Heat and Mass Transfer

Heat and Mass Transfer
A textbook for the students preparing for B.E., B.Tech., B.Sc. Engg., AMIE,
UPSC (Engg. Services) and GATE Examinations
IN
Er. R.K. RAJPUT
M.E. (Hons.), Gold Medalist; Grad. (Meeh. Engg. & Elec. Engg.); MIE (India)
MSESI; MISTE; CE (India)
Recipient of :
“Best Teacher (Academic) Award”
“Distinguished Author Award”
“Jawahar Lal Nehru Memorial Gold Medal”
for an Outstanding Research Paper
(Institution of Engineers-lndia)
Principal (Formerly)
Punjab College of Information Technology
PATIALA
CON
Chapters
Nomenclature

1. BASIC CONCEPTS
   Pages
   (xv)—(xvi)
   1- 24
   1.1.
   1.2.
   1.3.
   1.4.
   Heat Transfer—General Aspects, 1
   1.1.1. Heat, 1
   1.1.2. Importance of heat transfer, 2
   1.1.3. Thermodynamics, 2
   1.1.3.1. Definition, 2
   1.1.3.2. Thermodynamic systems, 3
   1.1.3.3. Macroscopic and microscopic points of view, 4
   1.1.3.4. Pure substance, 4
   1.1.3.5. Thermodynamic equilibrium, 5
   1.1.3.6. Properties of systems, 6
   1.1.3.7. State, 6
   1.1.3.8. Process, 6
   1.1.3.9. Cycle, 7
   1.1.3.10. Point function, 7
   1.1.3.11. Path function, 7
   1.1.3.12. Temperature, 7
   1.1.3.13. Pressure, 8
   1.1.3.14. Energy, 8
   1.1.3.15. Work, 8
   1.1.3.16. Heat, 9
   1.1.3.17. Comparison of work and heat, 11
   1.1.4 Differences between thermodynamics
   and heat transfer, 10
   1.1.5. Basic laws governing heat transfer, 10
   1.1.6. Modes of heat transfer, 11
   Heat Transfer by Conduction, 13
   1.2.1. Fourier’s law of heat conduction, 13
   1.2.2. Thermal conductivity of materials, 14
   1.2.3. Thermal resistance (Rth), 16
   Heat Transfer by Convection, 18
   Heat Transfer by Radiation, 19
   Highlights, 22
   Theoretical Questions, 24
   Unsolved Examples, 24
   PART I : HEAT TRANSFER BY “CONDUCTION”
2. CONDUCTION-STEADY-STATE ONE DIMENSION 27—268
   2.1. Introduction, 27
   2.2. General Heat Conduction Equation in Cartesian Coordinates, 27
   2.3. General Heat Conduction Equation in Cylindrical Coordinates, 32
   2.4. General Heat Conduction Equation in Spherical Coordinates, 35
   (vn)2.5. Heat Conduction Through Plane and
   Composite Walls, 38
   2.5.1. Heat conduction through a plane wall, 38
   2.5.2. Heat conduction through a composite
   wall, 42
   2.5.3. The overall heat transfer coefficient, 45
   2.6. Heat Conduction Through Hollow and
   Composite Cylinders, 87
   2.6.1. Heat conduction through a hollow cylinder, 87
   2.6.1.1. Logarithmic mean area for the hollow cylinder, 93
   2.6.2. Heat conduction through a composite cylinder, 94
   2.7. Heat Conduction Through Hollow and Composite Spheres, 128
   2.7.1. Heat conduction through a hollow sphere, 128
   2.7.1.1. Logarithmic mean area for the hollow sphere, 131
   2.7.2. Heat condition through a composite sphere, 132
   2.8.
   2.9.
   2.10.
