Transport Phenomena in Porous Media III (eBook)

Cover 1
Preface 6
Contributors 14
Contents 18
CHAPTER 1. THE DOUBLE-DECOMPOSITION CONCEPT FOR TURBULENT TRANSPORT IN POROUS MEDIA 28
1.1 Introduction 28
1.2 Instantaneous local transport equations 29
1.3 Time- and volume-averaging procedures 31
1.4 Time-averaged transport equations 32
1.5 The double-decomposition concept 33
1.6 Turbulent transport 36
1.7 Heat transfer 47
1.8 Mass transfer 55
1.9 Concluding remarks 58
References 58
CHAPTER 2. HEAT TRANSFER IN BIDISPERSE POROUS MEDIA 61
2.1 Introduction 61
2.2 Determination of transport properties 62
2.3 Two-phase flow and boiling heat transfer 64
2.4 Dispersion 64
2.5 Two-velocity model 64
2.6 Two-temperature model 67
2.7 Forced convection in a channel between plane parallel walls 67
2.8 Conclusions 85
References 86
CHAPTER 3. FROM CONTINUUM TO POROUS–CONTINUUM: THE VISUAL RESOLUTION IMPACT ON MODELING NATURAL CONVECTION IN HETEROGENEOUS MEDIA 87
3.1 Introduction 88
3.2 Horizontal heating 90
3.3 Heat-generating blocks 107
3.4 Conclusions 119
References 121
CHAPTER 4. INTEGRAL TRANSFORMS FOR NATURAL CONVECTION IN CAVITIES FILLED WITH POROUS MEDIA 124
4.1 Introduction 125
4.2 Two-dimensional problem 126
4.3 Three-dimensional problem 130
4.4 Results and discussion 135
4.5 Conclusions 144
References 144
CHAPTER 5. A POROUS MEDIUM APPROACH FOR THE THERMAL ANALYSIS OF HEAT TRANSFER DEVICES 147
5.1 Introduction 147
5.2 Thermal analysis of microchannel heat sinks 149
5.3 Thermal analysis of internally finned tubes 163
5.4 Conclusions 171
References 172
CHAPTER 6. LOCAL THERMAL NON-EQUILIBRIUM IN POROUS MEDIUM CONVECTION 174
6.1 Introduction 174
6.2 Governing equations 175
6.3 Conditions for the validity of LTE 179
6.4 Free convection boundary layers 181
6.5 Forced convection past a hot circular cylinder 188
6.6 Stability of free convection 193
6.7 Conclusions 197
References 197
CHAPTER 7. THREE-DIMENSIONAL NUMERICAL MODELS FOR PERIODICALLY FULLY-DEVELOPED HEAT AND FLUID FLOWS WITHIN POROUS MEDIA 201
7.1 Introduction 201
7.2 Three-dimensional numerical model for isotropic porous media 203
7.3 Quasi-three-dimensional numerical model for anisotropic porous media 209
7.4 Large eddy simulation of turbulent flow in porous media 217
7.5 Conclusions 225
References 226
CHAPTER 8. ENTROPY GENERATION IN POROUS MEDIA 228
8.1 Introduction 228
8.2 A short history of the second law of thermodynamics 229
8.3 Governing equations 231
8.4 Entropy generation in a porous cavity and channel 234
8.5 Conclusions 250
References 251
CHAPTER 9. THERMODIFFUSION IN POROUS MEDIA 254
9.1 Introduction 254
9.2 Literature review 255
9.3 Fundamental equations of thermodiffusion 250
9.4 Fundamental equations in porous media 263
9.5 Numerical solution technique 264
9.6 Mesh sensitivity analysis 266
9.7 Results and discussion 268
9.8 Conclusions 284
References 285
CHAPTER 10. EFFECT OF VIBRATION ON THE ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN POROUS MEDIA 288
10.1 Introduction 289
10.2 Mathematical formulation 290
10.3 Linear stability analysis 295
10.4 Comparison of the results with fluid media 302
10.5 Numerical method 303
10.6 The onset of thermo-solutal convection under the influence of vibration without Soret effect 307
10.7 Conclusions 310
References 311
CHAPTER 11. COMBUSTION IN POROUS MEDIA: FUNDAMENTALS AND APPLICATIONS 314
11.1 Introduction 314
11.2 Previous works 316
11.3 Characteristics of combustion in porous media 317
11.4 Applications 318
11.5 Porous burners 320
11.6 Mathematical modeling 321
11.7 Results and discussion 324
11.8 Radial burner 325
11.9 Conclusions 328
11.10 Possible future work 328
References 329
CHAPTER 12. REACTIVE TRANSPORT IN POROUS MEDIA„CONCEPTS AND NUMERICAL APPROACHES 332
12.1 Introduction 333
12.2 Quantitative geochemistry 334
12.3 Analytical description of reactive transport 337
12.4 Examples 340
12.5 Numerical approaches 345
12.6 Numerical errors 349
12.7 Implementation in MATLAB 351
12.8 Example models 352
12.9 Conclusions 363
References 364
CHAPTER 13. NUMERICAL AND ANALYTICAL ANALYSIS OF THE THERMOSOLUTAL CONVECTION IN AN ANNULAR FIELD: EFFECT OF THERMODIFFUSION 368
13.1 Introduction 369
13.2 Mathematical model 369
13.3 Analytical solution 373
13.4 Results and discussion 377
13.5 Conclusions 389
References 390
CHAPTER 14. PORE-SCALE TRANSPORT PHENOMENA IN POROUS MEDIA 393
14.1 Introduction 393
14.2 Conjugated transport phenomena with pore structure 394
14.3 Transport–reaction phenomena 401
14.4 Boiling and interfacial transport 406
14.5 Freezing and thawing 412
14.6 Two-phase flow behavior 417
14.7 Conclusion 423
References 423
CHAPTER 15. DYNAMIC SOLIDIFICATION IN A WATER-SATURATED POROUS MEDIUM COOLED FROM ABOVE 426
15.1 Introduction 427
15.2 Mathematical formulation 428
15.3 Numerical results 434
15.4 Experimental results 436
15.5 Conclusion 442
References 443
CHAPTER 16. APPLICATION OF FLUID FLOWS THROUGH POROUS MEDIA IN FUEL CELLS 445
16.1 Introduction 446
16.2 Operation principles of fuel cells 446
16.3 Governing equations for the fluid flows in porous electrodes 450
16.4 Multicomponent gas transport in porous electrodes 454
16.5 CFD model predictions of fuel cells 458
16.6 Concluding remarks 465
References 466
CHAPTER 17. MODELLING THE EFFECTS OF FAULTS AND FRACTURES ON FLUID FLOW IN PETROLEUM RESERVOIRS 468
17.1 Introduction 469
17.2 Single and multiphase flow 470
17.3 Modelling flow in petroleum reservoirs where faults act as barriers 473
17.4 Modelling flow in reservoirs where faults and fractures act as conduits 490
17.5 Discussion and conclusions 498
References 499