Incropera fundamentals heat mass transfer 7th txtbk

www.elsolucionario.net http://www.elsolucionario.net LIBROS UNIVERISTARIOS Y SOLUCIONARIOS DE MUCHOS DE ESTOS LIBROS LOS SOLUCIONARIOS CONTIENEN TODOS LOS EJERCICIOS DEL LIBRO RESUELTOS Y EXPLICADOS DE FORMA CLARA VISITANOS PARA DESARGALOS GRATIS www.elsolucionario.net This page intentionally left blank www.elsolucionario.net FMTitlePage.qxd 2/21/11 6:11 PM Page i SEVENTH EDITION Fundamentals of Heat and Mass Transfer THEODORE L BERGMAN Department of Mechanical Engineering University of Connecticut ADRIENNE S LAVINE Mechanical and Aerospace Engineering Department University of California, Los Angeles FRANK P INCROPERA College of Engineering University of Notre Dame DAVID P DEWITT School of Mechanical Engineering Purdue University JOHN WILEY & SONS www.elsolucionario.net FMTitlePage.qxd 2/21/11 6:11 PM Page ii VICE PRESIDENT & PUBLISHER EXECUTIVE EDITOR EDITORIAL ASSISTANT MARKETING MANAGER PRODUCTION MANAGER PRODUCTION EDITOR DESIGNER EXECUTIVE MEDIA EDITOR PRODUCTION MANAGEMENT SERVICES Don Fowley Linda Ratts Renata Marchione Christopher Ruel Dorothy Sinclair Sandra Dumas Wendy Lai Thomas Kulesa MPS Ltd This book was typeset in 10.5/12 Times Roman by MPS Limited, a Macmillan Company and printed and bound by R R Donnelley (Jefferson City) The cover was printed by R R Donnelley (Jefferson City) Founded in 1807, John Wiley & Sons, Inc has been a valued source of knowledge and understanding for more than 200 years, helping people around the world meet their needs and fulfill their aspirations Our company is built on a foundation of principles that include responsibility to the communities we serve and where we live and work In 2008, we launched a Corporate Citizenship Initiative, a global effort to address the environmental, social, economic, and ethical challenges we face in our business Among the issues we are addressing are carbon impact, paper specifications and procurement, ethical conduct within our business and among our vendors, and community and 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the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030-5774, (201) 748-6011, fax (201) 748-6008 Evaluation copies are provided to qualified academics and professionals for review purposes only, for use in their courses during the next academic year These copies are licensed and may not be sold or transferred to a third party Upon completion of the review period, please return the evaluation copy to Wiley Return instructions and a free of charge return shipping label are available at www.wiley.com/go/returnlabel If you have chosen to adopt this textbook for use in your course, please accept this book as your complimentary desk copy Outside of the United States, please contact your local representative ISBN 13 978-0470-50197-9 Printed in the United States of America 10 www.elsolucionario.net FMPreface.qxd 2/21/11 6:11 PM Page iii Preface In the Preface to the previous edition, we posed questions regarding trends in engineering education and practice, and whether the discipline of heat transfer would remain relevant After weighing various arguments, we concluded that the future of engineering was bright and that heat transfer would remain a vital and enabling discipline across a range of emerging technologies including but not limited to information technology, biotechnology, pharmacology, and alternative energy generation Since we drew these conclusions, many changes have occurred in both engineering education and engineering practice Driving factors have been a contracting global economy, coupled with technological and environmental challenges associated with energy production and energy conversion The impact of a weak global economy on higher education has been sobering Colleges and universities around the world are being forced to set priorities and answer tough questions as to which educational programs are crucial, and which are not Was our previous assessment of the future of engineering, including the relevance of heat transfer, too optimistic? Faced with economic realities, many colleges and universities have set clear priorities In recognition of its value and relevance to society, investment in engineering education has, in many cases, increased Pedagogically, there is renewed emphasis on the fundamental principles that are the foundation for lifelong learning The important and sometimes dominant role of heat transfer in many applications, particularly in conventional as well as in alternative energy generation and concomitant environmental effects, has reaffirmed its relevance We believe our previous conclusions were correct: The future of engineering is bright, and heat transfer is a topic that is crucial to address a broad array of technological and environmental challenges In preparing this edition, we have sought to incorporate recent heat transfer research at a level that is appropriate for an undergraduate student We have strived to include new examples and problems that motivate students with interesting applications, but whose solutions are based firmly on fundamental principles We have remained true to the pedagogical approach of previous editions by retaining a rigorous and systematic methodology for problem solving We have attempted to continue the tradition of providing a text that will serve as a valuable, everyday resource for students and practicing engineers throughout their careers www.elsolucionario.net FMPreface.qxd iv 2/21/11 6:11 PM Page iv Preface Approach and Organization Previous editions of the text have adhered to four learning objectives: The student should internalize the meaning of the terminology and physical principles associated with heat transfer The student should be able to delineate pertinent transport phenomena for any process or system involving heat transfer The student should be able to use requisite inputs for computing heat transfer rates and/or material temperatures The student should be able to develop representative models of real processes and systems and draw conclusions concerning process/system design or performance from the attendant analysis Moreover, as in previous editions, specific learning objectives for each chapter are clarified, as are means by which achievement of the objectives may be assessed The summary of each chapter highlights key terminology and concepts developed in the chapter and poses questions designed to test and enhance student comprehension It is recommended that problems involving complex models and/or exploratory, whatif, and parameter sensitivity considerations be addressed using a computational equationsolving package To this end, the Interactive Heat Transfer (IHT) package available in previous editions has been updated Specifically, a simplified user interface now delineates between the basic and advanced features of the software It has been our experience that most students and instructors will use primarily the basic features of IHT By clearly identifying which features are advanced, we believe students will be motivated to use IHT on a daily basis A second software package, Finite Element Heat Transfer (FEHT), developed by F-Chart Software (Madison, Wisconsin), provides enhanced capabilities for solving two-dimensional conduction heat transfer problems To encourage use of IHT, a Quickstart User’s Guide has been installed in the software Students and instructors can become familiar with the basic features of IHT in approximately one hour It has been our experience that once students have read the Quickstart guide, they will use IHT heavily, even in courses other than heat transfer Students report that IHT significantly reduces the time spent on the mechanics of lengthy problem solutions, reduces errors, and allows more attention to be paid to substantive aspects of the solution Graphical output can be generated for homework solutions, reports, and papers As in previous editions, some homework problems require a computer-based solution Other problems include both a hand calculation and an extension that is computer based The latter approach is time-tested and promotes the habit of checking a computer-generated solution with a hand calculation Once validated in this manner, the computer solution can