   Critical Thickness of Insulation, 142
   2.8.1. Insulation-General aspects, 142
   2.8.2. Critical thickness of insulation, 143
   Heat conduction with Internal Heat Generation, 150
   2.9.1. Plane wall with uniform heat generation, 150
   2.9.2. Dielectric heating, 167
   2.9.3. Cylinder with uniform heat generation, 171
   2.9.4. Heat transfer through the piston crown, 192
   2.9.5. Heat conduction with heat generation in the
   nuclear cylindrical fuel rod, 193
   2.9.6. Sphere with uniform heat generation, 200
   Heat Transfer from Extended Surfaces (Fins), 203
   2.10.1.Introduction, 203
   2.10.2. Heat flow through “Rectangular fin”, 205
   2.10.2.1. Heat dissipation from an infinitel
   2.10.2.2. Heat dissipation from a fin insulated at the tip, 213
   2.10.2.3. Heat dissipation from a fin losing heat at the tip, 224
   2.10.2.4. Efficiency and effectiveness of fin, 233
   2.10.2.5. Design of rectangular fins, 238
   2.10.3. Heat flow through “straight triangular fin”, 242
   2.10.4.Estimation of error in temperature measurement in a thermometer well, 245
   2.10.5.Heat transfer from a bar connected to the two heat sources at different
   temperatures, 250
   Highlights, 259
   Theoretical Questions, 263
   Unsolved Examples, 263
3. CONDUCTION-STEADY-STATE TWO DIMENSIONS AND THREE
   DIMENSIONS 269-289
   3.1. Introduction, 269
   3.2. Two Dimensional Steady State Conduction, 270
   3.2.1. Analytical method, 270
   (viii)3.2.1.1. Two-dimensional steady state heat con¬
   duction in rectangular plates, 270
   3.2.1.2. Two-dimensional steady state heat con
   duction in semi-infinite plates, 272
   3.2.2. Graphical method, 277
   3.2.3. Analogical method, 284
   3.2.4. Numerical methods, 285
   3.3. Three-dimensional Steady State Conduction, 287
   Highlights, 289
   Theoretical Questions, 289
   Unsolved Examples, 289
4. CONDUCTION-UNSTEADY-STATE (TRANSIENT) 290—336
   4.1. Introduction, 290
   4.2. Heat conduction in Solids having Infinite Thermal
   Conductivity (Negligible Internal Resistance) —
   Lumped Parameter Analysis, 291
   4.3. Time constant and Response of Temperature
   Measuring Instruments, 304
   4.4. Transient Heat Conduction in Solids with Finite
   Conduction and Convective Resistances
   (0 < B. < 100), 308 4.5. Transient Heat Conduction in Semi-infinite Solids (h or B. «>), 318
   4.6. Systems with Periodic Variation of Surface Tem¬
   perature, 326
   4.7. Transient Conduction with Given Temperature Distribution, 328
   Typical Examples, 328
   Highlights, 329
   Theoretical Questions, 333
   Unsolved Examples, 333
   PART II : HEAT TRANSFER BY “CONVECTION”
5. INTRODUCTION TO HYDRODYNAMICS
   5.1. Introduction, 339
   5.2. Ideal and Real Fluids, 339
   5.3. Viscosity, 340
   5.4. Continuity Equation in Cartesian Coordinates, 341
   5.5. Equation of Continuity in Polar Coordinates, 343
   5.6. Velocity Potential and Stream Function, 343
   5.6.1. Velocity potential, 343
   5.6.2 Stream function, 345
   5.7. Laminar and turbulent flows, 347
   Highlights, 350
   Theoretical Questions, 351
   339-351
   (.VC)6. DIMENSIONAL ANALYSIS 352 — 372
   7.
   A.
