اسم المؤلف
R.K. RAJPUT
التاريخ
25 أكتوبر 2022
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275
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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
- 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” - 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 - 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 - 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” - 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 - 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 - 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” - 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 - 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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