . . 19
2.1 Heat Exchanger Types . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
2.2 Classification According to Transfer Processes . . . . . . . . . . . . . . 22
2.2.1 Indirect Contact Type Heat Exchangers . . . . . . . . . . . . 22
2.2.2 Direct Contact Type Heat Exchangers . . . . . . . . . . . . . . 22
2.3 Classification of Heat Exchanger by Construction Type . . . . . . . 22
2.3.1 Tubular Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . 23
2.3.2 Plate Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.3.3 Plate Fin Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . 25
2.3.4 Tube Fin Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . 26
2.3.5 Printed Circuit Heat Exchanger . . . . . . . . . . . . . . . . . . 27
2.3.6 Regenerative Heat Exchangers . . . . . . . . . . . . . . . . . . . 29
xv
2.4 Condensers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Boilers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 Classification According to Compactness . . . . . . . . . . . . . . . . . . 30
2.7 Types of Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.8 Cooling Towers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.9 Regenerators and Recuperators . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.10 Heat Exchanger Analysis: Use of the LMTD . . . . . . . . . . . . . . . 38
2.11 Effectiveness-NTU Method for Heat Exchanger Design . . . . . . . 45
2.12 Special Operating Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.13 Compact Heat Exchangers and Their Classifications . . . . . . . . . . 51
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3 Compact Heat Exchangers Design for the Process Industry . . . . . . . 57
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Compact Heat Exchangers by Their Types . . . . . . . . . . . . . . . . . 58
3.2.1 Description of Plate Fin Heat Transfer Surfaces . . . . . . . 71
3.2.2 Flow Arrangement and Passage in Compact Heat
Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
3.3 Why Compact Heat Exchangers? . . . . . . . . . . . . . . . . . . . . . . . . 80
3.4 Characteristics of Compact Heat Exchangers . . . . . . . . . . . . . . . 89
3.5 Classification of Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . 95
3.6 Design Criteria for Process Heat Exchangers . . . . . . . . . . . . . . . 116
3.7 Thermal and Hydraulic Design . . . . . . . . . . . . . . . . . . . . . . . . . 119
3.7.1 Equations and Parameters . . . . . . . . . . . . . . . . . . . . . . . 121
3.8 The Overall Heat Exchanger Design Process . . . . . . . . . . . . . . . 167
3.8.1 Input Information Needed . . . . . . . . . . . . . . . . . . . . . . 168
3.9 Design Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 170
3.10 Compact Heat Exchangers in Practice . . . . . . . . . . . . . . . . . . . . 179
3.11 Heat Exchanger Materials and Comparisons . . . . . . . . . . . . . . . . 180
3.12 Guide to Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . . 180
3.12.1 Generic Advantages of Compact Design . . . . . . . . . . . . 183
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
4 Thermal Design of the Selected Compact Heat Exchanger . . . . . . . . 187
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187
4.2 Heat Transfer and Pressure Drop Correlations . . . . . . . . . . . . . . 189
4.3 A Short Introduction on Convection Heat Transfer . . . . . . . . . . . 189
4.4 Mathematics of Fluids and Differential Equations
with Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
4.4.1 Free Convection or Natural Heat Transfer Process . . . . . 192
4.4.2 Forced Convection Heat Transfer Process . . . . . . . . . . . 193
4.5 Velocity Problem for Developed and Developing
Laminar Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 193
4.5.1 Hydrodynamically Developed Flow . . . . . . . . . . . . . . . 196
4.5.2 Hydrodynamically Developing Flow . . . . . . . . . . . . . . . 198
xvi Contents
4.6 Conventional Convection Problem . . . . . . . . . . . . . . . . . . . . . . . 199
4.6.1 Thermally Developed Flow . . . . . . . . . . . . . . . . . . . . . 201
4.6.2 Thermally Developing Flow . . . . . . . . . . . . . . . . . . . . . 203
4.7 Thermal Boundary Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . 203
4.7.1 Thermal Boundary Conditions for Singly
Connected Ducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 204
4.8 Heat Exchanger Variables and Thermal Circuit . . . . . . . . . . . . . 207
4.9 Solving Convection Heat Transfer Coefficient
from Empirical Correlations . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
4.10 Internal Flow in a Pipe or Passage . . . . . . . . . . . . . . . . . . . . . . . 218
4.10.1 Fully Developed Turbulent Flow . . . . . . . . . . . . . . . . . 220