   6.1. Introduction, 352
   6.2. Dimensions, 353
   6.3. Dimensional Homogeneity, 353
   6.4. Methods of Dimensional Analysis, 354
   6.4.1. Rayleigh’s Method, 354
   6.4.2. Buckingham’sK-Method/Theorem, 356
   6.5. Dimensional Analysis Applied to Forced Convection
   Heat Transfer, 362
   6.6. Dimensional Analysis Applied to Natural or Free
   Convection, 364
   6.7. Advantages and Limitations of Dimensional
   Analysis, 365
   6.8. Dimensional Numbers and their Physical
   significance, 366
   6.9. Characteristic Length or Equivalent Diameter, 369
   6.10. Model Studies and Similitude, 371
   6.10.1. Model and prototype, 371
   6.10.2. Similitude, 371
   Highlights, 371
   Theoretical Questions, 372
   FORCED CONVECTION
   LAMINAR FLOW,373
   7.1. Laminar Flow over a Flat Plate, 373
   7.1.1. Introduction to boundary layer, 373
   7.1.1.1. Boundary layer definitions and
   characteristics, 374
   7.1.2. Momentum equation for hydrodynamic
   boundary layer over a flat plate, 380
   7.1.3. Blasius (exact) solution for laminar boundary
   layer flows, 382
   7.1.4. Van-Karman integral momentum equation
   (Approximate hydro-dynamic boundary layer
   analysis), 387
   7.1.5. Thermal boundary layer, 398
   7.1.6. Energy equation of thermal boundary layer
   over a flat plat, 399
   7.1.7. Integral energy equation (Approximate
   solution of energy equation), 406
   7.2. Laminar Tube Flow, 424
   7.2.1. Development of boundary layer, 424
   7.2.2. Velocity distribution, 425
   7.2.3. Temperature distribution, 428
   373- 505
   WB.TURBULENTFLOW,435
   7.3. Introduction, 435
   7.3.1. Turbulent boundary layer, 436
   7.3.2. Total drag due to laminar and turbulent
   layers, 439
   7.3.3. Reynolds analogy, 446
   7.4. Turbulent Tube Flow, 457
   7.5. Empirical Correlations 465
   7.5.1. Laminar flow over flat plates and walls, 465
   7.5.2. Laminar flow inside tubes, 466
   7.5.3. Turbulent flow over flat plate, 470
   7.5.4. Turbulent flow in tubes, 470
   7.5.5. Turbulent flow over cylinders, 480
   7.5.6. Turbulent flow over spheres, 486
   7.5.7. Flow across bluff objects, 487
   7.5.8. Flowthrough packed beds, 487
   7.5.9. Flow across a bank of tubes, 489
   7.5.10. Liquid metal heat transfer, 492
   Highlights, 495
   Theoretical Questions, 499
   Unsolved Examples, 500
6. FREE CONVECTION 506- 538
   8.1. Introduction, 506
   8.2. Characteristic Parameters in Free Convection, 507
   8.3. Momentum and Energy Equation for Laminar Free Convection Heat
   Transfer on a Flat Plate, 508
   8.4. Integral Equations for Momentum and Energy on a Flat Plate, 509
   8.4.1. Velocity and temperature profiles on a vertical flat plate, 509
   8.4.2. Solution of integral equations for vertical flat plate, 510
   8.4.3. Free convection heat transfer coefficient for a vertical wall, 511
   8.5. Transition and Turbulence in Free Convection, 512
   8.6. Empirical Correlations for Free Convection, 512
   8.6.1. Vertical platesand cylinders, 512
   8.6.2. Horizontal plates, 512
   8.6.3. Horizontal cylinders, 513
   8.6.4. Inclined plates, 513
   8.6.5. Spheres, 513
   8.6.6. Enclosed spaces, 513
   8.6.7. Concentric cylinders space 514
   8.6.8. Concentric spheres spaces, 514
   8.7. Simplified Free Convection Relations for Air, 514
   8.8. Combined Free and Forced Convection, 514
   8.8.1. External flows, 515
   8.8.2. Internal flows, 515
   Typical Examples, 533
   Highlights, 536
   Unsolved Examples, 537
   (xi)9. BOILING AND CONDENSATION 539- 573
   9.1. Introduction, 539
   9.2. BoilingHeat Transfer, 540
   9.2.1. General aspects, 540
