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 |  موضوع: كتاب Heat and Mass Transfer - Second, revised Edition الجمعة 29 سبتمبر 2017, 5:54 pm | |
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Heat and Mass Transfer - Second, revised Edition
Hans Dieter Baehr · Karl Stephan
ويتناول الموضوعات الأتية :
Contents
Nomenclature xvi
1 Introduction. Technical Applications 1
1.1 The different types of heat transfer 1
1.1.1 Heat conduction 2
1.1.2 Steady, one-dimensional conduction of heat . 5
1.1.3 Convective heat transfer. Heat transfer coefficient . 10
1.1.4 Determining heat transfer coefficients. Dimensionless numbers 15
1.1.5 Thermal radiation . 25
1.1.6 Radiative exchange 27
1.2 Overall heat transfer 30
1.2.1 The overall heat transfer coefficient . 30
1.2.2 Multi-layer walls 32
1.2.3 Overall heat transfer through walls with extended surfaces 33
1.2.4 Heating and cooling of thin walled vessels 37
1.3 Heat exchangers 40
1.3.1 Types of heat exchanger and flow configurations 40
1.3.2 General design equations. Dimensionless groups 44
1.3.3 Countercurrent and cocurrent heat exchangers . 49
1.3.4 Crossflow heat exchangers . 56
1.3.5 Operating characteristics of further flow configurations. Diagrams 63
1.4 The different types of mass transfer . 64
1.4.1 Diffusion 66
1.4.1.1 Composition of mixtures . 66
1.4.1.2 Diffusive fluxes 67
1.4.1.3 Fick’s law . 70
1.4.2 Diffusion through a semipermeable plane. Equimolar diffusion 72
1.4.3 Convective mass transfer . 76
1.5 Mass transfer theories . 80
1.5.1 Film theory . 80
1.5.2 Boundary layer theory . 84
1.5.3 Penetration and surface renewal theories 86
1.5.4 Application of film theory to evaporative cooling 87x Contents
1.6 Overall mass transfer . 91
1.7 Mass transfer apparatus 93
1.7.1 Material balances . 94
1.7.2 Concentration profiles and heights of mass transfer columns 97
1.8 Exercises 101
2 Heat conduction and mass diffusion 105
2.1 The heat conduction equation 105
2.1.1 Derivation of the differential equation for the temperature field 106
2.1.2 The heat conduction equation for bodies with constant
material properties . 109
2.1.3 Boundary conditions 111
2.1.4 Temperature dependent material properties . 114
2.1.5 Similar temperature fields . 115
2.2 Steady-state heat conduction . 119
2.2.1 Geometric one-dimensional heat conduction with heat sources 119
2.2.2 Longitudinal heat conduction in a rod 122
2.2.3 The temperature distribution in fins and pins 127
2.2.4 Fin efficiency 131
2.2.5 Geometric multi-dimensional heat flow 134
2.2.5.1 Superposition of heat sources and heat sinks 135
2.2.5.2 Shape factors . 139
2.3 Transient heat conduction . 140
2.3.1 Solution methods . 141
2.3.2 The Laplace transformation 142
2.3.3 The semi-infinite solid . 149
2.3.3.1 Heating and cooling with different boundary conditions . 149
2.3.3.2 Two semi-infinite bodies in contact with each other 154
2.3.3.3 Periodic temperature variations . 156
2.3.4 Cooling or heating of simple bodies in one-dimensional heat flow . 159
2.3.4.1 Formulation of the problem . 159
2.3.4.2 Separating the variables . 161
2.3.4.3 Results for the plate . 163
2.3.4.4 Results for the cylinder and the sphere . 167
2.3.4.5 Approximation for large times: Restriction to the first
term in the series . 169
2.3.4.6 A solution for small times 171
2.3.5 Cooling and heating in multi-dimensional heat flow 172
2.3.5.1 Product solutions . 172
2.3.5.2 Approximation for small Biot numbers . 175
2.3.6 Solidification of geometrically simple bodies . 177
2.3.6.1 The solidification of flat layers (Stefan problem) 178
2.3.6.2 The quasi-steady approximation 181
2.3.6.3 Improved approximations 184
2.3.7 Heat sources 185Contents xi
2.3.7.1 Homogeneous heat sources 186
2.3.7.2 Point and linear heat sources 187
2.4 Numerical solutions to heat conduction problems 192
2.4.1 The simple, explicit difference method for transient heat conduction
problems 193
2.4.1.1 The finite difference equation 193
2.4.1.2 The stability condition 195
2.4.1.3 Heat sources 196
2.4.2 Discretisation of the boundary conditions 197
2.4.3 The implicit difference method from J. Crank and P. Nicolson 203
2.4.4 Noncartesian coordinates. Temperature dependent material
properties 206
2.4.4.1 The discretisation of the self-adjoint differential operator . 207