4.10.2 Fully Developed Laminar Flow . . . . . . . . . . . . . . . . . . 223
4.10.3 Entry Length . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 224
4.11 Thermal Design of the Selected Compact Heat Exchanger . . . . . 226
4.12 Sizing the Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . 227
4.13 Thermal Design Formulation of Considered Compact Heat
Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229
4.14 Assumption Made in the Design of Considered
Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232
4.15 Relating Heat Transfer and Pressure Drop . . . . . . . . . . . . . . . . . 233
4.16 Heat Capacity Ratio Analysis for Considered
Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235
4.17 Mean Temperature Difference . . . . . . . . . . . . . . . . . . . . . . . . . . 235
4.18 Number of Transfer Units Analysis for Considered
Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
4.19 Fluid Mean Temperature Analysis for Considered
Compact Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . 236
4.20 Thermophysical Properties of the Gases for Considered
Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
4.21 Physical Dimensions and Other Important Geometrical
Feature of the PFHE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 238
4.22 Pressure Drop Analysis of the Exchanger . . . . . . . . . . . . . . . . . . 241
4.23 Printed Circuit Compact Heat Exchanger (PCHE) . . . . . . . . . . . 243
4.23.1 Pressure Drop Analysis of the PCHE . . . . . . . . . . . . . . 245
4.23.2 Sensitivity Analysis of the PCHE . . . . . . . . . . . . . . . . . 246
4.23.3 Overall Analysis of the PCHE . . . . . . . . . . . . . . . . . . . 246
4.23.4 Analysis Performed on the PFHE . . . . . . . . . . . . . . . . . 250
4.23.5 Conclusion for the Selection of a Suitable
Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 252
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 262
5 Three-Dimensional Modeling of Desired Compact
Heat Exchanger . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 267
5.1 Introduction to COMSOL Multiphysics . . . . . . . . . . . . . . . . . . . 267
5.2 Steps Involved in COMSOL Multiphysics . . . . . . . . . . . . . . . . . 268
Contents xvii
5.3 The Conjugate Heat Transfer Interface
for Laminar Flow Using COMSOL . . . . . . . . . . . . . . . . . . . . . . 269
5.3.1 Space Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
5.3.2 Adding Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 269
5.3.3 Selecting Study Type . . . . . . . . . . . . . . . . . . . . . . . . . . 270
5.3.4 Geometry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271
5.3.5 Boundary Conditions for Conjugate Heat
Transfer Interface . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274
5.3.6 Meshes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.3.7 Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 277
5.4 Simulation of the 3-D Model . . . . . . . . . . . . . . . . . . . . . . . . . . . 279
5.5 Mathematical Theory for Conjugate Heat Transfer Interface . . . . 280
5.5.1 The Momentum Equation . . . . . . . . . . . . . . . . . . . . . . . 280
5.5.2 The Continuity Equation . . . . . . . . . . . . . . . . . . . . . . . 282
5.5.3 The Energy Equation . . . . . . . . . . . . . . . . . . . . . . . . . . 283
5.6 Results, Discussions, and Conclusion . . . . . . . . . . . . . . . . . . . . . 284
5.6.1 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284
5.6.2 Discussions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 286
5.6.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 287
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
6 Thermodynamics of Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 291
6.2 Open Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 298
6.3 Closed Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 299
6.4 Gas Compressors and Brayton Cycle . . . . . . . . . . . . . . . . . . . . . 300
6.5 The Non-ideal Brayton Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . 304
6.6 Open Cycle Gas Turbines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306
6.6.1 Aeroderivative Intercooler Gas Turbines . . . . . . . . . . . . 308
6.6.2 Operational Issues/Risks . . . . . . . . . . . . . . . . . . . . . . . 309
6.6.3 Opportunities/Business Case . . . . . . . . . . . . . . . . . . . . . 309
6.6.4 Industrial Case Studies for Open Cycle Gas Turbine . . . 312
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 313
7 Compact Heat Exchangers Application in NGNP . . . . . . . . . . . . . . . 315
7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 315
7.2 Compact Heat Exchangers Driven Efficiencies
in Brayton Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321
7.3 Gas Turbine Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . 329
