Intermediate Heat Transfer

Contents......Page 0
Intermediate Heat Transfer......Page 1
Preface......Page 10
Contents......Page 12
1.1 Conduction......Page 17
1.2 Convection......Page 20
1.3 Radiation......Page 22
1.4 Combined Convection and Radiation......Page 25
PROBLEMS......Page 27
2.2 Governing Differential Equation of Heat Conduction......Page 29
2.5 Fourier\'s Equation......Page 31
2.6 Initial and Boundary Conditions......Page 32
2.8 Second Kind (Neumann) Boundary Conditions......Page 33
2.9 Third Kind (Robin or Mixed) Boundary Conditions......Page 34
2.10 Temperature-Dependent Thermal Conductivity......Page 35
2.11 Dimensionless Heat Conduction Numbers......Page 37
PROBLEMS......Page 39
3.1 The Slab (One-Dimensional Cartesian Coordinates)......Page 42
(a) Solid Cylinder......Page 43
(a) Solid Sphere......Page 44
(b) Hollow Cylinder......Page 45
(c) Hollow Sphere......Page 46
3.5 Conduction Through a Slab from One Fluid to Another Fluid......Page 47
(a) Parallel Slabs......Page 48
3.7 Thermal Contact Resistance......Page 50
3.8 Standard Method of Determining the Thermal Conductivity in a Solid......Page 51
(a) One-Dimensional with No Heat Generation......Page 52
(b) Poisson\'s Equation, with Heat Generation......Page 54
3.10 Critical Radius of Insulation......Page 58
3.11 Effects of Radiation......Page 59
3.12.1 Introduction......Page 60
3.12.2 One-Dimensional Fin Equations......Page 61
3.12.3 Temperature Distribution and Heat Flow in Fins of Uniform Cross Section......Page 62
3.12.4 Fin Efficiency......Page 69
3.12.5 Heat Transfer from a Finned Surface......Page 71
PROBLEMS......Page 72
4.1 Method of Separation of Variables......Page 75
4.2 Steady-State Heat Conduction in a Rectangular Region......Page 78
4.3 Heat Flow......Page 81
4.4 Separation into Simpler Problems......Page 84
4.5 Summary of Steps Used in the Method of Separation of Variables......Page 85
4.6 Steady-State Heat Conduction in a Two-Dimensional Fin......Page 86
4.7 Transient Heat Conduction in a Slab......Page 90
PROBLEMS......Page 92
5.2 Finite Difference of Derivatives......Page 96
5.3 Finite Difference Equations for 2-D Rectangular Steady-State Conduction......Page 99
5.4 Finite Difference Representation of Boundary Conditions......Page 101
5.5 Solution of Finite Difference Equations......Page 105
5.6 Finite Difference Equations for 1-D Unsteady- State Conduction in Rectangular Coordinates......Page 114
5.7 Finite Difference of 2-D Unsteady-State Problems in Rectangular Coordinates......Page 122
5.8 Finite Difference Method Applied in Cylindrical Coordinates......Page 126
5.9 Truncation Errors and Round-Off Errors in the Finite Difference Method......Page 128
5.10 Stability and Convergence......Page 130
PROBLEMS......Page 132
Gaussian Elimination Method......Page 137
6.1 Continuity......Page 138
6.2 Momentum Equations......Page 139
6.3 Energy Equation......Page 144
6.4 Summary of Governing Equations......Page 150
6.5 Dimensionless Numbers......Page 153
6.6 The Boundary Layer Equations......Page 156
PROBLEMS......Page 159
REFERENCES......Page 160
7. 1 Momentum Integral Method of Analysis......Page 162
7.1.1 Drag Coefficient......Page 165
7.2 Integral Method of Analysis for Energy Equation......Page 167
7.3 Hydrodynamic and Thermal Boundary Layers on a Flat Plate, Where Heating Starts at x = x0.......Page 170
7.4.1 Laminar Flow Along a Flat Plate......Page 192
PROBLEMS......Page 199
REFERENCES......Page 201
8.1 Couette Flow......Page 203
8.1.1 Case T0 # T,......Page 206
8.1.2 Case T0 = T,......Page 208
8.2 Heat Transfer and Velocity Distribution in Hydrodynamically and Thermally Developed Laminar Flow in Conduits......Page 209
8.2.1 Temperature Distribution......Page 212