be utilized to conduct parametric calculations Problems involving both hand- and computer-generated solutions are identified by enclosing the exploratory part in a red rectangle, as, for example, (b) , (c) , or (d) This feature also allows instructors who wish to limit their assignments of computer-based problems to benefit from the richness of these problems without assigning their computer-based parts Solutions to problems for which the number is highlighted (for example, 1.26 ) are entirely computer based www.elsolucionario.net FMPreface.qxd 2/21/11 6:11 PM Page v v Preface What’s New in the 7th Edition In the previous edition, Chapter Introduction was modified to emphasize the relevance of heat transfer in various contemporary applications Responding to today’s challenges involving energy production and its environmental impact, an expanded discussion of the efficiency of energy conversion and the production of greenhouse gases has been added Chapter has also been modified to embellish the complementary nature of heat transfer and thermodynamics The existing treatment of the first law of thermodynamics is augmented with a new section on the relationship between heat transfer and the second law of thermodynamics as well as the efficiency of heat engines Indeed, the influence of heat transfer on the efficiency of energy conversion is a recurring theme throughout this edition The coverage of micro- and nanoscale effects in Chapter Introduction to Conduction has been updated, reflecting recent advances For example, the description of the thermophysical properties of composite materials is enhanced, with a new discussion of nanofluids Chapter One-Dimensional, Steady-State Conduction has undergone extensive revision and includes new material on conduction in porous media, thermoelectric power generation, and micro- as well as nanoscale systems Inclusion of these new topics follows recent fundamental discoveries and is presented through the use of the thermal resistance network concept Hence the power and utility of the resistance network approach is further emphasized in this edition Chapter Two-Dimensional, Steady-State Conduction has been reduced in length Today, systems of linear, algebraic equations are readily solved using standard computer software or even handheld calculators Hence the focus of the shortened chapter is on the application of heat transfer principles to derive the systems of algebraic equations to be solved and on the discussion and interpretation of results The discussion of Gauss–Seidel iteration has been moved to an appendix for instructors wishing to cover that material Chapter Transient Conduction was substantially modified in the previous edition and has been augmented in this edition with a streamlined presentation of the lumpedcapacitance method Chapter Introduction to Convection includes clarification of how temperature-dependent properties should be evaluated when calculating the convection heat transfer coefficient The fundamental aspects of compressible flow are introduced to provide the reader with guidelines regarding the limits of applicability of the treatment of convection in the text Chapter External Flow has been updated and reduced in length Specifically, presentation of the similarity solution for flow over a flat plate has been simplified New results for flow over noncircular cylinders have been added, replacing the correlations of previous editions The discussion of flow across banks of tubes has been shortened, eliminating redundancy without sacrificing content Chapter Internal Flow entry length correlations have been updated, and the discussion of micro- and nanoscale convection has been modified and linked to the content of Chapter Changes to Chapter Free Convection include a new correlation for free convection from flat plates, replacing a correlation from previous editions The discussion of boundary layer effects has been modified Aspects of condensation included in Chapter 10 Boiling and Condensation have been updated to incorporate recent advances in, for example, external condensation on finned tubes The effects of surface tension and the presence of noncondensable gases in modifying Chapter-by-Chapter Content Changes www.elsolucionario.net FMPreface.qxd vi 2/21/11 6:11 PM Page vi Preface condensation phenomena and heat transfer rates are elucidated The coverage of forced convection condensation and related enhancement techniques has been expanded, again reflecting advances reported in the recent literature The content of Chapter 11 Heat Exchangers is experiencing a resurgence in interest due to the critical role such devices play in conventional and alternative energy generation technologies A new section illustrates the applicability of heat exchanger analysis to heat sink design and materials processing Much of the coverage of compact heat exchangers included in the previous edition was limited to a specific heat exchanger Although general coverage of compact heat exchangers has been retained, the discussion that is limited to the specific heat exchanger has been relegated to supplemental material, where it is available to instructors who wish to cover this topic in greater depth The concepts of emissive power, irradiation, radiosity, and net radiative flux are now introduced early in Chapter 12 Radiation: Processes and Properties, allowing early assignment of end-of-chapter problems dealing with surface energy balances and properties, as well as radiation detection The coverage of environmental radiation has undergone substantial revision, with the inclusion of separate discussions of solar radiation, the atmospheric radiation balance, and terrestrial solar irradiation Concern for the potential impact of anthropogenic activity on the temperature of the earth is addressed and related to the concepts of the chapter Much of the modification to Chapter 13 Radiation Exchange Between Surfaces emphasizes the difference between geometrical surfaces and radiative surfaces, a key concept that is often difficult for students to appreciate Increased coverage of radiation exchange between multiple blackbody surfaces, included in older editions of the text, has been returned to Chapter 13 In doing so, radiation exchange between differentially small surfaces is briefly introduced and used to illustrate the limitations of the analysis techniques included in Chapter 13 Chapter 14 Diffusion Mass Transfer was revised extensively for the previous edition, and only modest changes have been made in this edition Problem Sets Approximately 250 new end-of-chapter problems have been developed for this edition An effort has been made to include new problems that (a) are amenable to short solutions or (b) involve finite-difference solutions A significant number of solutions to existing end-of-chapter problems have been modified due to the inclusion of the new convection correlations in this edition Classroom Coverage The content of the text has evolved over many years in response to a variety of factors Some factors are obvious, such as the development of powerful, yet inexpensive calculators and software There is also the need to be sensitive to the diversity of users of the text, both in terms of (a) the broad background and research interests of instructors and (b) the wide range of missions associated with the departments and institutions at which the text is used Regardless of these and other factors, it is important that the four previously identified learning objectives be achieved Mindful of the broad diversity of users, the authors’ intent is not to assemble a text whose content is to be covered, in entirety, during a single semester- or quarter-long course Rather, the text includes both (a) fundamental material that we believe must be covered and www.elsolucionario.net FMPreface.qxd 2/21/11 6:11 PM Page vii vii Preface (b) optional material that instructors can use to address specific interests or that can be covered in a second, intermediate heat transfer course To assist instructors in preparing a syllabus for a first course in heat transfe , we have several recommendations Chapter Introduction sets the stage for any course in heat transfer It explains the linkage between heat transfer and thermodynamics, and