7.4 The Brayton Cycle with Recuperator . . . . . . . . . . . . . . . . . . . . . 331
7.5 The Brayton Cycle with Intercooling, Reheating,
and Regeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 333
7.6 Modeling the Brayton Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
7.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336
xviii Contents
8 Compact Heat Exchangers Application in New
Generation of CSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339
8.1 Introduction to Concentrated Solar Power (CSP) . . . . . . . . . . . . 339
8.2 New Generation of High Temperature
Solar Receivers for CSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344
8.3 Compact Heat Exchangers in High Temperature
Solar Receivers of CSP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 346
8.4 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 348
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354
9 Compact Heat Exchangers Driven Hydrogen
Production Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 355
9.1 Introduction to Hydrogen Production Plants . . . . . . . . . . . . . . . . 355
9.2 Electrical Energy on Supply and Demand . . . . . . . . . . . . . . . . . 360
9.3 Hydrogen as a Source of Renewable Energy . . . . . . . . . . . . . . . 365
9.3.1 Why Hydrogen as a Source of Renewable
Energy Now? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 368
9.3.2 Technical Development for Hydrogen Production . . . . . 369
9.3.3 Technical Development for Hydrogen Production . . . . . 373
9.4 Development of a Hydrogen Combustion Turbine . . . . . . . . . . . 374
9.5 Feasibility Study on Utilization of Hydrogen Energy . . . . . . . . . 374
9.6 Hydrogen Production Using Nuclear Energy . . . . . . . . . . . . . . . 377
9.7 Constraints Involved for Hydrogen Production
Using Nuclear Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 387
9.7.1 Safety: Hydrogen Generation . . . . . . . . . . . . . . . . . . . . 387
9.7.2 Safety: Hydrogen Generation by Facility Location . . . . . 389
9.8 Efficient Generation of Hydrogen Fuels
Utilizing Nuclear Power . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 391
9.9 Thermal Characteristics for Coupling a Hydrogen
Product Plant to HTR/VHTR . . . . . . . . . . . . . . . . . . . . . . . . . . 396
9.10 Next Generation Nuclear Plant Intermediate
Heat Exchanger Acquisition . . . . . . . . . . . . . . . . . . . . . . . . . . . 407
9.11 Applicability of Heat Exchanger to Process
Heat Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412
9.12 Applicability of Compact Heat Exchanger
to Process Heat Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . 415
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417
Appendix A Table and Graphs Compilations . . . . . . . . . . . . . . . . . . . . . 421
Appendix B Gas Property Tables for Selected Gases . . . . . . . . . . . . . . . 437
Appendix C Thermodynamic Properties for Water . . . . . . . . . . . . . . . . 465
Contents xix
Appendix D Thermodynamic Property Tables
for Carbon Dioxide . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 501
Appendix E Thermodynamic Property Tables for Sodium . . . . . . . . . . 509
Appendix F Practical Design Steps for Compact Heat Exchangers . . . . 521
Appendix G Cross-Flow Compact Heat ExchangerDesign by Comsol . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 533
Nuclear Systems Acronyms: Glossary of Nuclear
Terms (US NRC) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 553
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 557
xx Contents
About the Author
Bahman Zohuri is is currently at Galaxy Advanced Engineering, Inc. a consulting
company that he stared himself in 1991 when he left both semiconductor and
defense industries after many years working as a chief scientist. After graduating
from the University of Illinois in the field of Physics and Applied Mathematics, as
well as the University of New Mexico from the Nuclear Engineering Department,
he joined Westinghouse Electric Corporation where he performed thermal hydrau-
lic analysis and natural circulation for the Inherent Shutdown Heat Removal
System (ISHRS) in the core of a Liquid Metal Fast Breeder Reactor (LMFBR) as
a secondary fully inherent shut system for secondary loop heat exchange. All these
designs were used for Nuclear Safety and Reliability Engineering for Self-Actuated
Shutdown System. He designed the Mercury Heat Pipe and Electromagnetic Pumps
for Large Pool Concepts of LMFBR for heat rejection purpose for this reactor
around 1978 where he received a patent for it. He later on was transferred to the
defense division of Westinghouse where he was responsible for the dynamic
analysis and method of launch and handling of the MX missile out of canister.