   9.2.2. Boilingregimes, 541
   9.2.3. Bubble shape and size consideration, 542
   9.2.4. Bubble growth and collapse,543
   9.2.5. Critical diameter of bubble, 544
   9.2.6. Factors affectingnucleate boiling, 544
   9.2.7. Boilingcorrelations, 545
   9.2.7.1. Nucleate pool boiling, 545
   9.2.7.2. Critical heat flux for nucleate pool
   boiling, 546
   9.2.7.3. Film pool boiling, 546
   9.3. Condensation Heat Transfer, 550
   9.3.1. General aspects, 550
   9.3.2. Laminar film condensation on a vertical plate, 552
   9.3.3. Turbulent film condensation, 557
   9.3.4. Film condensation on horizontal tubes, 558
   9.3.5. Film condensation inside horizontal tubes, 558
   9.3.6. Influence ofthe presence of non-condensable gases, 559
   Highlights, 570
   Theoretical Questions, 572
   Unsolved Examples, 572
7. HEAT EXCHANGERS 574- 669
   10.1. Introduction, 574
   10.2. Types of Heat Exchangers, 574
   10.3. Heat Exchanger Analysis, 580
   10.4. Logarithmic Mean Temperature Difference (LMTD), 581
   10.4.1. Logarithmic mean temperature difference for
   parallel-flow, 581
   10.4.2. Logarithmic mean temperature difference
   for counter-flow, 583
   10.5. Overall Heat Transfer Coefficient, 585
   10.6. Correction Factors for Multi-pass
   Arrangements, 622
   10.7. Heat Exchanger Effectiveness and Number of
   Transfer Units (NTU), 627
   10.8. Pressure Drop and PumpingPower, 631
   10.9. Evaporators, 659
   10.9.1. Introduction, 659
   10.9.2. Classification of evaporators, 659
   Highlights, 665
   Theoretical Questions, 666
   Unsolved Examples, 666
   (xii)PART III : HEAT TRANSFER BY “RADIATION”
8. THERMAL RADIATION-BASIC RELATIONS 673- 687
   11.1. Introduction, 673
   11.2. Surface Emission Properties, 674
   11.3. Absorptivity,Reflectivity and Transmissivity, 675
   11.4. Concept of a Black body, 677
   11.5. The Stefan-Boltzmann Law, 678
   11.6. Kirchoff’s Law, 678
   11.7. Planck’s Law, 679
   11.8. Wien Displacement Law, 680
   11.9. Intensity of Radiation and Lambert’s
   Cosine Law, 681
   11.9.1. Intensity of radiation, 681
   11.9.2. Lambert’s cosine law, 683
   Highlights, 686
   Theoretical Questions, 687
   Unsolved Examples, 687
   12.RADIATION EXCHANGE BETWEEN SURFACES 688 — 764
   12.1. Introduction, 688
   12.2. Radiation Exchange Between Black
   Bodies Separated by an a Non-absor¬
   bingMedium, 688
   12.3. Shape Factor Algebra and Salient
   Features of the Shape Factor, 692
   12.4. Heat Exchange Between Non-black
   Bodies, 710
   12.4.1. Infinite parallel planes, 710
   12.4.2. Infinite longconcentric
   cylinders, 710-711
   12.4.3. Small gray bodies, 714
   12.4.4. Small body in a large enclosure, 714
   12.5. Electrical Network Analogy for Thermal Radiation Systems, 716
   12.6. Radiation Heat Exchange for Three Gray Surfaces, 718
   12.7. Radiation Heat Exchange for Two Black Surfaces Connected by a Single Refractory
   surface, 719
   12.8. Radiation Heat Exchange for Two Gray Surfaces Connected by Single Refractory
   Surface, 720
   12.9. Radiation Heat Exchange for Four Black Surfaces, 721
   12.10. Radiation Heat Exchange for Four Gray Surfaces, 721
   12.11. Radiation Shields, 742
   12.12. Coefficient of Radiant Heat Transfer and Radiation Combined with Convection, 754
   12.13. Error in Temperature Measurement due to Radiation, 756
   12.14. Radiation from Gases, Vapours and Flames, 760
   Highlights, 762
   Theoretical Questions, 763
   Unsolved Examples, 763
   (xiii)PART IV : MASS TRANSFER
   13.MASS TRANSFER 767—808
   13.1. Introduction, 767
