Heat and mass transfer

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This comprehensive presentation of the whole field of heat and mass transfer makes the reader familar with the fundamentals and enables him to solve practical problems. The basic theory is developed systematically, and the solution methods to all important problems are covered in detail. Therefore, this book will be useful not only to students, but likewise to scientists and practising engineers. All areas of heat and mass transfer are dealt with. Many calculated examples in the text and numerous exercises and elaborate solutions will facilitate learning and understanding.For the second edition, changes apply to heat and mass transfer correlations based on theoretical results or experimental findings. They were adapted to the state-of -the-art. Some of the worked examples as well as the compilation were revised or updated.

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This new edition (1st ed., 1998) by Baehr (Univ. of Hannover, Germany) and Stephan (Univ. of Stuttgart, Germany), translated from German, presents the classic, basic theoretical background for heat and mass transport operations. Most of the book is concerned with fundamentals, as opposed to applications to industrial equipment, and the bulk of the material concerns heat transfer, with a lesser emphasis on mass transport. For example, chapter 1 includes a limited treatment of heat exchanger design; only about six pages are devoted to mass transfer equipment design. The book has five chapters, each with a selection of exercises at the end for the student and a number of worked examples. Chapter 1 discusses technical applications; chapter 2, heat conduction and diffusion; chapter 3, convective heat and mass flow--single phase; chapter 4, convective heat and mass transfer with phase change; and chapter 5, thermal radiation. Three appendixes are included, with material on theoretical supplements, property data, and exercise solutions. There is a list of notations and an extensive list of references. The approach is traditional and classical, and is intended for advanced students of mechanical and chemical engineering. ^BSumming Up: Recommended. Upper-division undergraduates through professionals. R. Darby emeritus, Texas A&M University

Nomenclature	p. xvi
1 Introduction. Technical Applications	p. 1
1.1 The different types of heat transfer	p. 1
1.1.1 Heat conduction	p. 2
1.1.2 Steady, one-dimensional conduction of heat	p. 5
1.1.3 Convective heat transfer. Heat transfer coefficient	p. 10
1.1.4 Determining heat transfer coefficients. Dimensionless numbers	p. 15
1.1.5 Thermal radiation	p. 25
1.1.6 Radiative exchange	p. 27
1.2 Overall heat transfer	p. 30
1.2.1 The overall heat transfer coefficient	p. 30
1.2.2 Multi-layer walls	p. 32
1.2.3 Overall heat transfer through walls with extended surfaces	p. 33
1.2.4 Heating and cooling of thin walled vessels	p. 37
1.3 Heat exchangers	p. 40
1.3.1 Types of heat exchanger and flow configurations	p. 40
1.3.2 General design equations. Dimensionless groups	p. 44
1.3.3 Countercurrent and cocurrent heat exchangers	p. 49
1.3.4 Crossflow heat exchangers	p. 56
1.3.5 Operating characteristics of further flow configurations. Diagrams	p. 63
1.4 The different types of mass transfer	p. 64
1.4.1 Diffusion	p. 66
1.4.1.1 Composition of mixtures	p. 66
1.4.1.2 Diffusive fluxes	p. 67
1.4.1.3 Fick's law	p. 70
1.4.2 Diffusion through a semipermeable plane. Equimolar diffusion	p. 72
1.4.3 Convective mass transfer	p. 76
1.5 Mass transfer theories	p. 80
1.5.1 Film theory	p. 80
1.5.2 Boundary layer theory	p. 84
1.5.3 Penetration and surface renewal theories	p. 86
1.5.4 Application of film theory to evaporative cooling	p. 87
1.6 Overall mass transfer	p. 91
1.7 Mass transfer apparatus	p. 93