2.4.4.2 Constant material properties. Cylindrical coordinates 208
2.4.4.3 Temperature dependent material properties 209
2.4.5 Transient two- and three-dimensional temperature fields 211
2.4.6 Steady-state temperature fields 214
2.4.6.1 A simple finite difference method for plane, steady-state
temperature fields 214
2.4.6.2 Consideration of the boundary conditions . 217
2.5 Mass diffusion . 222
2.5.1 Remarks on quiescent systems 222
2.5.2 Derivation of the differential equation for the concentration field . 225
2.5.3 Simplifications . 230
2.5.4 Boundary conditions 231
2.5.5 Steady-state mass diffusion with catalytic surface reaction . 234
2.5.6 Steady-state mass diffusion with homogeneous chemical reaction . 238
2.5.7 Transient mass diffusion 242
2.5.7.1 Transient mass diffusion in a semi-infinite solid 243
2.5.7.2 Transient mass diffusion in bodies of simple geometry
with one-dimensional mass flow . 244
2.6 Exercises 246
3 Convective heat and mass transfer. Single phase flow 253
3.1 Preliminary remarks: Longitudinal, frictionless flow over a flat plate . 253
3.2 The balance equations . 258
3.2.1 Reynolds’ transport theorem . 258
3.2.2 The mass balance . 260
3.2.2.1 Pure substances 260
3.2.2.2 Multicomponent mixtures 261
3.2.3 The momentum balance 264
3.2.3.1 The stress tensor . 266
3.2.3.2 Cauchy’s equation of motion . 269
3.2.3.3 The strain tensor . 270xii Contents
3.2.3.4 Constitutive equations for the solution of the
momentum equation . 272
3.2.3.5 The Navier-Stokes equations . 273
3.2.4 The energy balance 274
3.2.4.1 Dissipated energy and entropy . 279
3.2.4.2 Constitutive equations for the solution of the energy
equation 281
3.2.4.3 Some other formulations of the energy equation 282
3.2.5 Summary 285
3.3 Influence of the Reynolds number on the flow 287
3.4 Simplifications to the Navier-Stokes equations . 290
3.4.1 Creeping flows . 290
3.4.2 Frictionless flows 291
3.4.3 Boundary layer flows . 291
3.5 The boundary layer equations 293
3.5.1 The velocity boundary layer . 293
3.5.2 The thermal boundary layer . 296
3.5.3 The concentration boundary layer 300
3.5.4 General comments on the solution of boundary layer equations 300
3.6 Influence of turbulence on heat and mass transfer . 304
3.6.1 Turbulent flows near solid walls 308
3.7 External forced flow 312
3.7.1 Parallel flow along a flat plate 313
3.7.1.1 Laminar boundary layer . 313
3.7.1.2 Turbulent flow 325
3.7.2 The cylinder in crossflow . 330
3.7.3 Tube bundles in crossflow . 334
3.7.4 Some empirical equations for heat and mass transfer in
external forced flow 338
3.8 Internal forced flow 341
3.8.1 Laminar flow in circular tubes 341
3.8.1.1 Hydrodynamic, fully developed, laminar flow . 342
3.8.1.2 Thermal, fully developed, laminar flow . 344
3.8.1.3 Heat transfer coefficients in thermally fully developed,
laminar flow 346
3.8.1.4 The thermal entry flow with fully developed velocity
profile . 349
3.8.1.5 Thermally and hydrodynamically developing flow . 354
3.8.2 Turbulent flow in circular tubes . 355
3.8.3 Packed beds 357
3.8.4 Fluidised beds . 361
3.8.5 Some empirical equations for heat and mass transfer in flow
through channels, packed and fluidised beds . 370
3.9 Free flow 373Contents xiii
3.9.1 The momentum equation . 376
3.9.2 Heat transfer in laminar flow on a vertical wall . 379
3.9.3 Some empirical equations for heat transfer in free flow . 384
3.9.4 Mass transfer in free flow . 386
3.10 Overlapping of free and forced flow 387
3.11 Compressible flows . 389
3.11.1 The temperature field in a compressible flow 389
3.11.2 Calculation of heat transfer 396
3.12 Exercises 399
4 Convective heat and mass transfer. Flows with phase change 405
4.1 Heat transfer in condensation . 405
4.1.1 The different types of condensation . 406
4.1.2 Nusselt’s film condensation theory 408
4.1.3 Deviations from Nusselt’s film condensation theory . 412
4.1.4 Influence of non-condensable gases 416
4.1.5 Film condensation in a turbulent film 422
4.1.6 Condensation of flowing vapours . 426
4.1.7 Dropwise condensation 431
4.1.8 Condensation of vapour mixtures . 435
4.1.8.1 The temperature at the phase interface . 439
4.1.8.2 The material and energy balance for the vapour 443
4.1.8.3 Calculating the size of a condenser . 445
4.1.9 Some empirical equations . 446
4.2 Heat transfer in boiling 448
4.2.1 The different types of heat transfer 449
4.2.2 The formation of vapour bubbles . 453
4.2.3 Bubble frequency and departure diameter 456
4.2.4 Boiling in free flow. The Nukijama curve 460
4.2.5 Stability during boiling in free flow 461
4.2.6 Calculation of heat transfer coefficients for boiling in free flow 465
4.2.7 Some empirical equations for heat transfer during nucleate
boiling in free flow . 468
4.2.8 Two-phase flow . 472
4.2.8.1 The different flow patterns 473
4.2.8.2 Flow maps . 475
4.2.8.3 Some basic terms and definitions 476
4.2.8.4 Pressure drop in two-phase flow . 479
4.2.8.5 The different heat transfer regions in two-phase flow . 487
4.2.8.6 Heat transfer in nucleate boiling and convective
evaporation 489
4.2.8.7 Critical boiling states . 492
4.2.8.8 Some empirical equations for heat transfer in two-phase
flow 495
4.2.9 Heat transfer in boiling mixtures . 496xiv Contents
4.3 Exercises 501
5 Thermal radiation 503
5.1 Fundamentals. Physical quantities 503
5.1.1 Thermal radiation . 504
5.1.2 Emission of radiation . 506
5.1.2.1 Emissive power 506
5.1.2.2 Spectral intensity . 507
5.1.2.3 Hemispherical spectral emissive power and total intensity 509
5.1.2.4 Diffuse radiators. Lambert’s cosine law . 513
5.1.3 Irradiation . 514
5.1.4 Absorption of radiation 517
5.1.5 Reflection of radiation . 522
5.1.6 Radiation in an enclosure. Kirchhoff’s law . 524
5.2 Radiation from a black body . 527
5.2.1 Definition and realisation of a black body 527
5.2.2 The spectral intensity and the spectral emissive power . 528
5.2.3 The emissive power and the emission of radiation in a wavelength
interval . 532
5.3 Radiation properties of real bodies 537
5.3.1 Emissivities . 537
5.3.2 The relationships between emissivity, absorptivity and reflectivity.
The grey Lambert radiator 540
5.3.2.1 Conclusions from Kirchhoff’s law 540
5.3.2.2 Calculation of absorptivities from emissivities . 541
5.3.2.3 The grey Lambert radiator . 542
5.3.3 Emissivities of real bodies . 544
5.3.3.1 Electrical insulators . 545
5.3.3.2 Electrical conductors (metals) 548
5.3.4 Transparent bodies . 550
5.4 Solar radiation . 555
5.4.1 Extraterrestrial solar radiation 555
5.4.2 The attenuation of solar radiation in the earth’s atmosphere . 558
5.4.2.1 Spectral transmissivity 558
5.4.2.2 Molecular and aerosol scattering 561
5.4.2.3 Absorption 562
5.4.3 Direct solar radiation on the ground . 564
5.4.4 Diffuse solar radiation and global radiation . 566
5.4.5 Absorptivities for solar radiation . 568
5.5 Radiative exchange 569
5.5.1 View factors 570
5.5.2 Radiative exchange between black bodies 576
5.5.3 Radiative exchange between grey Lambert radiators 579
5.5.3.1 The balance equations according to the net-radiation
method 580Contents xv
5.5.3.2 Radiative exchange between a radiation source, a radiation
receiver and a reradiating wall 581
5.5.3.3 Radiative exchange in a hollow enclosure with two zones . 585
5.5.3.4 The equation system for the radiative exchange between
any number of zones . 587
5.5.4 Protective radiation shields 590
5.6 Gas radiation 594
5.6.1 Absorption coefficient and optical thickness . 595
5.6.2 Absorptivity and emissivity 597
5.6.3 Results for the emissivity . 600
5.6.4 Emissivities and mean beam lengths of gas spaces . 603
5.6.5 Radiative exchange in a gas filled enclosure . 607
5.6.5.1 Black, isothermal boundary walls 607
5.6.5.2 Grey isothermal boundary walls . 608
5.6.5.3 Calculation of the radiative exchange in complicated cases 611
5.7 Exercises 612
Appendix A: Supplements 617
A.1 Introduction to tensor notation 617
A.2 Relationship between mean and thermodynamic pressure . 619
A.3 Navier-Stokes equations for an incompressible fluid of constant viscosity
in cartesian coordinates 620
A.4 Navier-Stokes equations for an incompressible fluid of constant viscosity
in cylindrical coordinates . 621
A.5 Entropy balance for mixtures . 622
A.6 Relationship between partial and specific enthalpy . 623
A.7 Calculation of the constants an of a Graetz-Nusselt problem (3.246) . 624
Appendix B: Property data 626
Appendix C: Solutions to the exercises 640
Literature 654
Index
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