it reveals the relevance and richness of the subject It should be covered in its entirety Much of the content of Chapter Introduction to Conduction is critical in a first course, especially Section 2.1 The Conduction Rate Equation, Section 2.3 The Heat Diffusion Equation, and Section 2.4 Boundary and Initial Conditions It is recommended that Chapter be covered in its entirety Chapter One-Dimensional, Steady-State Conduction includes a substantial amount of optional material from which instructors can pick-and-choose or defer to a subsequent, intermediate heat transfer course The optional material includes Section 3.1.5 Porous Media, Section 3.7 The Bioheat Equation, Section 3.8 Thermoelectric Power Generation, and Section 3.9 Micro- and Nanoscale Conduction Because the content of these sections is not interlinked, instructors may elect to cover any or all of the optional material The content of Chapter Two-Dimensional, Steady-State Conduction is important because both (a) fundamental concepts and (b) powerful and practical solution techniques are presented We recommend that all of Chapter be covered in any introductory heat transfer course The optional material in Chapter Transient Conduction is Section 5.9 Periodic Heating Also, some instructors not feel compelled to cover Section 5.10 Finite-Difference Methods in an introductory course, especially if time is short The content of Chapter Introduction to Convection is often difficult for students to absorb However, Chapter introduces fundamental concepts and lays the foundation for the subsequent convection chapters It is recommended that all of Chapter be covered in an introductory course Chapter External Flow introduces several important concepts and presents convection correlations that students will utilize throughout the remainder of the text and in subsequent professional practice Sections 7.1 through 7.5 should be included in any first course in heat transfer However, the content of Section 7.6 Flow Across Banks of Tubes, Section 7.7 Impinging Jets, and Section 7.8 Packed Beds is optional Since the content of these sections is not interlinked, instructors may select from any of the optional topics Likewise, Chapter Internal Flow includes matter that is used throughout the remainder of the text and by practicing engineers However, Section 8.7 Heat Transfer Enhancement, and Section 8.8 Flow in Small Channels may be viewed as optional Buoyancy-induced flow and heat transfer is covered in Chapter Free Convection Because free convection thermal resistances are typically large, they are often the dominant resistance in many thermal systems and govern overall heat transfer rates Therefore, most of Chapter should be covered in a first course in heat transfer Optional material includes Section 9.7 Free Convection Within Parallel Plate Channels and Section 9.9 Combined Free and Forced Convection In contrast to resistances associated with free convection, thermal resistances corresponding to liquid-vapor phase change are typically small, and they can sometimes be neglected Nonetheless, the content of Chapter 10 Boiling and Condensation that should be covered in a first heat transfer course includes Sections 10.1 through 10.4, Sections 10.6 through 10.8, and Section 10.11 Section 10.5 Forced Convection Boiling may be material appropriate for an intermediate heat transfer course Similarly, Section 10.9 Film Condensation on Radial Systems and Section 10.10 Condensation in Horizontal Tubes may be either covered as time permits or included in a subsequent heat transfer course www.elsolucionario.net BAPP07.qxd 2/21/11 1036 6:09 PM Page 1036 Appendix G ᭿ An Integral Laminar Boundary Layer Solution An alternative approach to solving the boundary layer equations involves the use of an approximate integral method The approach was originally proposed by von Kárman [1] in 1921 and first applied by Pohlhausen [2] It is without the mathematical complications inherent in the exact (similarity) method of Section 7.2.1; yet it can be used to obtain reasonably accurate results for the key boundary layer parameters (␦, ␦t, ␦c, Cƒ, h, and hm) Although the method has been used with some success for a variety of flow conditions, we restrict our attention to parallel flow over a flat plate, subject to the same restrictions enumerated in Section 7.2.1, that is, incompressible laminar flo with constant fluidproperties and negligible viscous dissipation To use the method, the boundary layer equations, Equations 7.4 through 7.7, must be cast in integral form These forms are obtained by integrating the equations in the y-direction across the boundary layer For example, integrating Equation 7.4, we obtain ͵ ѨuѨx dy ϩ ͵ ѨvѨy dy ϭ ␦ ␦ (G.1) or, since ␷ ϭ at y ϭ 0, ͵ ѨuѨx dy ␦ v( y ϭ ␦) ϭ Ϫ (G.2) Similarly, from Equation 7.5, we obtain ͵ u ѨuѨx dy ϩ ͵ v ѨuѨy dy ϭ ␯ ͵ ѨyѨ ΂ѨuѨy΃ dy ␦ ␦ ␦ 0 or, integrating the second term on the left-hand side by parts, ͵ u ѨuѨx dy ϩ uv ͯ Ϫ ͵ u ѨvѨy dy ϭ ␯ ѨuѨy ͯ ␦ ␦ 0 ␦ ␦ 0 Substituting from Equations 7.4 and G.2, we obtain ͵ u ѨuѨx dy Ϫ u ͵ ѨuѨx dy ϩ ͵ u ѨuѨx dy ϭ Ϫ␯ ѨuѨy ͯ ␦ ␦ ȍ or ␦ yϭ0 ͵ ѨuѨx dy Ϫ ͵ 2u ѨuѨx dy ϭ ␯ ѨuѨy ͯ ␦ uȍ Therefore ␦ yϭ0 ͵ ѨxѨ (u ⅐ u Ϫ u ⅐ u) dy ϭ ␯ ѨuѨy ͯ ␦ ȍ yϭ0 Rearranging, we then obtain d dx ΄͵ (u ␦ ȍ ΅ Ϫ u)u dy ϭ ␯ Ѩu Ѩy ͯ yϭ0 (G.3) Equation G.3 is the integral form of the boundary layer momentum equation In a similar fashion, the following integral forms of the boundary layer energy and species continuity equations may be obtained: d dx ΄͵ (T ␦t ȍ ΅ Ϫ T )u dy ϭ ␣ www.elsolucionario.net ѨT Ѩy ͯ yϭ0 (G.4) BAPP07.qxd 2/21/11 6:09 PM Page 1037 Appendix G ᭿ 1037 An Integral Laminar Boundary Layer Solution d dx ΄͵ (␳ ␦c A,ȍ Ϫ ΅ ␳A)u dy ϭ DAB Ѩ␳A Ѩy ͯ yϭ0 (G.5) Equations G.3 through G.5 satisfy the x-momentum, the energy, and the species conservation requirements in an integral (or average) fashion over the entire boundary layer In contrast, the original conservation equations, (7.5) through (7.7), satisfy the conservation requirements locally, that is, at each point in the boundary layer The integral equations can be used to obtain approximate boundary layer solutions The procedure involves first assuming reasonable functional forms for the unknowns u, T, and ␳A in terms of the corresponding (unknown) boundary layer thicknesses The assumed forms must satisfy appropriate boundary conditions Substituting these forms into the integral equations, expressions for the boundary layer thicknesses may be determined and the assumed functional forms may then be completely specified Although this method is approximate, it frequently leads to accurate results for the surface parameters Consider the hydrodynamic boundary layer, for which appropriate boundary conditions are u(y ϭ 0) ϭ Ѩu Ѩy ͯ yϭ␦ ϭ0 u(y ϭ ␦) ϭ uȍ and From Equation 7.5 it also follows that, since u ϭ v ϭ at y ϭ 0, Ѩ2u Ѩy2 ͯ yϭ0 ϭ0 With the foregoing conditions, we could approximate the velocity profile as a third-degree polynomial of the form ΂΃ ΂΃ y y u uȍ ϭ a1 ϩ a2 ␦ ϩ a3 ␦ ϩ a4 ΂΃ y ␦ and apply the conditions to determine the coefficients a1 to a4 It is easily verified that a1 ϭ a3 ϭ 0, a2 ϭ and a4 ϭ Ϫ2, in which case ΂΃ 3y y u uȍ ϭ ␦ Ϫ ␦ (G.6) The velocity profile is then specified in terms of the unknown boundary layer thickness ␦ This unknown may be determined by substituting Equation G.6 into G.3 and integrating over y to obtain ΂ ΃ d 39 u2 ␦ ϭ ␯uȍ dx 280 ȍ ␦ Separating variables and integrating over x, we obtain ␦2 ϭ 140 ␯x ϩ constant 13 uȍ However, since ␦ ϭ at the leading edge of the plate (x ϭ 0), the integration constant must be zero and ΂ ΃ ␯x ␦ ϭ 4.64 u ȍ 1/2 www.elsolucionario.net ϭ 4.64x Re1/2 x (G.7) BAPP07.qxd 2/21/11 6:09 PM 1038 Page 1038 Appendix G ᭿ An Integral Laminar Boundary Layer Solution Substituting Equation G.7 into Equation G.6 and evaluating ␶s ϭ ␮(Ѩu/Ѩy)s, we also obtain Cf,x ϭ ␶s ϭ 0.646 ␳u2ȍ/2 Re1/2 x (G.8) Despite the approximate nature of the foregoing procedure, Equations G.7 and G.8 compare quite well with results obtained from the exact solution, Equations 7.19 and 7.20 In a similar fashion one could assume a temperature profile of the form T* ϭ ΂ ΃ ΂ ΃ ϩ b ΂␦y ΃ T Ϫ Ts y y ϭ b1 ϩ b2 ϩ b3 Tȍ Ϫ Ts ␦t ␦t and determine the coefficients from the conditions T *(y ϭ 0) ϭ ѨT * Ѩy ͯ yϭ␦t t ϭ0 T * ( y ϭ ␦t) ϭ as well as Ѩ2T * Ѩy2 ͯ yϭ0 ϭ0 which is inferred from the energy equation (7.6) We then obtain ΂΃ y y T* ϭ Ϫ ␦t ␦t (G.9) Substituting Equations G.6 and G.9 into Equation G.4, we obtain, after some manipulation and assuming Pr տ 1, ␦t PrϪ1/3 ϭ ␦ 1.026 (G.10) This result is in good agreement with that obtained from the exact solution, Equation 7.24 Moreover, the heat transfer coefficient may then be computed from hϭ Ϫk ѨT/Ѩy͉yϭ0 Ts Ϫ Tȍ ϭ3 k ␦t Substituting from Equations G.7 and G.10, we obtain 1/3 Nux ϭ hx ϭ 0.332 Re1/2 x Pr k (G.11) This result agrees precisely with that obtained from the exact solution, Equation 7.23 Using the same procedures, analogous results may be obtained for the concentration boundary layer References von Kárman, T., Z Angew Math Mech., 1, 232, 1921 Pohlhausen, K., Z Angew Math Mech., 1, 252, 1921 www.elsolucionario.net bindex.qxd 2/25/11 6:21 AM Page 1039 Index NOTE: Page references preceded by a “W” refer to pages that are located on the Web site www.wiley.com/college/incropera Page numbers followed by “n” refer to footnotes on the page A Absolute species flux, 939–942 Absolute temperature, Absorption: gaseous, 897–901 volumetric, 896–897 Absorptivity, 9, 802–803 Accommodation coefficient: momentum, 378n, 558–559 thermal, 189, 380n, 558 Adiabatic surfaces, 91, 230, 246 Adiabats, 230 plotting, W1–W2 Advection, 13, W25, 378, 381, 396, 398, 940, 943 definition of, American Society of Mechanical Engineers (ASME), on SI units, 36 Analogies: Chilton-Colburn, 417 heat and mass transfer, 410–416, 934, 947, 966 heat diffusion and electrical charge, 114–115 Reynolds analogy, 416–417 Angle: azimuthal, 774 plane, 773 solid, 773 zenith, 774 Annular fins, 155–156, 167, 685 Azimuthal angle, 774 B Band emission, 785–792 Beer’s law, 897 Bessel equations, modified, 167–168 Bessel functions: of the first kind (table), 1017 modified, of the first and second kinds (table), 1018 Binary diffusion coefficients, 381, 937 at one atmosphere (table), 1006 Bioheat equation, 178–182 Biot number, 283–284, 408, 966 Blackbodies: concept of, 782–783 definition of, Blackbody radiation, 9, 782–792 and band emission, 785–792 and Kirchhoff’s law, 810–811 Planck distribution and, 783–784 radiation exchange, 872–876 and the Stefan-Boltzmann law, 784–785 and Wien’s displacement law, 784 Body forces, W26, 594, 1029 Boiling, 7, 8, 15, 653–673 convection coefficients, typical (table), dimensionless parameters in, 654–655, 672 forced convection, 655, 669–673 two-phase flow in, 670–673 modes of, 655 pool boiling, see Pool boiling saturated and subcooled, 655 Boiling crisis, 660 Boiling curve, in pool boiling, 656–657 Bond number, 408, 655 Boundary conditions, 90–91 adiabatic, 91 catalytic surface, 960–962 Dirichlet, 90 discontinuous, 954–956 of the first kind, 90, 1020–1021 mass diffusion and, 954–962 Neumann, 91 of the second kind, 91, 150, 1021–1023 of the third kind, 91, 150, 1021–1023 Boundary layer(s), 378–418, 434–468 approximations, 395–396 concentration boundary layer, 380–382 dimensionless parameters in, 398–402, 407–409, 598–599 equations, 394–397, 398–406, 597–598, 1031–1033, 1035–1038 evaporative cooling, 413–416 heat and mass transfer analogy, 410–416 hydrodynamic, laminar and turbulent flow, 389–393 mixed conditions in external flow, 444–445 normalized equations, 398–402 functional forms, 400–406 similarity parameters, 398–400 www.elsolucionario.net bindex.qxd 2/25/11 1040 6:21 AM ᭿ Page 1040 Index Boundary layer(s) (continued) Reynolds analogy, 416–417 separation, 455–457, 465 significance of, 382 thermal boundary layer, 6, 379–380 velocity boundary layer, 378–379 Boussinesq approximation, 598 Bulk fluid motion, W29 Bulk temperature, 524–525 Buoyancy forces, 6–7, 594, 654 Buoyant jets, 595–596 Burnout point, 660 C Carnot efficiency, 32–36 Catalytic surface reactions, 960–962 Celsius temperature scale, 37 Characteristic length, 238, 284–285, 398 Chemical component, of internal energy, 15 Chemical reactions, 960–965 Chilton-Colburn analogies, 417 Circular tubes, see Tubes Coefficient of friction, see Friction coefficient Coiled tubes, 555–558 Colburn j factors, 409, 417 Cold plates, 93 Columns, evaporation in, 942–947 Compact heat exchangers, W44–W49, 708, 739 Complementary error function, 314, 1015n Composite wall systems: heat transfer in, 115–119 porous media as, 119–121 thermal contact resistance in, 117–119, 120 Compressible flow, 397 Concentration boundary layer, 380–382 and laminar or turbulent flow, 391–393 Concentration entry length, 563 Concentration penetration depth, 970 Concentric tube annulus, 553–555 Concentric tube heat exchangers, 706 Condensation, 7, 8, 15, 673–691 convection coefficients, typical (table), dimensionless parameters in, 654–655, 689 dropwise, 690 film laminar, 675–679 on radial systems, 684–688 turbulent, 679–683 in horizontal tubes, 689–690 mechanisms of, 673–675 types of, 674 Conduction, 2–5, 46 analysis methods, 112–114, 132–135 and boundary/initial conditions, 90–93 definition of, and Fourier’s law, 4, 68–70, 86–87 and heat diffusion equation, 82–90 micro- and nanoscale effects, 72–75, 77–78, 90, 189–190 one-dimensional steady-state, see One-dimensional steady-state conduction rate equation, 4, 46 shape factors, W3–W5, 235–240 in surface energy balance, 27–30 with thermal energy generation, see Thermal energy generation, conduction with and thermophysical properties of matter, 70–79 transient, see Transient conduction two-dimensional steady-state, see Two-dimensional steady-state conduction Conduction rate equation (Fourier’s law), 4, 68–70, 86–87 Conduction shape factor(s), W3–W5, 235–240 for selected systems (table), 236–237 Configuration factor(s), view factor, 862–872 Confinement number, 663, 672, 673 Conservation of energy, 12–31, W29–W31, 83–87 application methodology, 31 for control volumes, 13–31, W29–W31, 394–397, 1029–1030 equations, 14, 16, 17 surface energy balance, 27–30 Conservation of mass, W25–W26, 1028 Conservation of species, W32–W36 and boundary layer equations, 394–397 for nonstationary media, 1030 for stationary media, 947–954 Constriction resistance, 690 Contact resistance, 117–119, 120 Continuity equation, W26 Control surface, 13 Control volume(s): definition of, 13, 31 differential, 31, 83–85, 394, 948–949 Convection, 377–418 See also Boiling; Condensation; External flow; Free convection; Internal flow boundary conditions (table), 91 boundary layers concentration boundary layer, 380–382 dimensionless parameters, 398–402, 407–409 equations for, W25–W36, 394–406, 1027–1030, 1031–1033 evaporative cooling, 413–416 heat and mass transfer analogy, 410–416 laminar and turbulent, 389–393 normalized equations, 398–406 Reynolds analogy, 416–417 significance of, 382 thermal boundary layer, 379–380 velocity boundary layer, 378–379 coefficients, 8, 289, 380–385, 400–406 definition of, dimensionless parameter significance, 407–409 forced, 6–7, 398 See also Boiling, forced convection; External flow; Internal flow free (natural), see Free convection laminar flow and boundary layers, 389–393 mass and heat transfer analogy, 378 micro- and nanoscale effects, 558–562 mixed, 7, 628 problem of, 385 rate equation, 8, 46 in surface energy balance, 27–28 transfer equations, W25–W36, 1027–1030 turbulent flow and boundary layers, 389–393 Convection heat transfer coefficient, 8, 289, 380, 382–383, 385, 400–401 local and average, 382–383 Convection mass transfer coefficient, 381–382, 383–385, 401–402 local and average, 383–385 Cooling, evaporative, 413–416 Counterflow heat exchangers, 706–707, 714–715, 722–727 Creeping flow, 465 Critical film thickness for microscale conduction, 73–74 Critical heat flux, 658, 659, 662–663, 670, 673 www.elsolucionario.net bindex.qxd 2/25/11 6:21 AM Page 1041 ᭿ 1041 Index Cross-flow heat exchangers, 706–707, 715,724–727 Cylinder(s): in cross flow, 455–465 flow considerations, 455–456 heat and mass transfer (convection), 457–465 free convection with concentric cylinders, 624–625 long horizontal cylinder, 613–616, 618 one-dimensional steady-state conduction in, 136–141, 1019–1024 shape factors for, 236–237 transient conduction in, 300–301, 303–307, 318–320 graphical representation of, W12, W14–W15 summary (table), 321–322 D Dalton’s law of partial pressures, 936 