1.7.1 Material balances	p. 94
1.7.2 Concentration profiles and heights of mass transfer columns	p. 97
1.8 Exercises	p. 101
2 Heat conduction and mass diffusion	p. 105
2.1 The heat conduction equation	p. 105
2.1.1 Derivation of the differential equation for the temperature field	p. 106
2.1.2 The heat conduction equation for bodies with constant material properties	p. 109
2.1.3 Boundary conditions	p. 111
2.1.4 Temperature dependent material properties	p. 114
2.1.5 Similar temperature fields	p. 115
2.2 Steady-state heat conduction	p. 119
2.2.1 Geometric one-dimensional heat conduction with heat sources	p. 119
2.2.2 Longitudinal heat conduction in a rod	p. 122
2.2.3 The temperature distribution in fins and pins	p. 127
2.2.4 Fin efficiency	p. 131
2.2.5 Geometric multi-dimensional heat flow	p. 134
2.2.5.1 Superposition of heat sources and heat sinks	p. 135
2.2.5.2 Shape factors	p. 139
2.3 Transient heat conduction	p. 140
2.3.1 Solution methods	p. 141
2.3.2 The Laplace transformation	p. 142
2.3.3 The semi-infinite solid	p. 149
2.3.3.1 Heating and cooling with different boundary conditions	p. 149
2.3.3.2 Two semi-infinite bodies in contact with each other	p. 154
2.3.3.3 Periodic temperature variations	p. 156
2.3.4 Cooling or heating of simple bodies in one-dimensional heat flow	p. 159
2.3.4.1 Formulation of the problem	p. 159
2.3.4.2 Separating the variables	p. 161
2.3.4.3 Results for the plate	p. 163
2.3.4.4 Results for the cylinder and the sphere	p. 167
2.3.4.5 Approximation for large times: Restriction to the first term in the series	p. 169
2.3.4.6 A solution for small times	p. 171
2.3.5 Cooling and heating in multi-dimensional heat flow	p. 172
2.3.5.1 Product solutions	p. 172
2.3.5.2 Approximation for small Biot numbers	p. 175
2.3.6 Solidification of geometrically simple bodies	p. 177
2.3.6.1 The solidification of flat layers (Stefan problem)	p. 178
2.3.6.2 The quasi-steady approximation	p. 181
2.3.6.3 Improved approximations	p. 184
2.3.7 Heat sources	p. 185
2.3.7.1 Homogeneous heat sources	p. 186
2.3.7.2 Point and linear heat sources	p. 187
2.4 Numerical solutions to heat conduction problems	p. 192
2.4.1 The simple, explicit difference method for transient heat conduction problems	p. 193
2.4.1.1 The finite difference equation	p. 193
2.4.1.2 The stability condition	p. 195
2.4.1.3 Heat sources	p. 196
2.4.2 Discretisation of the boundary conditions	p. 197
2.4.3 The implicit difference method from J. Crank and P. Nicolson	p. 203
2.4.4 Noncartesian coordinates. Temperature dependent material properties	p. 206
2.4.4.1 The discretisation of the self-adjoint differential operator	p. 207
2.4.4.2 Constant material properties. Cylindrical coordinates	p. 208
2.4.4.3 Temperature dependent material properties	p. 209
2.4.5 Transient two- and three-dimensional temperature fields	p. 211
2.4.6 Steady-state temperature fields	p. 214
2.4.6.1 A simple finite difference method for plane, steady-state temperature fields	p. 214
2.4.6.2 Consideration of the boundary conditions	p. 217
2.5 Mass diffusion	p. 222
2.5.1 Remarks on quiescent systems	p. 222
2.5.2 Derivation of the differential equation for the concentration field	p. 225
2.5.3 Simplifications	p. 230
2.5.4 Boundary conditions	p. 231
2.5.5 Steady-state mass diffusion with catalytic surface reaction	p. 234
2.5.6 Steady-state mass diffusion with homogeneous chemical reaction	p. 238
2.5.7 Transient mass diffusion	p. 242
2.5.7.1 Transient mass diffusion in a semi-infinite solid	p. 243
2.5.7.2 Transient mass diffusion in bodies of simple geometry with one-dimensional mass flow	p. 244
2.6 Exercises	p. 246
3 Convective heat and mass transfer. Single phase flow	p. 253
3.1 Preliminary remarks: Longitudinal, frictionless flow over a flat plate	p. 253
3.2 The balance equations	p. 258
3.2.1 Reynolds' transport theorem	p. 258