The results are applied to MX launch seal performance and muzzle blast phenom-
ena analysis (i.e., missile vibration and hydrodynamic shock formation). He also
was involved in analytical calculation and computation in the study of Nonlinear
Ion Wave in Rarefying Plasma. The results are applied to the propagation of
“Soliton Wave” and the resulting charge collector traces, in the rarefactions char-
acteristic of the corona of a laser irradiated target pellet. As part of his graduate
research work at Argonne National Laboratory, he performed computation and
programming of multi-exchange integral in surface physics and solid state physics.
He holds different patents in areas such as diffusion processes and design of
diffusion furnace while he was senior process engineer working for different
semiconductor industries such as Intel, Varian, and National Semiconductor cor-
porations. Later on he joined Lockheed Missile and Aerospace Corporation as
Senior Chief Scientist and was responsible for the Research and Development
(R&D) and the study of vulnerability, survivability and both radiation and laser
hardening of different components Strategic Defense Initiative known as Star Wars.
xxi
This included of payload (i.e., IR Sensor) for Defense Support Program (DSP),
Boost Surveillance and Tracking Satellite (BSTS) and Space Surveillance and
Tracking Satellite (SSTS) against laser or nuclear threat. While there, he also
studied and performed the analysis of characteristics of laser beam and nuclear
radiation interaction with materials, Transient Radiation Effects in Electronics
(TREE), Electromagnetic Pulse (EMP), System Generated Electromagnetic Pulse
(SGEMP), Single-Event Upset (SEU), Blast and, Thermo-mechanical, hardness
assurance, maintenance, device technology.
He did a few years of consulting under his company Galaxy Advanced Engi-
neering with Sandia National Laboratories (SNL), where he was supporting devel-
opment of operational hazard assessments for the Air Force Safety Center (AFSC)
in connection with other interest parties. Intended use of the results was their
eventual inclusion in Air Force Instructions (AFIs) specifically issued for Directed
Energy Weapons (DEW) operational safety. He completed the first version of a
comprehensive library of detailed laser tools for Airborne Laser (ABL), Advanced
Tactical Laser (ATL), Tactical High Energy Laser (THEL), Mobile/Tactical High
Energy Laser (M-THEL), etc.
He also was responsible for SDI computer programs involved with Battle
Management C3 and artificial Intelligent, and autonomous system. He is author of
a few publications and holds various patents such as Laser Activated Radioactive
Decay and Results of Thru-Bulkhead Initiation.
Recently he has published five books with CRC and Francis Taylor and Springer
on the following subjects:
1. Heat Pipe Design and Technology: A Practical Approach, Published by CRC
Publishing Company
2. Dimensional Analysis and Self-Similarity Methods for Engineering and Scien-
tist Published by Springer Publishing Company
3. High Energy Laser (HEL): Tomorrow’s Weapon in Directed Energy Weapons
Volume I, Published by Trafford Publishing Company
4. Thermodynamics In Nuclear Power Plant Systems, Published by Springer Pub-
lishing Company
5. Thermal-Hydraulic Analysis of Nuclear Reactors, Published by Springer Pub-
lishing Company
6. Application of Compact Heat Exchangers for Combined Cycle Driven Effi-
ciency in Next Generation Nuclear Power Plants: A Novel Approach, Springer
Publishing Company.
7. Next Generation Nuclear Plants Driven Hydrogen Production Plants via Inter-
mediate Heat Exchanger a Renewable Source of Energy, Springer Publishing
Company.
xxii About the Author
Chapter 1
Definitions and Basic Principlesof Thermodynamics
Any subject that deals with energy, or heat in general, requires an understanding of
at least the basic principles of thermodynamics and, as in any science we encounter
in our life, thermodynamics has its own unique language and vocabulary associated
with it. Understanding of such language and vocabulary as well as abbreviations or
acronyms and an accurate definition of basic concepts forms a sound foundation for
the development of the science of thermodynamics, where it will lead us to have a
better understanding of heat, energy, etc. and allow us to have a better grasp of
fields and sciences that at least encounter the lateral parameters. In the case of a
thermodynamic system, this science can be simply defined as a quantity of matter or
a region in a space of consideration for study, and anything external to this system is
called the system’s surroundings and what separates this region from the rest of the
space is defined as the boundary of the system. So, in this chapter we will talk about
the basic principles that make up the science of thermodynamics [1–6].