Darcy friction factor, for internal flow, 522–523 Density, 78 gradients, 594, 654 mass, 935 Differential control volumes, 31, 83–85, 394, 948–949 Diffuse emitters, 776, 782, 794 Diffuse radiation, 823 Diffusion: energy transfer by, 3, 6, W30 mass, see Mass diffusion Diffusion-limited processes, 962 Diffusive reflectors, 782 Diffusive species flux, 939–942 Diffusivity mass, 937 momentum, 407 thermal, 78 Dilute gas or liquid, 947 Dimensionless conduction heat rate, 235–240, 317–322 Dimensionless parameters: boiling and condensation, 654–655 boundary layers, 379, 390, 398–402, 407–409 conduction, 284–319 free convection, 598–599 of heat and mass transfer (table), 408–409 Dimensions, 36–38 Direct radiation, 823 Dirichlet conditions, 90 Discontinuous boundary conditions, 954–956 Discretization of the heat equation: explicit method of, 330–337 implicit method of, 337–345 Dittus-Boelter equation, 544–545 Drag coefficient, 456 Dropwise condensation, 674–675, 690 Dynamic viscosity, 80, 379 E Eckert number, 408 Effective thermal conductivity, 119–121 Effectiveness fin, 164 heat exchanger, 722–723 Effectiveness-NTU analysis method, 722–730, 739–746 definitions in, 722–723 Efficiency: Carnot, 32–36 fin, 165–172 of heat engines, 31–36 Eigenvalues, 300 Electrical energy, and thermoelectric power, 182–188 Electromagnetic spectrum, 769–770 Electromagnetic waves, 769–770 Emission, 768–770 band, 785–792 gaseous, 897–901 and intensity, 774–779 Emissive power, 9, 771, 775–776, 784–785 of a blackbody, 9, 784–785 Emissivity, 9–10 definition of, 792 of real surfaces, 792–796 representative values (table), 796 of selected surfaces (table), 1008–1010 Empirical method, 435–436 Enclosed fluids, free convection with, 621–627 Energy balance: atmospheric radiation, 821–823 for internal flow, 529–536 method for discretization, 243–249 surface, 27–30 Energy carriers, 71 Energy generation, 14–16, 84, 142–154, 182–188 Energy sources, 42–43, 84, 183–184 Energy storage, 14, 84 Energy use and sustainability, 41–43, 182–188 Enhancement, heat transfer boiling, 665 condensation, 685 fins, 155, 165 internal flow, 555–558 Enhancement surface(s), 665 Enthalpy, and steady-flow energy equation, 16–17 Entry length(s): concentration, 563 hydrodynamic, 519 thermal, 524 Entry region(s): hydrodynamic, 518–519 and internal flow, 542–544 thermal and combined, 524, 542–544 Environmental radiation, 818–826 atmospheric irradiation, 824 atmospheric radiation balance, 821–823 extraterrestrial solar, 819 scattering, 821 solar, 818–821 solar constant, 819 spectral distributions, 820 terrestrial solar irradiation, 823–824 Error function, 313, 1015 Evaporation, 15 See also Boiling in column, 942–947 cooling and, 413–416 mass transfer and, 563–565, 955 Evaporators, 654 Excess temperature, 158, 655 Extended surfaces, heat transfer from, 112, 154–178 conduction analysis, 156–158 fin characteristics and parameters, 154–156 fin effectiveness, 164 fin efficiency, 165–172 overall surface efficiency, 170–178, 709–710 nonuniform cross-sectional area fins, 167–170 uniform cross-sectional area fins, 158–164 www.elsolucionario.net bindex.qxd 2/25/11 1042 6:21 AM ᭿ Page 1042 Index External flow, 433–486 across banks of tubes, 468–476 cylinder in cross flow, 455–465 flow considerations, 455–456 heat and mass transfer (convection) in, 457–465 empirical method for, 434, 435–436 flat plate in parallel flow, 436–447 with constant heat flux conditions, 446 laminar flow, 437–443 with mixed boundary layer conditions, 444–445 turbulent flow, 443 with unheated starting length, 445–446 forced convection boiling, 669–670 free convection horizontal cylinder, 613–616 inclined and horizontal plates, 608–613 over vertical plate, 605–608 spheres, 617–618 friction coefficients of, 379 heat transfer correlations (table), 484–485 impinging jet(s) considerations, 477–478 heat and mass transfer (convection) in, 477–482 methodology for convection calculation, 447 over sphere, 465–468 packed bed(s), 482–483 similarity method for, 434–435, 437–443 F Fanning friction factor, 522 Fick’s law, 381–382, 936–937 Film boiling, 658–660, 663–665 Film condensation, 674–690 definition of, 674 laminar, 675–679 in tubes, 689–690 on tubes, 684–686 turbulent, 679–681 wavy, 680 Film temperature, 414, 436 Film(s), thermal conductivity of, 73–75, 77, 190 Finite control volumes, energy conservation of, 31 Finite-difference method: transient conduction explicit method of discretization of the heat equation, 330–337 implicit method of discretization of the heat equation, 337–345 two-dimensional steady-state conduction, 241–256 energy balance method in, 243–249 Gauss-Seidel iteration method, W5–W9, 250, 1025–1026 heat equation form, 242–243 nodal network selection, 241–242 solving, 250–256 Fins, 154–178 annular, 155–156, 167, 685 conduction analysis, 156–158 effectiveness, 164 efficiency, 165–172 film condensation on, 684–686, 690 free convection with, 618 of nonuniform cross-sectional area, 167–170 overall surface efficiency, 170–178, 709–710 performance measures, 164–167 pin, 155–156 straight, 155–156, 166 of uniform cross-sectional area, 158–164 First law of thermodynamics, 12–14 First-order chemical reactions, 961–964 Flat plate: boundary layers and, 378–382 parallel flow over, 436–447 with constant heat flux conditions, 446 integral boundary layer solution for, 1035–1038 laminar flow, 389–393, 437–443 with mixed boundary layer conditions, 444–445 turbulent flow over, 389–393, 443 with unheated starting length, 445–446 Flow See also External flow; Internal flow compressible, 397 creeping, 465 steady, two-dimensional, W25–W36, 394, 1027–1030 Flow work, 16 Fluidized beds, 482 Fluids: convection and, 378 free convection with enclosed, 621–627 incompressible, 394, 1028 nanofluid, 77, 80–82 Newtonian, W28, 379 and problem of convection, 385 thermal conductivity of, 75–77 thermophysical properties of (table), 1000–1005 viscous, W25–W36, 1027–1030 Flux-plotting method, W1–W5, 231 Forced convection, 6–7, 398, 669–673 combined free and forced, 627–628 and external flow, see External flow and internal flow, see Internal flow Forced convection boiling, 655, 669–673 external, 669–670 two-phase flow, 670–673 flow regimes, 671 Form drag, 456 Fouling: in condensation, 675 in heat exchangers, 709–711 Fouling factor, 709 Fourier number, 285, 408 Fourier’s law, 4–5, 68–70, 86–87 Free boundary flows, 595–596 Free convection, 6–8, 593–631 applications of, 594 buoyancy and, 594–596 combined free and forced, 627–628 dimensionless parameters for, 598–599 empirical correlations (table), 617–618 with enclosed fluids, 621–627 concentric cylinders, 624–625 concentric spheres, 625–627 rectangular cavities, 621–624 external flows, 604–618 horizontal cylinder, 613–616 inclined and horizontal plates, 608–613 spheres, 617–618 vertical plate, 605–608 free convection boiling, 657–658 governing equations, 597–598 laminar free convection on a vertical surface, 599–602 and mass transfer, 628–629 mixed convection, 627–628 physical considerations of, 594–596 www.elsolucionario.net bindex.qxd 2/25/11 6:21 AM Page 1043 ᭿ 1043 Index turbulence effects, 602–604 within parallel plate channels, 618–621 inclined channels, 621 vertical channels, 619–621 Free convection boiling, 657–658 Free stream, 379 Freezing, 15 Friction coefficient, 379, 382, 400, 408, 440, 442, 443, 444, 522 Friction drag, 456 Friction factor, 408 for external flow, 472–473 for internal flow, 522–523, 553, 557 Froude number, 672 G Gas(es): conduction in, convection coefficients, typical (table), emission from, 768–769 ideal, thermal energy equations for, 16–20 mass diffusion in, 934–935 micro- and nanoscale conduction effects, 189–190 micro- and nanoscale convection effects, 558–559 radiation exchange with, 896–901 solubility of, 955–960, 1007 thermal conductivity of, 75–78 thermal radiation and, 10 thermophysical properties of (table), 995–999 Gauss-Seidel iteration method, 250, 1025–1026 example, W5–W9 Gaussian error function, 313, 1015 Generation, see Thermal energy generation Graphical methods: for two-dimensional steady-state conduction, 231 conduction shape factors, W3–W5 flux-plot construction, W1–W2 heat transfer rate determination, W2–W3 Grashof number, 408–409, 599, 628 Gravitational field, and pool boiling, 664 Gray surfaces: radiation behavior, 812–814 radiation exchange, 876–893 net radiation exchange, 877–878 radiation shields, 886 reradiating surfaces, 888–893 surface radiation exchanges, 878–880 thermal radiation and, 10 H Heat diffusion equation (heat equation), 82–91 boundary conditions, 90–91 finite-difference form, 242–243, 330–345 microscale effects, 90 Heat engines, efficiency of, 31–36 Heat equation, see Heat diffusion equation Heat exchangers, 705–748 compact, W44–W49, 708, 739 design problems, 730 effectiveness (table), 724 effectiveness-NTU analysis method, 722–730, 739–746 definitions in, 722–723 relations, 723–727 log mean temperature difference (LMTD) analysis, 711–721 analysis with, 711–712, 739–746 for counterflow heat exchangers, 714–715 for multipass and cross-flow heat exchangers, W40–W44 for parallel-flow heat exchangers, 712–714 NTU (table), 725 overall heat transfer coefficient for, 708–711 performance calculation problems, 730 types of, 706–708 Heat flow lines, 230 plotting, W1–W2 Heat flux, 4–5, 8, 9–12, 85 critical, 658, 659, 662–663, 673 radiation fluxes, 771–772 Heat rate, 4–5, 10, 33 Heat sinks, 44 Heat transfer: in convection, 382–383 definition of, dimensionless groups in, 407–409 efficiency and, 32–36 enhancement research, 739 from extended surfaces, 112, 154–178 conduction analysis, 156–158 fin characteristics and parameters, 154–156 fin effectiveness, 164 fin efficiency, 165–172 overall surface efficiency, 170–178, 709–710 nonuniform cross-sectional area fins, 167–170 uniform cross-sectional area fins, 158–164 in insulation systems, 77–78 methodology for problem-solving, 38–41, 114 multimode, 893–895 physical mechanisms of, 3–12 rate determination (two-dimensional steady-state conduction), W2–W3 relevance of, 41–45 summary of modes (table), 46 thermodynamics vs., 12–13 Henry’s constant, 956 for selected gases in water (table), 1007 Henry’s law, 956 Heterogeneous chemical reactions, 960–962 Homogeneous chemical reactions, 949, 960n, 962–965 Hydraulic diameter, 552 Hydrodynamic boundary layers, See also Velocity boundary layer Hydrodynamic considerations: with impinging jet(s), 477–478 with internal flow, 518–523 Hydrodynamic entry length, 519 Hyperbolic functions (table), 1014 I Ideal gases, 16–17 Impingement zones, 477–478 Impinging jet(s): considerations, 477–478 heat and mass transfer (convection) through, 478–482 nozzle considerations, 480–482 Incident radiation, 779 Incompressible liquids, 16–17, W26, W29, 394, 1027–1030 Initial conditions, 90–91 Insulation: micro- and nanoscale effects, 77–78 systems and types, 77 thermophysical properties of (table), 990–992 typical thermal conductivities, 71 Intensity, radiation, 773–782 Internal energy, 13–15, W31 www.elsolucionario.net bindex.qxd 2/25/11 1044 6:21 AM ᭿ Page 1044 Index Internal flow, 517–568 in circular tubes convection correlations (table), 567 laminar flow, 537–544 turbulent flow, 544–552 in coiled tubes, 556–558 convection mass transfer, 563–565 energy balance in, 529–536 with constant surface heat flux, 530–533 with constant surface temperature, 533–536 general considerations, 529–530 heat transfer enhancement in, 555–558 hydrodynamic considerations, 518–523 flow conditions, 518–519 friction factor, 522–523 mean velocity, 519–520 velocity profile, 520–522 micro- and nanoscale effects, 558–562 in noncircular tubes, 552–555 thermal considerations, 523–529 with fully developed conditions, 525–527 mean temperature, 524–525 Newton’s law of cooling in, 525 Irradiation, 9–12, 771, 779–781, 801 Isothermal surfaces, 69 Isotherms, 69–70, 230, 235 Isotropic media, 70 effective thermal conductivities in, 121 J Jakob number, 409, 655 Jet(s): in boiling, 658–659 buoyant, 595–596 impinging, see Impinging jet(s) Joule heating, see Ohmic heating K Kelvin, 37 Kelvin-Planck statement, 31 Kinematic viscosity, 407 Kirchhoff’s law, 810–811 L Laminar boundary layer, 389–393 Laminar film condensation, 675–679 Laminar flow: boundary layers and equations, 389–397, 597–598 in circular tubes, 537–544 in noncircular tubes, 552–555 over flat plate, 437–443 Latent component, of internal energy, 15 Latent energy, in convection, Latent heat, in boiling/condensation, 654 Latent heat of fusion, 26–27 Lattice waves, conduction and, 4, 71–72 Leidenfrost point, 660 Length, units for, 36–37 Lewis number, 407–409 Liquid metals: convection coefficients for, 442–443, 546 thermophysical properties of (table), 1005 Liquid(s): conduction in, 3–4 convection coefficients, typical (table), gas solubility in, 955–960 mass diffusion in, 935 microscale convection in, 559–560 radiation from, 768–769 thermal conductivity of, 75–77 thermal energy equations for, 16–17 thermal radiation and, 8, 10 Log mean temperature difference method (LMTD), 711–721, 739–746 for counterflow heat exchangers, 714–715 for multipass and cross-flow heat exchangers, W40–W44 for parallel-flow heat exchangers, 712–714 Longitudinal pitch, 468–469 Lumped capacitance method, 280–297 calculations for, 281–283 conditions for, 280–281 general lumped capacitance analysis, 287–297 validity of, 283–286 Lumped thermal capacitance, 282 M Mach number, 409 Martinelli parameter, 689 Mass: conservation of, see Conservation of mass units for, 36–37 Mass diffusion, 933–972 boundary conditions and discontinuous interface concentrations, 954–962 catalytic surface reactions, 960–962 evaporation and sublimation, 955 solubility of gases in liquids and solids, 955–960 with homogeneous chemical reactions, 962–965 mass diffusion equation, 948–950 in nonstationary media, 939–947 absolute and diffusive species fluxes, 939–942 evaporation in column, 942–947 physical process of, 934–935 Fick’s law and, 936–937 mass diffusivity, 937–939 mixture composition, 935–936 in stationary media, 947–954 conservation of species for control volumes, 948 mass diffusion equation, 948–950 with specified surface concentrations, 950–954 stationary medium approximation, 947 transient diffusion, 965–971 Mass diffusion equation, 948–950 Mass diffusivity, 937–939 Mass flow rate, 16, 17 Mass transfer by convection, 383–385 dimensionless groups in, 407–409 external flow, 434, 441–444, 447 cylinder in cross flow, 457–465 impinging jet(s), 477–482 packed bed(s), 482–483 in free convection, 628–629 heat transfer analogy, 410–416 internal flow, 563–565 Matrix equation method, 250 Mean beam length, 900 Mean free path, 71, 73–75 Mean temperature, of internal flow, 524–525 Mean velocity, of internal flow, 519–520 Melting, 15 Metabolic heat generation, 178–182 www.elsolucionario.net bindex.qxd 2/25/11 6:21 AM Page 1045 ᭿ 1045 Index Metals and metallic solids: emissivity of (table), 1008 thermal conductivity of, 71–72, 77 thermophysical properties of, 983–986, 1005, 1008 Microchannels in boiling, 673 in condensation, 690 effects, 378 in internal flow, 558–560 Microfluidic devices, 558 Microscale effects: in conduction, 72–75, 77–78, 90, 189–190 in convection, 380n, 558–562 Mie scattering, 821 Mixed convection, 7, 628 Mixtures, characteristics of, 935–936 Modes of heat transfer, definition of, Modified Bessel equations, 167–168 Molar concentration, 935 Momentum accommodation coefficients, 378n, 558–559 Momentum diffusivity, 407 Moody diagram, 523 Moody friction factor, for internal flow, 522–523 Multimode heat transfer, 893–895 Multipass heat exchangers, W40–W44, 708, 715 N Nanofluid, 77, 80–82 Nanoscale effects: in conduction, 72–75, 77–78, 189–190 in convection, 380n, 560 in radiation, 769 Nanostructured materials, 74, 77–78, 186 Natural convection, see Free convection Net radiation exchange, 877–878 Net radiative flux, 771–772, 782 Neumann conditions, 90–91 Newtonian fluids, W28, 379 Newton’s law of cooling, 8, 115, 380, 525, 655 Newton’s second law of motion, W26–W29, 1028–1029 Nodal network, 241–242, 879–880 Nodal points, 241–242, 879–880 Noncircular tubes, see Tubes Nonmetallic materials: emissivity of solids (table), 1009–1010 thermal conductivity of, 71–72, 76–77 thermophysical properties of solids, 987–988 Nonparticipating media, 862 Nonstationary media: absolute and diffusive species fluxes, 939–942 evaporation in column, 942–947 Nuclear component, of internal energy, 15 Nucleate boiling, 658–659, 660–664 Number of transfer units (NTU), 723–725 Nusselt number, 401, 409 O Ohmic heating, 143 