3.2.2 The mass balance	p. 260
3.2.2.1 Pure substances	p. 260
3.2.2.2 Multicomponent mixtures	p. 261
3.2.3 The momentum balance	p. 264
3.2.3.1 The stress tensor	p. 266
3.2.3.2 Cauchy's equation of motion	p. 269
3.2.3.3 The strain tensor	p. 270
3.2.3.4 Constitutive equations for the solution of the momentum equation	p. 272
3.2.3.5 The Navier-Stokes equations	p. 273
3.2.4 The energy balance	p. 274
3.2.4.1 Dissipated energy and entropy	p. 279
3.2.4.2 Constitutive equations for the solution of the energy equation	p. 281
3.2.4.3 Some other formulations of the energy equation	p. 282
3.2.5 Summary	p. 285
3.3 Influence of the Reynolds number on the flow	p. 287
3.4 Simplifications to the Navier-Stokes equations	p. 290
3.4.1 Creeping flows	p. 290
3.4.2 Frictionless flows	p. 291
3.4.3 Boundary layer flows	p. 291
3.5 The boundary layer equations	p. 293
3.5.1 The velocity boundary layer	p. 293
3.5.2 The thermal boundary layer	p. 296
3.5.3 The concentration boundary layer	p. 300
3.5.4 General comments on the solution of boundary layer equations	p. 300
3.6 Influence of turbulence on heat and mass transfer	p. 304
3.6.1 Turbulent flows near solid walls	p. 308
3.7 External forced flow	p. 312
3.7.1 Parallel flow along a flat plate	p. 313
3.7.1.1 Laminar boundary layer	p. 313
3.7.1.2 Turbulent flow	p. 325
3.7.2 The cylinder in crossflow	p. 330
3.7.3 Tube bundles in crossflow	p. 334
3.7.4 Some empirical equations for heat and mass transfer in external forced flow	p. 338
3.8 Internal forced flow	p. 341
3.8.1 Laminar flow in circular tubes	p. 341
3.8.1.1 Hydrodynamic, fully developed, laminar flow	p. 342
3.8.1.2 Thermal, fully developed, laminar flow	p. 344
3.8.1.3 Heat transfer coefficients in thermally fully developed, laminar flow	p. 346
3.8.1.4 The thermal entry flow with fully developed velocity profile	p. 349
3.8.1.5 Thermally and hydrodynamically developing flow	p. 354
3.8.2 Turbulent flow in circular tubes	p. 355
3.8.3 Packed beds	p. 357
3.8.4 Fluidised beds	p. 361
3.8.5 Some empirical equations for heat and mass transfer in flow through channels, packed and fluidised beds	p. 370
3.9 Free flow	p. 373
3.9.1 The momentum equation	p. 376
3.9.2 Heat transfer in laminar flow on a vertical wall	p. 379
3.9.3 Some empirical equations for heat transfer in free flow	p. 384
3.9.4 Mass transfer in free flow	p. 386
3.10 Overlapping of free and forced flow	p. 387
3.11 Compressible flows	p. 389
3.11.1 The temperature field in a compressible flow	p. 389
3.11.2 Calculation of heat transfer	p. 396
3.12 Exercises	p. 399
4 Convective heat and mass transfer. Flows with phase change	p. 405
4.1 Heat transfer in condensation	p. 405
4.1.1 The different types of condensation	p. 406
4.1.2 Nusselt's film condensation theory	p. 408
4.1.3 Deviations from Nusselt's film condensation theory	p. 412
4.1.4 Influence of non-condensable gases	p. 416
4.1.5 Film condensation in a turbulent film	p. 422
4.1.6 Condensation of flowing vapours	p. 426
4.1.7 Dropwise condensation	p. 431
4.1.8 Condensation of vapour mixtures	p. 435
4.1.8.1 The temperature at the phase interface	p. 439
4.1.8.2 The material and energy balance for the vapour	p. 443
4.1.8.3 Calculating the size of a condenser	p. 445
4.1.9 Some empirical equations	p. 446
4.2 Heat transfer in boiling	p. 448
4.2.1 The different types of heat transfer	p. 449
4.2.2 The formation of vapour bubbles	p. 453
4.2.3 Bubble frequency and departure diameter	p. 456
4.2.4 Boiling in free flow. The Nukijama curve	p. 460
4.2.5 Stability during boiling in free flow	p. 461
4.2.6 Calculation of heat transfer coefficients for boiling in free flow	p. 465
4.2.7 Some empirical equations for heat transfer during nucleate boiling in free flow	p. 468
4.2.8 Two-phase flow	p. 472
4.2.8.1 The different flow patterns	p. 473
4.2.8.2 Flow maps	p. 475