1.1 Thermodynamics and Energy
Thermodynamics can be defined as the study of energy, energy transformations,
and its relation to matter. Matter may be described at a molecular (or microscopic)
level using the techniques of statistical mechanics and kinetic theory. For engineer-
ing purposes, however, we want “averaged” information, i.e., a macroscopic (i.e.,
bulk energy flow), not a microscopic, description. The reasons behind acquiring
such averaged information in a macroscopic form are twofold:
1. Microscopic description of an engineering device may produce too much infor-
mation to manage.
2. More importantly, microscopic positions and velocities for example are gener-
ally not useful and lack enough information to determine how macroscopic
systems will act or react unless, for instance, their total effect is integrated.
© Springer International Publishing Switzerland 2017
B. Zohuri, Compact Heat Exchangers, DOI 10.1007/978-3-319-29835-1_11
The observation driven macroscopic point of view deals with bulk energy flow
which we encounter in Classical Thermodynamics; whereas, the theory driven
microscopic point of view is about molecular interactions which we encounter in
statistical physics/mechanics or kinetic theory.
We therefore neglect the fact that real substances are composed of discrete
molecules and model matter from the start as a smoothed-out continuum. The
information we have about a continuum represents the microscopic information
averaged over a volume. Classical thermodynamics is concerned only with
continua.
A thermodynamic system is a quantity of matter of fixed identity, around which
we can draw a boundary (see Fig. 1.1 for an example). The boundaries may be fixed
or moveable. Work or heat can be transferred across the system boundary. Every-
thing outside the boundary is the Surroundings.However, restricting ourselves by surroundings requires definition of a boundary
that separates the system from the rest of the space of consideration (see Fig. 1.2),
which results in defining a control volume.
When working with devices such as engines it is often useful to define the system
to be an identifiable volume with flow in and out. This is termed a control volume.
An example is shown in Fig. 1.3.
Another definition that we need to know is the concept of a “state” in thermo-
dynamic. The thermodynamic state of a system is defined by specifying values of a
set of measurable properties sufficient to determine all other properties. For fluid
systems, typical properties are pressure, volume, and temperature. More complex
systems may require the specification of more unusual properties. As an example,
the state of an electric battery requires the specification of the amount of electric
charge it contains.
Properties may be extensive or intensive. Extensive properties are additive.
Thus, if the system is divided into a number of sub-systems, the value of the
property for the whole system is equal to the sum of the values for the parts.
Volume is an extensive property. Intensive properties do not depend on the quantity
of matter present. Temperature and pressure are intensive properties.
Specific properties are extensive properties per unit mass and are denoted by
lower case letters:
Gas, FluidSystem
Boundary
Fig. 1.1 Piston (boundary)
and Gas (system)
2 1 Definitions and Basic Principles of Thermodynamics
Specific Volume ¼ V
m¼ υ
Specific properties are intensive because they do not depend on the mass of the
system.
The properties of a simple system are uniform throughout. In general, however,
the properties of a system can vary from point to point. We can usually analyze a
general system by sub-dividing it (either conceptually or in practice) into a number
of simple systems in each of which the properties are assumed to be uniform.
It is important to note that properties describe states only when the system is in
equilibrium.
In summary, the science of thermodynamics, through its two most important
laws, drives the analysis of thermal systems which is achieved through the appli-
cation of the governing conservation equations, namely Conservation of Mass,
Conservation of Energy (first law of thermodynamics), the second law of thermo-
dynamics, and the property relations. While the Energy part can be viewed as the
ability to cause changes, as we have learned from our early physics in college,
energy is conserved and it transforms from one form into another. For example, a
car moving along a straight line on a level road skids to a stop. Its energy was
initially kinetic energy (the energy due to motion). What is taking place in this case
can be described as:
System boundary
Electrical energy(work)
Fig. 1.2 Boundary around
electric motor (system)
System boundary
complexprocess
m, p2, T
2
.
m, p1, T
1
.
