Transport phenomena in porous media. Volume III

Fluid and flow problems in porous media have attracted the attention of industrialists, engineers and scientists from varying disciplines, such as chemical, environmental, and mechanical engineering, geothermal physics and food science. There has been an increasing interest in heat and fluid flows through porous media, making this book a timely and appropriate resource. Each chapter is systematically detailed to be easily grasped by a research worker with basic knowledge of fluid mechanics, heat transfer, and computational and experimental methods. At the same time, the readers will be informed of the most recent research literature in the field, giving it dual usage as both a post-graduate text book and professional reference. Written by the recent directors of the NATO Advanced Study Institute session on 'Emerging Technologies and Techniques in Porous Media' (June 2003), this book is a timely and essential reference for scientists and engineers within a variety of fields Front Cover......Page 1 TRANSPORT PHENOMENA IN POROUS MEDIA......Page 4 Copyright Page......Page 5 Preface......Page 6 Contributors......Page 14 Contents......Page 18 1.1 Introduction......Page 28 1.2 Instantaneous local transport equations......Page 29 1.3 Time- and volume-averaging procedures......Page 31 1.4 Time-averaged transport equations......Page 32 1.5 The double-decomposition concept......Page 33 1.6 Turbulent transport......Page 36 1.7 Heat transfer......Page 47 1.8 Mass transfer......Page 55 References......Page 58 2.1 Introduction......Page 61 2.2 Determination of transport properties......Page 62 2.5 Two-velocity model......Page 64 2.7 Forced convection in a channel between plane parallel walls......Page 67 2.8 Conclusions......Page 85 References......Page 86 CHAPTER 3. FROM CONTINUUM TO POROUS–CONTINUUM: THE VISUAL RESOLUTION IMPACT ON MODELING NATURAL CONVECTION IN HETEROGENEOUS MEDIA......Page 87 3.1 Introduction......Page 88 3.2 Horizontal heating......Page 90 3.3 Heat-generating blocks......Page 107 3.4 Conclusions......Page 119 References......Page 121 CHAPTER 4. INTEGRAL TRANSFORMS FOR NATURAL CONVECTION IN CAVITIES FILLED WITH POROUS MEDIA......Page 124 4.1 Introduction......Page 125 4.2 Two-dimensional problem......Page 126 4.3 Three-dimensional problem......Page 130 4.4 Results and discussion......Page 135 References......Page 144 5.1 Introduction......Page 147 5.2 Thermal analysis of microchannel heat sinks......Page 149 5.3 Thermal analysis of internally finned tubes......Page 163 5.4 Conclusions......Page 171 References......Page 172 6.1 Introduction......Page 174 6.2 Governing equations......Page 175 6.3 Conditions for the validity of LTE......Page 179 6.4 Free convection boundary layers......Page 181 6.5 Forced convection past a hot circular cylinder......Page 188 6.6 Stability of free convection......Page 193 References......Page 197 7.1 Introduction......Page 201 7.2 Three-dimensional numerical model for isotropic porous media......Page 203 7.3 Quasi-three-dimensional numerical model for anisotropic porous media......Page 209 7.4 Large eddy simulation of turbulent flow in porous media......Page 217 7.5 Conclusions......Page 225 References......Page 226 8.1 Introduction......Page 228 8.2 A short history of the second law of thermodynamics......Page 229 8.3 Governing equations......Page 231 8.4 Entropy generation in a porous cavity and channel......Page 234 9.3 Fundamental equations of thermodiffusion......Page 250 References......Page 251 9.1 Introduction......Page 254 9.2 Literature review......Page 255 9.4 Fundamental equations in porous media......Page 263 9.5 Numerical solution technique......Page 264 9.6 Mesh sensitivity analysis......Page 266 9.7 Results and discussion......Page 268 9.8 Conclusions......Page 284 References......Page 285 CHAPTER 10. EFFECT OF VIBRATION ON THE ONSET OF DOUBLE-DIFFUSIVE CONVECTION IN POROUS MEDIA......Page 288 10.1 Introduction......Page 289 10.2 Mathematical formulation......Page 290 10.3 Linear stability analysis......Page 295 10.4 Comparison of the results with fluid media......Page 302 10.5 Numerical method......Page 303 10.6 The onset of thermo-solutal convection under the influence of vibration without Soret effect......Page 307 10.7 Conclusions......Page 310 References......Page 311 11.1 Introduction......Page 314 11.2 Previous works......Page 316 11.3 Characteristics of combustion in porous media......Page 317 11.4 