One-dimensional steady-state conduction, 111–193 alternative analysis approach, 132–135, 141–142 bioheat equation, 178–182 extended surfaces and, see Extended surface(s), heat transfer from micro- and nanoscale effects, 189–190 in plane wall systems composite walls, 115–117 contact resistance in, 117–119, 120 temperature distribution, 112–114 with thermal energy generation, 143–149 thermal resistance in, 114–115, 708–709 within porous media, 119–125 in radial systems, 136–142 cylinders, 136–141 spheres, 141–142 with thermal energy generation, 149–150 summary solutions (table), 143 temperature distribution in, 4–5, 85 with thermal energy generation, 142–154 in plane wall systems, 143–149 in radial systems, 149–154 thermal conditions with uniform generation, 1019–1024 and thermoelectric power generation, 182–188 uniform generation thermal conditions, 1019–1024 Opaque media, 772, 781–782, 805–806 Open systems, 13–17 Ordinary diffusion, 937 Orthogonal functions, 233–234 Overall heat transfer coefficient, 116, 137–138 and heat exchangers, 708–711 Overall surface efficiency, 170–178, 709–710 P Packed bed(s): definition of, 119 heat and mass transfer (convection) through, 482–483 Parallel-flow heat exchangers, 706–707, 712–714, 723–727 Parallel plates, free convection with, 618–621 Parameter sensitivity study, 38 Participating media, 862 radiation exchange with, 896–901 Peclet number, 409 Peltier effect, 183–184 Penetration depth: concentration, 970 thermal, 314 Pennes equation, 178–182 Perfusion, and bioheat equation, 178–182 Phase change, 7, 15 convection coefficients, typical (table), Phonons, 71–75 Photons, 769 Pin fins, 155–156 Pitch (tubes), 468–469 Planck constant, 783 Planck distribution, 783–784 Planck’s law, 783–784, 827 Plane angle, 773 Plane wall systems: one-dimensional steady-state conduction in, 112–132 composite walls, 115–117 contact resistance in, 117–119, 120 temperature distribution, 112–114 with thermal energy generation, 143–149, 1019–1024 thermal resistance in, 114–115, 708–709 within porous media, 119–121 shape factors for, W3–W4, 236 transient conduction in, 283–286, 298–303, 318–323 approximate solution, 300–301, 318–323 with convection, 299–303 exact solution, 300 graphical representation of, W12–W13 roots of transcendental equation for, 1016 summary (table), 321–322 www.elsolucionario.net bindex.qxd 2/25/11 1046 6:21 AM ᭿ Page 1046 Index Plumes, 595–596 Pool boiling, 655, 656–669 boiling curve and, 656–657 critical heat flux, 658, 659, 662–663 film boiling, 658, 660, 663–664 free convection boiling, 657–658 Leidenfrost point, 660 minimum heat flux, 658, 660, 663 nucleate boiling, 658–659, 660–663 parametric effects on, 664–665 transition boiling, 658, 659–660 Porosity, 483 Porous media, conduction in, 119–121 Power-controlled heating, 656–657 Prandtl number, 398–399, 407–409 Problems, methodology for analysis, 38 Q Quality of fluid, 671 Quanta, 769 Quasi-steady approximation, 616 Quenching, 283 Quiescent fluid(s), 596, 596n R Radial systems: film condensation in, 684–688 one-dimensional steady-state conduction in, 136–142 cylinders, 136–141 spheres, 141–142 with thermal energy generation, 149–154 transient conduction in, 303–310, 318–322 Radiation See also Radiation exchange and absorptivity, 802–803 blackbody, see Blackbody radiation emission from real surfaces, 792–800 environmental, see Environmental radiation gaseous, 896–901 gray surface, see Gray surfaces heat fluxes, 771–772 intensity, 773–782 definitions in, 773–774 and emission, 774–779 and irradiation, 779–781 and net radiative flux, 782 and radiosity, 781–782 and Kirchhoff’s law, 810–811 nature and properties of, 768–770 rate equation, 10, 46 and reflectivity, 803–804 surface characteristics considerations, 805–806 in surface energy balance, 27–30 terminology glossary (table), 827–828 thermal, see Thermal radiation and transmissivity, 805 Radiation balance (atmospheric), 821–823 Radiation exchange, 861–902 between diffuse gray surfaces (enclosed), 876–893 net radiation exchange, 877–878 radiation shields, 886 reradiating surfaces, 888–893 surface radiation exchanges, 878–880 two-surface enclosures, 884–885 blackbody radiation, 872–876 gaseous, 896–901 emission and absorption, 897–901 volumetric absorption, 896–897 and multimode heat transfer, 893–895 view factors in, 862–872 definition, 862 for two-dimensional geometries (table), 865–867 view factor integral, 862–863 view factor relations, 863–870 Radiation heat transfer coefficient, 10 Radiation intensity, see Radiation, intensity Radiative resistance, 877–879 Radiosity, 771–772, 781–782 Raoult’s law, 955 Rate equations: for conduction, 4–5 for convection, for radiation heat transfer, 10 summary (table), 46 Rayleigh number, 603 Rayleigh scattering, 821 Reaction-limited processes, 962 Reciprocity relation, 863 Rectangular cavities, free convection in, 621–624 Reflection, 558–559, 801–802 and reflectivity, 772 Reflectivity, 803–804 Reradiating surfaces, 888–893 Resistance: constriction, 690 contact, 117–119, 120 fin, 165 radiative, 877–879 thermal, 12, 114–115, 137, 142 Resistance heating, see Ohmic heating Reynolds analogy, 416–417 Reynolds number, 390, 398–399, 407–409 Reynolds stress, 1033 S Saturated boiling, 655, 656, 671 Saturated porous media, 119–120 Schmidt number, 398–399, 407–409 Second law of thermodynamics, 31–36 Seebeck effect and coefficient, 182–188 Semi-infinite solid(s): transient conduction in, 310–318, 319 solutions summarized, 313–314 Semitransparent media, 771, 805–806 Sensible energy, 7, 15, 84 Separation of variables, method, 231–235, 299 Separation point(s), 455 Shape factor(s): conduction, W3–W5, 235–240 view factor, 862–872 Shear stresses, 379 Shell-and-tube heat exchangers, W40–W44, 707, 723–727 Sherwood number, 402, 409 Shields, radiation, 886–888 SI (Système International d’Unités) system, 36–38 Similarity solution(s), 438, 600 Similarity variable(s), 311, 438 Simplified steady-flow thermal energy equation, 17 Sinks (energy), 16, 84, 183–184 www.elsolucionario.net bindex.qxd 2/25/11 6:21 AM Page 1047 ᭿ 1047 Index Solar radiation, 818–824 properties for selected materials (table), 1010 representative values for surfaces (table), 824 Solid angle, 773 Solidification, 15 Solid(s): conduction in, 3–5, 118–119, 190 gas solubility in, 955–960 mass diffusion in, 935 radiation from, 9–12, 768–769 semi-infinite, see Semi-infinite solid(s) solubility of (table), 1007 thermal conductivity of, 71–75 micro- and nanoscale effects, 72–75, 190 Solubility: of gases in liquids and solids, 955–960 of selected gases and solids (table), 1007 Species: characteristics of, 934–936 concentration in mass transfer, 563–565 conservation of, see Conservation of species Species fluxes, 939–942 Specific heat, 78 Spectral absorptivity, 802 Spectral emission, 775 Spectral emissivity, 793 Spectral intensity, 774–775 Spectral irradiation, 779, 801 Spectral radiosity, 781–782 Spectral reflectivity, 804 Sphere(s): dimensionless conduction heat rate for, 238 film condensation on, 684 free convection with, 617–618 concentric spheres, 625–626 heat and mass transfer (convection) from, 465–468 one-dimensional steady-state conduction in, 141–142, 1019–1024 shape factors for, 236–238 transient conduction in, 300–301, 303–305, 308–310, 318–320 graphical representation of, W12, W15–W16 summary (table), 321–322 Stagnation point(s), 455 Stagnation zone(s), 477–478 Stanton number, 409, 416–417 Stationary media: diffusion approximation for, 947 mass diffusion in, 947–954 with specified surface concentrations, 950–954 Steady-state conditions, 4, 14, 16, 112 Stefan-Boltzmann constant, Stefan-Boltzmann law, 9, 784–785 Stokes’ law, 465 Straight fins, 155–156, 166 Stratification parameter, 672 Streaks, 389 Stresses: shear, 379 viscous, W26–W29, 1029 Structural building materials, thermophysical properties of (table), 989 Subcooled boiling, 655, 664–665, 670–671 Sublimation, mass transfer and, 563–565, 955 Summation rule, 864 Surface energy balance, 27–30 Surface forces, W26–W29, 1029 Surface friction, and boundary layers, 382 Surface phenomena, 16 radiation as, 769, 801–802 Surface roughness, 665 Surface tension, 654, 655 Surface(s): radiation exchange between gray, 876–893 surface energy balance, 27–30 Surroundings, 9–10 T Temperature: conduction and, 2–5 and efficiency, 32–33 excess, 158, 655 film, 414, 436 mean, of internal flow, 524–525 scales, 37 units for, 36–37 Temperature distribution, 82 during thermal treatment, 45 one-dimensional steady-state conduction, 4–5, 112–114 two-dimensional steady-state conduction, 230–231, 231–232, 242–243 Thermal accommodation coefficient, 189–190, 380n Thermal boundary layer, 6, 379–380, 382 and laminar or turbulent flow, 391–393 Thermal circuits, 112–117, 171–172 Thermal conductivity, 70–78 bulk solid, 72 conduction and, 4–5 effective, 119–121 of fluids, 75–78 and Fourier’s law, 68–70 of insulation systems, 77–78 of porous media, 119–121 of solids, 71–75 Thermal contact resistance, 117–119, 120, 171–172 Thermal diffusivity, 78–80, 85 Thermal energy, components of, 15 Thermal energy equation, W31 Thermal energy generation: conduction with, 142–154, 1019–1024 bioheat, 178–182 in plane wall systems, 143–149 in radial systems, 149–154 Thermal entry length, 542–544 Thermal penetration depth, 314 Thermal radiation, 8–12 and boiling, 663–664 definition of, 2, 769–770 emission of, 768–770 resistance for, 115 Thermal resistance, 12, 114–115, 137–142 fouling factor, 709 in plane wall systems, 114–117, 708–709 thermal contact resistance, 117–119, 120 Thermal time constant, 282 Thermodynamic properties, 78–82 Thermodynamics, heat transfer vs., 12–13 Thermoelectric power generation, 182–188 Thermophysical properties, 78–82, 981–1010 of common materials (table), 989–994 industrial insulation, 991–992 www.elsolucionario.net bindex.qxd 2/25/11 1048 6:21 AM ᭿ Page 1048 Index Thermophysical properties (continued) insulating materials/systems, 990 structural building materials, 989 of gases at atmospheric pressure (table), 995–999 of liquid metals (table), 1005 of saturated fluids (table), 1000–1002 of saturated water (table), 1003–1004 of selected metallic solids (table), 983–986 of selected nonmetallic solids (table), 987–988 of thermoelectric modules, 183–186 Thermoregulation, 28–30, 44–45, 121–125 Time, units for, 36–37 Transient conduction, 279–346 coefficients for one-dimensional conduction (table), 301 finite-difference methods for explicit method of discretization of the heat equation, 330–337 implicit method of discretization of the heat equation, 337–345 graphical representation of, W12–W22 lumped capacitance method, 280–297 multidimensional effects with, W16–W22 roots of transcendental equation (plane wall), 1016 objects with constant surface heat flux, 319–320, 322 objects with constant surface temperature, 317–319, 321 periodic heating, 327–330 plane wall with convection, 299–303 solutions for, W12–W13, 300–301 radial systems with convection, 303–310 solutions for, W14–W16, 303–304 in semi-infinite solids, 310–317 solutions summarized, 313–314 spatial effects, 298–299 Transient diffusion, 965–971 Transition boiling, 658, 659–660 Transition to turbulence, 389–391 Transmissivity, 771–772, 805 Transport properties, 70, 78–79 Transverse pitch, 468–469 Triangular fins, 168–170 Tubes See also Heat exchangers arrangements of, 468–470 banks, 468–477 boiling in, 672–673 boiling on, 664 circular convection correlations (table), 567 laminar flow in, 537–544 turbulent flow in, 544–552 concentric tube annulus, 553–555 condensation in, 689–690 condensation on, 684–688 in cross flow, 468–476 configurations, 468–469 flow conditions, 468–470 noncircular, 552–555 rough vs smooth, 545–546 Turbulent boundary layer, 389–391, 602 Turbulent film condensation, 679–683 Turbulent flow: and boundary layers, 389–393, 602–604, 1031–1033 in circular tubes, 544–552 across cylinders, 455–459 over flat plate, 443 Two-dimensional steady flow, heat and mass transfer in, W25–W36, 1027–1030 Two-dimensional steady-state conduction, 229–257 alternative approaches to, 230–231 conduction shape factors in, W3–W5, 235–240 dimensionless conduction heat rate in, 235–240 finite-difference method for, 241–256 solving, 250–256 graphical method for conduction shape factors, W3–W5 flux-plot construction, W1–W2 heat transfer rate determination, W2–W3 separation of variables method with, 231–235 Two-phase flow, forced convection boiling, 670–673 U Unheated starting length, 445 Unit mass, in flow work, 16 Units: derived, 37 English system, 36 SI system, 36–38 Unsaturated porous media, 119 V Vapor blanket, 660, 663 Vaporization, 15 Velocity boundary layer, 378–379, 382 and laminar or turbulent flow, 389–391 Velocity profile, boundary layer, 379 Velocity profile(s), for internal flow, 519–522 View factor(s), 862–872 definition of, 862 integral, 862–863 for two-dimensional geometries (table), 865–867 view factor relations, 863–870 Viscosity: dynamic, 80, 379 kinematic, 78 Viscous dissipation, 17, W31, 396, 1029 Viscous fluids, heat and mass transfer in, W25–W36, 1027–1030 Viscous stresses, W26–W29, 1029 Void fraction, 483 Volumetric flow rate, 17 Volumetric heat capacity, 78 Volumetric phenomena, 15–16 radiation, 768–769, 801, 896–901 Volumetric thermal expansion coefficient, 597 W Wall jet(s), 477–478 Water, thermophysical properties of (saturated), 1003–1004 Weber number, 409, 670 Wien’s displacement law, 784 Z Zenith angle, 774, 819 Zero-order chemical reactions, 962–963 www.elsolucionario.net BMConversionFactors.qxd 2/21/11 6:07 PM Page Conversion Factors Acceleration Area m/s2 m2 Density Energy Force Heat transfer rate Heat flux Heat generation rate Heat transfer coefficient Kinematic viscosity and diffusivities Latent heat Length kg/m3 J (0.2388 cal) 1N 1W W/m2 W/m3 W/m2 • K ϭ 4.2520 ϫ 107 ft/h2 ϭ 1550.0 in.2 ϭ 10.764 ft2 ϭ 0.06243 lbm/ft3 ϭ 9.4782 ϫ 10Ϫ4 Btu ϭ 0.22481 lbf ϭ 3.4121 Btu/h ϭ 0.3170 Btu/h • ft2 ϭ 0.09662 Btu/h • ft3 ϭ 0.17611 Btu/h • ft2 • ЊF m2/s ϭ 3.875 ϫ 104 ft2/h J/kg 1m ϭ 4.2992 ϫ 10Ϫ4 Btu/lbm ϭ 39.370 in ϭ 3.2808 ft ϭ 0.62137 mile ϭ 2.2046 lbm ϭ 0.06243 lbm/ft3 ϭ 7936.6 lbm/h ϭ 1.1811 ϫ 104 ft/h Mass Mass density Mass flow rate Mass transfer coefficient Power km kg kg/m3 kg/s m/s kW Pressure and stress1 N/m2 (1 Pa) Specific heat Temperature 1.0133 ϫ 105 N/m2 ϫ 105 N/m2 kJ/kg •K K Temperature difference 1K Thermal conductivity Thermal resistance Viscosity (dynamic)2 W/m • K K/W N • s/m2 Volume m3 Volume flow rate m3/s ϭ 3412.1 Btu/h ϭ 1.341 hp ϭ 0.020885 lbf /ft2 ϭ 1.4504 ϫ 10Ϫ4 lbf /in.2 ϭ 4.015 ϫ 10Ϫ3 in water ϭ 2.953 ϫ 10Ϫ4 in Hg ϭ standard atmosphere ϭ bar ϭ 0.2388 Btu/lbm • ЊF ϭ (5/9)ЊR ϭ (5/9)(ЊF ϩ 459.67) ϭ ЊC ϩ 273.15 ϭ 1ЊC ϭ (9/5)ЊR ϭ (9/5)°F ϭ 0.57779 Btu/h • ft • ЊF ϭ 0.52753 ЊF/h • Btu ϭ 2419.1 lbm/ft • h ϭ 5.8015 ϫ 10Ϫ6 lbf • h/ft2 ϭ 6.1023 ϫ 104 in.3 ϭ 35.315 ft3 ϭ 264.17 gal (U.S.) ϭ 1.2713 ϫ 105 ft3/h ϭ 2.1189 ϫ 103 ft3/min ϭ 1.5850 ϫ 104 gal/min The SI name for the quantity pressure is pascal (Pa) having units N/m2 or kg/m • s2 Also expressed in equivalent units of kg/s • m www.elsolucionario.net BMPhysicalConstants.qxd 2/21/11 6:08 PM Page Physical Constants Universal Gas Constant: ᏾ ϭ 8.205 ϫ 10Ϫ2 m3 • atm/kmol • K ϭ 8.314 ϫ 10Ϫ2 m3• bar/kmol • K ϭ 8.315 kJ/kmol • K ϭ 1545 ft• lbf /lbmole • °R ϭ 1.986 Btu/lbmole • °R Avogadro’s Number: ᏺ ϭ 6.022 ϫ 1023 molecules/mol Planck’s Constant: h ϭ 6.626 ϫ 10Ϫ34 J • s Boltzmann’s Constant: kB ϭ 1.381 ϫ 10Ϫ23 J/K Speed of Light in Vacuum: co ϭ 2.998 ϫ 108 m/s Stefan-Boltzmann Constant: ␴ ϭ 5.670 ϫ 10Ϫ8 W/m2 • K4 Blackbody Radiation Constants: C1 ϭ 3.742 ϫ 108 W • ␮m4/m2 C2 ϭ 1.439 ϫ 104 ␮m • K C3 ϭ 2898 ␮m • K Solar Constant: Sc ϭ 1368 W/m2 Gravitational Acceleration (Sea Level): g ϭ 9.807 m/s2 ϭ 32.174 ft/s2 Standard Atmospheric Pressure: p ϭ 101,325 N/m2 ϭ 101.3 kPa Heat of Fusion of Water at Atmospheric Pressure: hsf ϭ 333.7 kJ/kg Heat of Vaporization of Water at Atmospheric Pressure: hfg ϭ 2257 kJ/kg www.elsolucionario.net ... constant, J ⅐ s latent heat of vaporization, J/kg modified heat of vaporization, J/kg latent heat of fusion, J/kg convection mass transfer coefficient, m/s radiation heat transfer coefficient,... pressure, N/m2 energy transfer, J heat transfer rate, W rate of energy generation per unit volume, W/m3 heat transfer rate per unit length, W/m heat flux, W/m2 dimensionless conduction heat rate cylinder... is heat transfer? Heat transfer (or heat) is thermal energy in transit due to a spatial temperature difference Whenever a temperature difference exists in a medium or between media, heat transfer