Fig. 1.3 Sample of control volume
1.1 Thermodynamics and Energy 3
• The transfer of energy across boundaries, where
Heat +Gas in piston-cylinder assembly Work Move piston
• The storage of energy in molecules
Bulk motion Work and Heat Internal energy
The fundamental thing to understand is that a PWR converts nuclear energy to
electrical energy and it does this by converting the nuclear energy first to thermal
energy and then converting the thermal energy to mechanical energy, which is
finally converted to electrical energy. The science of thermodynamics deals with
each of these conversion processes. To quantify how each of these processes takes
place we must understand and apply the laws of thermodynamics.
1.2 Scope of Thermodynamics
Thermodynamics is the science that deals with energy production, storage, transfer,
and conversion. It is a very broad subject that affects most fields of science
including biology and microelectronics. The primary forms of energy considered
in this text will be nuclear, thermal, chemical, mechanical, and electrical. Each of
these can be converted to a different form with widely varying efficiencies. Pre-
dominantly thermodynamics is most interested in the conversion of energy from
one form to another via thermal means. However, before addressing the details of
thermal energy conversion, consider a more familiar example. Newtonian mechan-
ics defines work as force acting through a distance on an object. Performing work is
a way of generating mechanical energy. Work itself is not a form of energy, but a
way of transferring energy to a mass. So when one mass gains energy, another mass,
or field, must lose that energy.
Consider a simple example. A 65-kg woman decides to go over Niagara Falls in
a 25-kg wooden barrel. (The first person to go over the fall in a barrel was a woman,
Annie Taylor.) Niagara Falls has a vertical drop of 50 m and has the highest flow
rate of any waterfall in the world. The force acting on the woman and barrel is the
force of gravity, which at the surface of the earth produces a force of 9.8 N for every
kilogram of matter that it acts on. So we have
W ¼ F� D F ¼ 65þ 25ð Þ � 9:8 ¼ 882:0N D ¼ 50m
W ¼ 882:0� 50:0 ¼ 44, 100N-m ¼ 44:1kJ
A Newton meter is a Joule and 1000 J is a kilo-Joule. Therefore, when the woman
and barrel went over the falls, by the time they had reached the bottom, the force of
gravity had performed 44.1 kJ of work on them. The gravitational field had 44.1 kJ
of potential energy stored in it, when the woman and the barrel were at the top of the
falls. This potential energy was converted to kinetic energy by the time the barrel
reached the bottom of the falls. Kinetic energy is also measured in Joules, as with all
other forms of energy. However, we are usually most interested in velocities when
4 1 Definitions and Basic Principles of Thermodynamics
we talk about kinetic energies, so let us extract the velocity with which she hit the
waters of the inlet to Lake Ontario.
ΔKE ¼ ΔPE ¼ 44:1kJ ¼ 1=2mV2 ¼ 90=2ð Þkg� V2 V2 ¼ 44:1kJ= 90=2ð Þkg
Now it is a matter of converting units. A Joule is a Newton-meter. 1 N is defined as
1 kg accelerated at the rate of 1 m/s/s. So
44:1kJ ¼ 44, 100N-m
¼ 44, 100kgm=s=sm¼ 44, 100kg m=sð Þ2
V2 ¼ 44, 100kg m=sð Þ2= 90=2ð Þkg¼ 490= 1=2ð Þ ¼ 980 m=sð Þ2
V ¼ 31:3m=s � 70mphð Þ
Needless to say she recommended that no one ever try that again. Of course, others
have, some have made it, and some have drowned.
Before leaving this example, it is worth pointing out that when we went to
calculate the velocity, it was unaffected by the mass of the object that had dropped
the 50 m. So one-half the velocity squared represents what we will call a specific
energy, or energy per kilogram. In addition, the potential energy at the top of the
falls could be expressed as a specific potential energy relative to the waters below.