   13.2. Modes of Mass Transfer, 768
   13.3. Concentrations, Velocities and Fluxes, 768
   13.3.1. Concentrations, 768
   13.3.2. Velocities, 769
   13.3.3. Fluxes, 770
   13.4. Fick’s Law, 772
   13.5. General Mass Diffusion Equation in
   Stationary Media, 777
   13.6. Steady-State Diffusion in Common
   Geometries, 779
   13.6.1. Steady state diffusion through
   a plain membrane, 779
   13.6.2. Steady state diffusion through
   a cylindrical shell 781
   13.6.3. Steady state diffusion through
   aspherical shell, 783
   13.7. Steady-State Equimolar Counter Diffusion, 785
   13.8. Steady State Undirectional Diffusion (Steady state Diffusion through a stagnant Gas
   Film), 788
   13.9. Steady State Diffusion in Liquids, 794
   13.10. Transient Mass Diffusion in Semi-finite Stationary Medium, 795
   13.11. Mass Transfer Co-efficient, 796
   13.12. Convective Mass Transfer, 799
   13.13. Correlations for Connective Mass Transfer, 800
   13.14. Reynolds and Colburn Analogies for Mass Transfer-Combined Heat and
   Mass Transfer, 801
   Highlights, 805
   Theoretical Questions,806
   Unsolved Examples, 807
9. UNIVERSITIES’ QUESTIONS (Latest) – with Solutions 809-821
   ADDITIONAL/TYPICAL WORKED EXAMPLES 822-845
   (QuestionsselectedfromUniversities’and Competitive Examinations)
   PART V : OBJECTIVE TYPE QUESTIONS
   BANK WITH ANSWERS & INDEX
   Objective Type Questions
   Index
   849-901
   902-903
   (xiv)INDEX
   B
   Biot number, 294
   Black body, 676
   Blasius exact solution for laminar boundary
   layer flow, 382
   Boiling and condensation, 539
   Boiling heat transfer, 540

• boilingcorrelations,545
• boilingregimes,541
• bubble growth and collapse, 543
• bubble shape and size consideration, 542
• critical diameterof bubble,544
• factorsaffecting nucleateboiling,544
  c
  Characteristic length, 369
  Condensation heat transfer, 550
• dropwise condensation, 551
• film condensation,551
• laminar film condensation on a
  vertical plate, 552
• turbulent film condensation, 557
  Convective mass transfer, 799
  correlation for, 800
  Conduction-unsteady state, 290
• in semi-finite solids, 318
• lumped parameter analysis, 291
• thermal time constant, 293
  Conduction shape factor, 279
  Continuity equation, 341
• in cartesian coordinates, 342
• in polar coordinates, 343
  Critical thickness of insulation, 143
• for cylinder, 143
• for sphere, 145
  Cycle, 7
  D
  Dimensional analysis, 352
  Dimensions, 353
  Dimensional homogeneity, 353
• advantages and limitations of, 365
• applications of, 353
• applied to forced convention heat
  transfer, 362
• applied to natural or free convection heat
  transfer, 364
• methods of, 354
• Buckingham’s method, 356
  Dimensional numbers, 366
  E
  Energy, 8
  Evaporators, 659
  F
  Fick’s law, 772
  Forced convection, 373
• empirical correlationsfor, 465
• laminar flowover flat platesand walls, 465
• laminar flow inside tubes, 466
• turbulent flow over flat plate, 470
• turbulent flow in tubes, 470
• turbulent flow over cylinders, 480
• turbulent flow over spheres, 486
• flow across bluff bodies, 487
• flow through packed beds, 489
• flow across a bank of tubes, 489
• liquid metal heat transfer, 492
• laminar flowovera flat plate, 373
• boundary layer thickness, 375
• displacement thickness, 375
• energy thickness, 377
• integral energy equation, 406
• momentum thickness, 376
• momentum equation for hydrodynamic
  layer, 380
• thermal boundary layer, 398
• Fourier’s law, 13
  Fourier number, 294
  Free convection, 506
• characteristics parameters in, 507
• empiricalcorrelations,512
