Preface to the Second Edition |
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xi | |
Preface to the First Edition |
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xiii | |
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1 | (18) |
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1 | (2) |
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Mass Transfer and Fluid Flow |
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3 | (1) |
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4 | (2) |
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Importance of Analytical and Experimental Methods |
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6 | (3) |
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9 | (3) |
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Basic Considerations in a Numerical Solution |
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12 | (3) |
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Outline and Scope of the Book |
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15 | (4) |
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17 | (2) |
Part 1 Mathematical Background |
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19 | (100) |
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21 | (16) |
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21 | (2) |
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Representative Differential Equations from Heat Transfer and Fluid Flow |
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23 | (3) |
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Boundary and Initial Conditions |
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26 | (2) |
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28 | (3) |
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31 | (6) |
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31 | (2) |
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33 | (1) |
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34 | (1) |
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35 | (2) |
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37 | (48) |
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39 | (16) |
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Direct Approximation Approach |
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39 | (2) |
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Polynomial Representation |
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41 | (3) |
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Taylor Series Approach and Accuracy |
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44 | (4) |
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Control Volume Approach and Conservation |
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48 | (2) |
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50 | (1) |
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51 | (1) |
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Discretization and Roundoff Errors |
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52 | (1) |
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53 | (1) |
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Numerical Stability and the Equivalence Theorem |
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53 | (2) |
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55 | (15) |
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55 | (3) |
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Solution of Simultaneous Equations |
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58 | (1) |
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59 | (6) |
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65 | (5) |
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70 | (15) |
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Two-Level Time Discretization |
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70 | (2) |
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Matrix Stability Analysis |
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72 | (4) |
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Fourier Series Stability Analysis |
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76 | (2) |
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An Example of Numerical Instability |
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78 | (2) |
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Other Explicit and Implicit Schemes |
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80 | (1) |
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81 | (1) |
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82 | (3) |
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85 | (34) |
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86 | (8) |
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88 | (1) |
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88 | (1) |
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Integral Representations and Galerkin's Method |
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89 | (1) |
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90 | (1) |
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90 | (1) |
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Condensation and Substructuring |
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91 | (2) |
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93 | (1) |
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94 | (14) |
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Matrix Equations with Boundary Conditions |
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94 | (3) |
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One-Dimensional Diffusion |
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97 | (2) |
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Two-Dimensional Diffusion |
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99 | (3) |
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102 | (6) |
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108 | (11) |
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108 | (1) |
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Finite Differences in Time |
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109 | (2) |
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111 | (1) |
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Transient One-Dimensional Diffusion |
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111 | (1) |
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Other Methods and Solutions |
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112 | (1) |
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113 | (1) |
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114 | (5) |
Part 2 Simulation of Transport Processes |
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119 | (296) |
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Numerical Methods for Conduction Heat Transfer |
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121 | (94) |
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122 | (2) |
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Numerical Solution of Steady-State Conduction |
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124 | (42) |
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One-Dimensional Conduction |
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124 | (1) |
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124 | (3) |
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Finite Difference Approximation of the Boundary Conditions |
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127 | (3) |
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An Example: Numerical Solution of Heat Transfer in an Extended Surface |
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130 | (2) |
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132 | (3) |
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135 | (2) |
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Multidimensional Steady-State Conduction |
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137 | (2) |
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Finite Difference Formulation |
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139 | (5) |
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Solution: Iterative and Direct Methods |
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144 | (5) |
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Improvement in Accuracy of Numerical Results |
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149 | (1) |
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Finite Element Formulation |
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150 | (2) |
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Variable Property and Other Considerations |
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152 | (14) |
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Numerical Solution of Unsteady-State Conduction |
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166 | (37) |
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One-Dimensional Unsteady-State Conduction |
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168 | (1) |
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169 | (9) |
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178 | (2) |
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Numerical Approximation of Lumped Mass and Semi-infinite Solids |
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180 | (4) |
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Multidimensional Unsteady-State Conduction |
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184 | (5) |
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Numerical Methods for Time-Varying Boundary Conditions |
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189 | (6) |
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195 | (3) |
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198 | (5) |
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203 | (3) |
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206 | (9) |
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207 | (2) |
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209 | (6) |
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Numerical Methods for Convection Heat Transfer |
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215 | (138) |
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217 | (3) |
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Computation of Forced Convection with Constant Fluid Properties |
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220 | (88) |
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Inviscid Flow: Introduction to Stream Function and Vorticity |
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221 | (7) |