4.2.8.3 Some basic terms and definitions	p. 476
4.2.8.4 Pressure drop in two-phase flow	p. 479
4.2.8.5 The different heat transfer regions in two-phase flow	p. 487
4.2.8.6 Heat transfer in nucleate boiling and convective evaporation	p. 489
4.2.8.7 Critical boiling states	p. 489
4.2.8.8 Some empirical equations for heat transfer in two-phase flow	p. 495
4.2.9 Heat transfer in boiling mixtures	p. 496
4.3 Exercises	p. 501
5 Thermal radiation	p. 503
5.1 Fundamentals. Physical quantities	p. 503
5.1.1 Thermal radiation	p. 504
5.1.2 Emission of radiation	p. 506
5.1.2.1 Emissive power	p. 506
5.1.2.2 Spectral intensity	p. 507
5.1.2.3 Hemispherical spectral emissive power and total intensity	p. 509
5.1.2.4 Diffuse radiators. Lambert's cosine law	p. 513
5.1.3 Irradiation	p. 514
5.1.4 Absorption of radiation	p. 517
5.1.5 Reflection of radiation	p. 522
5.1.6 Radiation in an enclosure. Kirchhoff's law	p. 524
5.2 Radiation from a black body	p. 527
5.2.1 Definition and realisation of a black body	p. 527
5.2.2 The spectral intensity and the spectral emissive power	p. 528
5.2.3 The emissive power and the emission of radiation in a wavelength interval	p. 532
5.3 Radiation properties of real bodies	p. 537
5.3.1 Emissivities	p. 537
5.3.2 The relationships between emissivity, absorptivity and reflectivity. The grey Lambert radiator	p. 540
5.3.2.1 Conclusions from Kirchhoff's law	p. 540
5.3.2.2 Calculation of absorptivities from emissivities	p. 541
5.3.2.3 The grey Lambert radiator	p. 542
5.3.3 Emissivities of real bodies	p. 544
5.3.3.1 Electrical insulators	p. 545
5.3.3.2 Electrical conductors (metals)	p. 548
5.3.4 Transparent bodies	p. 550
5.4 Solar radiation	p. 555
5.4.1 Extraterrestrial solar radiation	p. 555
5.4.2 The attenuation of solar radiation in the earth's atmosphere	p. 558
5.4.2.1 Spectral transmissivity	p. 558
5.4.2.2 Molecular and aerosol scattering	p. 561
5.4.2.3 Absorption	p. 562
5.4.3 Direct solar radiation on the ground	p. 564
5.4.4 Diffuse solar radiation and global radiation	p. 566
5.4.5 Absorptivities for solar radiation	p. 568
5.5 Radiative exchange	p. 569
5.5.1 View factors	p. 570
5.5.2 Radiative exchange between black bodies	p. 576
5.5.3 Radiative exchange between grey Lambert radiators	p. 579
5.5.3.1 The balance equations according to the net-radiation method	p. 580
5.5.3.2 Radiative exchange between a radiation source, a radiation receiver and a reradiating wall	p. 581
5.5.3.3 Radiative exchange in a hollow enclosure with two zones	p. 585
5.5.3.4 The equation system for the radiative exchange between any number of zones	p. 587
5.5.4 Protective radiation shields	p. 590
5.6 Gas radiation	p. 594
5.6.1 Absorption coefficient and optical thickness	p. 595
5.6.2 Absorptivity and emissivity	p. 597
5.6.3 Results for the emissivity	p. 600
5.6.4 Emissivities and mean beam lengths of gas spaces	p. 603
5.6.5 Radiative exchange in a gas filled enclosure	p. 607
5.6.5.1 Black, isothermal boundary walls	p. 607
5.6.5.2 Grey isothermal boundary walls	p. 608
5.6.5.3 Calculation of the radiative exchange in complicated cases	p. 611
5.7 Exercises	p. 612
Appendix A Supplements	p. 617
A.1 Introduction to tensor notation	p. 617
A.2 Relationship between mean and thermodynamic pressure	p. 619
A.3 Navier-Stokes equations for an incompressible fluid of constant viscosity in cartesian coordinates	p. 620
A.4 Navier-Stokes equations for an incompressible fluid of constant viscosity in cylindrical coordinates	p. 621
A.5 Entropy balance for mixtures	p. 622
A.6 Relationship between partial and specific enthalpy	p. 623
A.7 Calculation of the constants a[subscript n] of a Graetz-Nusselt problem (3.246)	p. 624
Appendix B Property data	p. 626
Appendix C Solutions to the exercises	p. 640
Literature	p. 654
Index	p. 671

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