Applications......Page 318 11.5 Porous burners......Page 320 11.6 Mathematical modeling......Page 321 11.7 Results and discussion......Page 324 11.8 Radial burner......Page 325 11.10 Possible future work......Page 328 References......Page 329 CHAPTER 12. REACTIVE TRANSPORT IN POROUS MEDIA—CONCEPTS AND NUMERICAL APPROACHES......Page 332 12.1 Introduction......Page 333 12.2 Quantitative geochemistry......Page 334 12.3 Analytical description of reactive transport......Page 337 12.4 Examples......Page 340 12.5 Numerical approaches......Page 345 12.6 Numerical errors......Page 349 12.7 Implementation in MATLAB......Page 351 12.8 Example models......Page 352 12.9 Conclusions......Page 363 References......Page 364 CHAPTER 13. NUMERICAL AND ANALYTICAL ANALYSIS OF THE THERMOSOLUTAL CONVECTION IN AN ANNULAR FIELD: EFFECT OF THERMODIFFUSION......Page 368 13.2 Mathematical model......Page 369 13.3 Analytical solution......Page 373 13.4 Results and discussion......Page 377 13.5 Conclusions......Page 389 References......Page 390 14.1 Introduction......Page 393 14.2 Conjugated transport phenomena with pore structure......Page 394 14.3 Transport–reaction phenomena......Page 401 14.4 Boiling and interfacial transport......Page 406 14.5 Freezing and thawing......Page 412 14.6 Two-phase flow behavior......Page 417 References......Page 423 CHAPTER 15. DYNAMIC SOLIDIFICATION IN A WATER-SATURATED POROUS MEDIUM COOLED FROM ABOVE......Page 426 15.1 Introduction......Page 427 15.2 Mathematical formulation......Page 428 15.3 Numerical results......Page 434 15.4 Experimental results......Page 436 15.5 Conclusion......Page 442 References......Page 443 CHAPTER 16. APPLICATION OF FLUID FLOWS THROUGH POROUS MEDIA IN FUEL CELLS......Page 445 16.2 Operation principles of fuel cells......Page 446 16.3 Governing equations for the fluid flows in porous electrodes......Page 450 16.4 Multicomponent gas transport in porous electrodes......Page 454 16.5 CFD model predictions of fuel cells......Page 458 16.6 Concluding remarks......Page 465 References......Page 466 CHAPTER 17. MODELLING THE EFFECTS OF FAULTS AND FRACTURES ON FLUID FLOW IN PETROLEUM RESERVOIRS......Page 468 17.1 Introduction......Page 469 17.2 Single and multiphase flow......Page 470 17.3 Modelling flow in petroleum reservoirs where faults act as barriers......Page 473 17.4 Modelling flow in reservoirs where faults and fractures act as conduits......Page 490 17.5 Discussion and conclusions......Page 498 References......Page 499 Fluid and flow problems in porous media have attracted the attention of industrialists, engineers and scientists from varying disciplines, such as chemical, environmental, and mechanical engineering, geothermal physics and food science. There has been a increasing interest in heat and fluid flows through porous media, making this book a timely and appropriate resource.

Each chapter is systematically detailed to be easily grasped by a research worker with basic knowledge of fluid mechanics, heat transfer and computational and experimental methods. At the same time, the readers will be informed of the most recent research literature in the field, giving it dual usage as both a post-grad text book and professional reference.

Written by the recent directors of the NATO Advanced Study Institute session on 'Emerging Technologies and Techniques in Porous Media' (June 2003), this book is a timely and essential reference for scientists and engineers within a variety of fields. Research interest in heat and fluid flow through porous media has experienced an explosive increase of interest over the last few years. Therefore it is very timely to produce this third book in the series and it emphasises the recent advances in both the fundamentals and applications of transport phenomena in porous media. The book contains 17 interrelated chapters on a broad range of technologically important applications.As an up-to-date summary of recent research in heat and fluid flow in porous media, this book will be of interest to individuals in certain areas of applied mathematics, engineering, physics, geology, and chemistry. It is primarily aimed at advanced research workers but it will also be of interest to practising engineers. It was in 1856 that Henry Philibert Gaspard Darcy, then the Inspecteur General de Ponts et Chaussees, or "Dean of the School of Bridges and Roadways," had his report on the public fountains of Dijon, a middle size city in the central-eastern region of France, published [1].