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Equations for Viscous Flow: Primitive and Derived Variables |
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228 | (1) |
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Linear Viscous Flow (Creeping Flow) |
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229 | (4) |
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Computation of Boundary Layer Flows |
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233 | (1) |
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Similarity Solution: Ordinary Differential Equations |
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234 | (4) |
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Finite Difference Approach |
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238 | (12) |
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Numerical Solution of the Full Equations |
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250 | (2) |
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252 | (1) |
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Upwind, Hybrid and Other Lower-Order Differencing Schemes |
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253 | (3) |
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Higher-Order Differencing Schemes for Convection |
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256 | (3) |
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Other Numerical Methods and Considerations |
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259 | (6) |
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265 | (1) |
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Primitive Variables Approach |
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266 | (3) |
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269 | (5) |
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Finite Difference Considerations of the Conservative Form |
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274 | (5) |
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Concluding Remarks on Flow Calculations |
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279 | (1) |
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280 | (1) |
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280 | (4) |
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284 | (5) |
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289 | (8) |
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Numerical Solution of Turbulent Flows |
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297 | (11) |
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Computation of Natural Convection Flow and Transport |
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308 | (17) |
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310 | (5) |
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Finite Difference Methods |
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315 | (9) |
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Additional Considerations |
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324 | (1) |
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Convection with Variable Fluid Properties |
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325 | (5) |
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330 | (8) |
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Discretization and Interpolation Functions |
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331 | (1) |
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331 | (2) |
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Element Equations and Assembly |
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333 | (2) |
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335 | (1) |
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Examples and Other Considerations |
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335 | (2) |
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Comparison of Finite Element and Finite Difference Methods |
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337 | (1) |
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338 | (15) |
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339 | (6) |
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345 | (8) |
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Numerical Methods for Radiation Heat Transfer |
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353 | (62) |
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354 | (5) |
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Numerical Techniques for Enclosures with Diffuse-Gray Surfaces |
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359 | (11) |
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359 | (5) |
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364 | (1) |
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Additional Considerations |
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365 | (1) |
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Computation of View Factors |
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365 | (1) |
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Temperature Dependence of Surface Properties |
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366 | (3) |
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369 | (1) |
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Nonuniform Irradiation and Emission: Discrete Integral Equations |
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370 | (9) |
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Numerical Solution of Radiation in the Presence of Other Modes |
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379 | (15) |
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Combined Modes at Boundaries: Nonparticipating Media |
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380 | (5) |
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385 | (9) |
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Other Methods For Participating Media |
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394 | (9) |
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403 | (3) |
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406 | (9) |
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407 | (2) |
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409 | (6) |
Part 3 Combined Modes and Process Applications |
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415 | (68) |
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Applications of Computational Heat Transfer |
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417 | (66) |
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Numerical Simulation of Thermal Systems in Manufacturing |
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418 | (24) |
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Heat Treatment: Temperature Regulation |
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418 | (4) |
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Surface Treatment: Semi-infinite Approximation |
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422 | (2) |
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Continuously Moving Materials: Moving Boundary Effects |
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424 | (3) |
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Melting and Solidification: Phase Change Considerations |
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427 | (9) |
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436 | (6) |
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Numerical Simulation of Environmental Heat Transfer Problems |
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442 | (26) |
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Cooling Ponds: Periodic Processes |
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442 | (5) |
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Recirculating Flows in Enclosed Spaces |
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447 | (7) |
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Fire-Induced Flows in Partial Enclosures |
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454 | (3) |
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Free Boundary Flows and Other Problems |
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457 | (9) |
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466 | (2) |
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Computer Simulation and Computer-Aided Design of Thermal Systems |
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468 | (15) |
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468 | (2) |
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Example of Computer Simulation of a Thermal System |
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470 | (5) |
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475 | (4) |
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479 | (4) |
Appendices |
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483 | (50) |
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A Finite Difference Approximations |
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483 | (4) |
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B Sample Computer Programs |
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487 | (36) |
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B.1 Successive Over-Relaxation (SOR) Method |
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488 | (3) |
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B.2 Tridiagonal Matrix Algorithm (TDMA) or Thomas Algorithm |
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491 | (1) |
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B.3 Gauss-Jordan Elimination Method |
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492 | (3) |
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B.4 Forward-Time-Central-Space (FTCS) Method |
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495 | (2) |
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B.5 Crank-Nicolson Method |
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497 | (6) |
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B.6 Newton-Raphson Method |
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503 | (1) |
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B.7 Finite Difference Method for ODEs |
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504 | (3) |
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507 | (5) |
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B.9 Alternating-Direction-Implicit (ADI) Method |
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512 | (11) |
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523 | (10) |
Nomenclature |
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533 | (4) |
Index |
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537 | |