• concentric cylinders spaces, 514
• enclosed spaces, 513
• horizontal plates, 512
• horizontal cylinders, 513
• inclined plates, 512
• spheres, 513
• vertical plates and cylinders, 512
• transition and turbulence in, 512
  G
  Gaussian error function, 319
  H
  Heat, 1, 9
  Heat exchangers, 574
• analysis of, 580
• compact, 579
• concentric tubes, 578
• condensers, 579
• counter-flow, 576
• cross-flow, 577
• effectiveness and NTU, 627
• logarithmic mean temperature
  difference, 581
• for parallel-flow,581
• for counter-flow, 583
• overall heat transfercoefficient, 585
• parallel-flow,576
• pressure drop and pumping power, 631
• recuperators, 576
• regenerators,575
• types of, 563
  Heat transfer, 1
• from fins, 203
  902Chapter : 9 : Boiling and Condensation 903
• straight triangular fin, 242
• rectangular fin, 205
• modes of, 11
• conduction, 11
• convection, 12
• radiation, 12
  Heister charts, 309
  I
  Integral energy equation, 406
  K
  Kirchhoff’s law, 19, 678
  L
  Laminar flow, 347, 373
• over a flat plate, 373
  Lambert’s cosine law, 681
  Laminar tube flow, 424
• development of boundary layer, 424
• temperature distribution, 428
• velocity distribution, 425
  M
  Mass transfer, 767
• concentrations, 768
• mass concentration, 768
• mass fraction, 769
• molar concentration, 768
• mole fraction, 769
• convective mass transfer, 799
• mass diffusion coefficient, 774
• fluxes,770
• mass diffusion equation, 777
• mass transfer coefficient, 796
• modes of, 768
• by change of phase, 768
• by convection, 768
• by diffusion, 768
• steady state equimolar counter
  diffusion, 785
• velocities, 769
• mass-average velocity,769
• mass-diffusion velocity, 770
• molar-average velocity,769
• molar-diffusion velocity, 770
  Model studies and similitude, 371
  o
  Opaque body, 676
  Overall heat transfer coefficient, 45
  P
  Path function, 7
  Planck’s law, 679
  Point function, 7
  Process, 6
  Pure substance, 4
  R
  Radiation exchange between surfaces, 688
• electrical network analogy, 716
• gray body factor, 718
• irradiation, 716
• radiosity, 716
• space resistance, 717
• heatexchange between non-black
  bodies, 710
• infinite parallel planes, 710
• infinite long concentric cylinders, 711
• small gray bodies, 714
• small body in a largeenclosure, 714
• radiation shields, 742
• shape factor algebra, 692
  Radiation heat transfer, 673
• absorptivity, reflectivity and
  transmissivity, 675
• black body, 676
• intensity of radiation, 681
• surface emission properties, 674
• monochromatic emissive power, 674
• total emissive power, 674
• the Stefan-Boltzmann law, 678
  Rayleigh’s method, 354
  Rectangular fin, 205
• design of, 238
• effectiveness of, 233
• efficiency of, 233
  Recuperators, 576
  Regenerators, 575
  Reynolds number, 349
  s
  Shape factor algebra, 692
  State, 6
  Stefan-Boltzmann law, 678
  Stefan’s law for diffusion, 790
  Stream function, 345
• properties of, 346
  T
  Temperature, 7
  Thermal conductivity, 14
  Thermal resistance, 16
  Thermal boundary layer, 398
• energy equation of, 399
• Pohlhausen solution, 401
  Thermal contact resistance, 44
  Thermal diffusivity, 30
  Thermodynamics, 3
  Thermodynamic equilibrium, 5
  Thermodynamic systems, 3
  Turbulent flow, 348, 435
  Turbulent boundary layer, 436
  Turbulent tube flow, 457
  V
  Velocity potential, 343
  Viscosity, 340
• Newton’s law of, 341
• units of, 341
  Von Karman integral momentum equation, 387
  W
  White body, 676
  Wien’s displacement law, 680
  Wien’s law, 19
  Work, 8

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