The potential energy per pound mass would just be the acceleration of gravity times
the height of the falls. Typically, we will use lower case letters to represent specific
quantities and upper case letters to represent extensive quantities. Extensive quan-
tities are dependent upon the amount of mass present. Specific quantities are also
referred to as intensive variables, though there are some intensive variables that
have no extensive counterpart, such as pressure or temperature.
p:e: ¼ mgh =m ¼ gh ¼ 9:8� 50 ¼ 0:49kJ=kg
It is also worth pointing out that Newton’s law of gravity states that
F ¼ Gm1M2
R2ðEq: 1:1Þ
where m1 is the smaller mass and M2 is the mass of the Earth. We can find the
specific force on an object by dividing the gravitational force by the mass of the
object. For distances like 50 m on the surface of the Earth (R¼ 6,378,140 m) we can
treat R as constant, but if the distance the gravitational force acts through is
comparable to the radius of the Earth, an integration would be required. Even on
the top of Mount Everest, the gravitational potential is within 0.25% of that at Sea
Level, so gravity is essentially constant for all systems operating on the face of the
Earth.
1.2 Scope of Thermodynamics 5
1.3 Units and Dimensions
Any physical quantity can be characterized by dimensions. The arbitrary magni-
tudes assigned to the dimensions are called units. There are two types of dimen-
sions, primary or fundamental and secondary or derived dimensions.
Primary dimensions are: mass, m; length, L; time, t; temperature, TSecondary dimensions can be derived from primary dimensions such as: velocity
(m/s2), pressure (Pa¼ kg/m s2).
There are two unit systems currently available SI (International System) and
USCS (United States Customary System) or English (E) system, and they are
discussed in this section.
1.3.1 Fundamental Units
Before going further it is a very good idea to discuss units for physical quantities
and the conversion of units from one system to another. Unfortunately, the field of
thermodynamics is beset with two popular systems of units. One is the International
System (SI) consisting of the kilogram, meter, and second. The other is the English
(E) system consisting of the pound-mass, foot, and second.
Starting with the SI system, the unit of force is the Newton. The unit of work or
energy is the Joule, and the unit of pressure is the Pascal. We have,
1 N¼ 1 kg m/s2
1 J¼ 1 N-m
1 Pa¼ 1 N/m2
Now the acceleration of gravity at Sea Level on Earth is 9.8066 m/s2, so a 100 kg
mass will have weight 980.66 N. Also when we want to avoid spelling out very
large or small quantities we will usually use the standard abbreviations for powers
of ten in units of 1000. We have,
kilo¼ 103
mega¼ 106
giga¼ 109
deci¼ 10�1
centi¼ 10�2
milli¼ 10�3
micro¼ 10�6
nano¼ 10�9
For the English system we have
6 1 Definitions and Basic Principles of Thermodynamics
lbm⟹ 1 lbf (at Sea Level)
1 ft lbf¼ 1 lbf� 1 ft
1 British Thermal Unit (BTU)¼ 778 ft lbf
1 psi¼ 1 lbf/in.2
Note that the fact that 1 lbf¼ 1 lbm at Sea Level on Earth, means that a mass of
100 lbm will weigh 100 lbf at Sea Level on Earth. The acceleration of gravity at Sea
Level on Earth is 32.174 ft/s2. Thus we have 1 lbf/(1 lbm ft/s2)¼ 32.174. If we
move to another planet where the acceleration of gravity is different, the statement
that 1 lbm� 1 lbf doesn’t hold.Consider comparative weights on Mars. The acceleration of gravity on Mars is
38.5% of the acceleration of gravity on Earth. So in the SI system we have:
W ¼ 0:385� 9:8066m=s2 � 100kg ¼ 377:7N
In the English system we have,
W ¼ 0:385� 100 lbm ¼ 38:5 lbf
1.3.2 Thermal Energy Units
The British thermal unit (Btu) is defined to be the amount of heat that must be
absorbed by a 1 lb-mass to raise its temperature 1 �F. The calorie is the SI unit that isdefined in a similar way. It is the amount of heat that must be absorbed by 1 g of
water to raise its temperature 1 �C. This raises the question as to how a calorie
compares with a Joule since both appear to be measures of energy in the SI system.
James Prescott Joule spent a major part of his life proving that thermal energy was
simply another form of energy like mechanical, kinetic or potential energy. Even-
tually his hypothesis was accepted and the conversion factor between the calorie
and Joule is defined by,
1 cal¼ 4.1868 J
The constant 4.1868 is called the mechanical equivalent of heat.
1.3.3 Unit Conversion
As long as one remains in either the SI system or the English system, calculations
and designs are simple. However, that is no longer possible as different organiza-
tions and different individuals usually think and work in their favorite system.
1.3 Units and Dimensions 7