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

© Springer International Publishing Switzerland 2017This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part ofthe material is concerned, specifically the rights of translation, reprinting, reuse of illustrations,recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmissionor information storage and retrieval, electronic adaptation, computer software, or by similar ordissimilar methodology now known or hereafter developed.The use of general descriptive names, registered names, trademarks, service marks, etc. in thispublication does not imply, even in the absence of a specific statement, that such names are exemptfrom the relevant protective laws and regulations and therefore free for general use.The publisher, the authors and the editors are safe to assume that the advice and information in thisbook are believed to be true and accurate at the date of publication. Neither the publisher nor theauthors or the editors give a warranty, express or implied, with respect to the material containedherein or for any errors or omissions that may have been made.

Printed on acid-free paper

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