8.3 The Circular Tube Thermal-Entry-Length, with Hydrodynamically Fully Developed Laminar Flow......Page 217
8.3.1 Constant Surface Temperature......Page 219
8.3.2 Uniform Heat Flux......Page 220
8.4 The Rectangular Duct Thermal-Entry Hydrodynamically Fully Developed Laminar Flow Length, with......Page 223
8.4.1 Constant Wall Heat Flux......Page 224
8.4.2 Constant Wall Temperature......Page 227
PROBLEMS......Page 228
Internal Flows......Page 232
9.1. Boundary Layer Concept for Free Convection......Page 233
9.2 Similarity Solution: Boundary Layer with Uniform Temperature......Page 237
9.3 Similarity Solution: Boundary Layer with Uniform Heat Flux......Page 242
9.4 Integral Method of Solution......Page 246
PROBLEMS......Page 250
REFERENCES......Page 252
10.1 Introduction......Page 254
10.2 Burgers Equation......Page 255
10.3 Convection Equations......Page 256
10.4 Numerical Algorithms......Page 258
10.4.3 DuFort-Frankel Explicit......Page 259
10.4.4 MacCormack Explicit......Page 260
10.4.5 MacCormack Implicit......Page 261
10.4.6 Backward Time Central Space (BTCS) Implicit Scheme......Page 262
10.5 Boundary Layer Equations......Page 264
10.5.1 Fully Implicit and Crank-Nicholson Methods......Page 268
10.6 Convection with Incompressible Flow......Page 270
10.7 Two-Dimensional Convection with Incompressible Flow......Page 272
10.8 Convection in a Two-Dimensional Porous Medium......Page 273
10.8.1 Thomas Algorithm for Tridiagonal Systems......Page 278
PROBLEMS......Page 280
APPENDIX A......Page 282
11.1 Thermal Radiation......Page 285
11.2 Radiation Intensity and Blackbody......Page 286
11.3 Reflectivity, Absorptivity, Emissivity and Transmissivity......Page 291
11.4 Kirchhoff s Law of Radiation......Page 294
PROBLEMS......Page 295
12.1 Radiative Exchange Between Two Differential Area Elements......Page 297
12.2 Concept of View Factor......Page 301
12.3 Properties of Diffuse View Factors......Page 303
12.4 Determination of Diffuse View Factor by Contour Integration......Page 305
12.5 Relations Between View Factors......Page 314
12.6 Diffuse View Factor Between an Elemental Surface and an Infinitely Long Strip......Page 317
12.7 Diffuse View Factor Algebra......Page 318
PROBLEMS......Page 322
REFERENCES......Page 327
13.1 Diffuse View Factor in Long Enclosures......Page 329
13.3.......Page 351
13.4. A tube bundle is as configured in the figure.......Page 352
13.6. Find an expression for the view factor between two parallel plates, Fj.2,......Page 353
13.7. Consider radiation between two parallel surfaces,......Page 354
13.9. Find the view factor between the two parallel surfaces, with the 4 opaque objects in between.......Page 355
13.10. Find the view factor between the parallel surfaces,......Page 356
13.11. In an annealing process, a steel sheet is passed under an electric heater in order to raise its temperature and increase its hardness.......Page 357
13.13. The Hottel crossed-string method allows us to calculate the view factor......Page 358
13.14. (a) A patient is receiving radiation therapy to diminish a certain group of cells......Page 361
13.15. The inlet manifold depicted is used to supply air to a large displacement rotary engine (10 liters).......Page 363
13.16. Below is a cross-sectional view of a heat exchanger consisting of a multi-pass configuration......Page 364
PROBLEMS......Page 350
14.2 Radiation with Conduction......Page 366
14.2.1 Radiating Longitudinal Plate Fins......Page 367
14.3 Radiation with Convection......Page 377
14.4 Radiation with Conduction and Convection......Page 386
PROBLEMS......Page 392
REFERENCES......Page 395
Appendix A Bessel Functions......Page 397
REFERENCES......Page 403
Appendix B Physical Constants and Thermophysical Properties......Page 405