Emerging topics in heat and mass transfer in porous media : from bioengineering and microelectronics to nanotechnology

This book is a synthesis of emerging topics in heat and mass transfer in porous media. It brings together some of the world leaders in research on transport p- nomena in porous media to present the state of the art of its theory as well as the applicationofthetheoryinemerging?eldssuchasbioengineering,microelectronics and nanotechnology. The well renowned scientists presenting their ?ndings in the review chapters presented are not only among the best world leaders in their ?eld, they also capture the research that is undertaken in all the parts of the globe, from the Far East (Hong-Kong), the Southern Hemisphere (New Zealand and South Africa) to Europe and America. The book is separated into two parts. The ?rst presents the state of the art of the theory of heat and mass transfer in porous media and can be used in both the traditional (underground ?ow, ?ltering and reservoir engineering) as well as in the more recent emerging applications. The second part deals with emerging topics and applications of the theory to bioengineering, microelectronics, and nanotechnology. Traditionally,thetopicoftransportphenomenainporousmediawasalmostexc- sivelyreservedtothe?eldofunderground?ow(water,oil,gas,etc.)and?ltering.With some singular exceptions on applications to drying processes of fabric, the devel- ment of the theory of transport phenomena in porous media was historically driven by the needs of technologies linked to reservoir engineering or civil engineering. A turningpointinthisdevelopmentwasreachedintheearlypartofthesecondhalfinthe twentycenturywhenspecialattentiontoheattransferinporousmediayieldedan- ceedingexpansionofinterest.Thisdevelopmentcontinuedinthetwenty?rstcentury and reached recently such an impressive use in a diverse collection oftechnological applications that created the motivation behind the preparation of this book.

Liqiu Wang and Mingtian Xu and Xiaohao WeiA. Haji-Sheikh and W.J. MinkowyczD.A. NieldD.A.S. Rees and A. Selim and J.P. Ennis-KingPeter VadaszSaneshan GovenderYazdan Pedramrazi and Marie-Catherine Charrier-Mojtabi and Abdelkader MojtabiA.V. KuznetsovK. Khanafer and K. VafaiKhalil Khanafer and Abdalla AlAmiri and Ioan Pop and Joseph L. BullShankar Krishnan and Jayathi Y. Murthy and Suresh V. GarimellaPeter Vadasz

Preface	p. v
Dual-Phase-Lagging and Porous-Medium Heat Conduction Processes	p. 1
1 Introduction	p. 1
2 Well-Posedness	p. 3
2.1 Existence	p. 4
2.2 Inequality	p. 6
2.3 Uniqueness	p. 7
2.4 Stability	p. 9
3 Solution Structure	p. 13
4 Thermal Oscillation and Resonance	p. 17
4.1 Thermal Oscillation	p. 17
4.2 Resonance	p. 25
5 Equivalence Between Dual-Phase-Lagging and Porous-Medium Heat Conduction Processes	p. 27
6 Concluding Remarks	p. 35
References	p. 36
Heat Transfer Analysis Under Local Thermal Non-equilibrium Conditions	p. 39
1 Introduction	p. 39
2 Theoretical Model	p. 40
2.1 Energy Equation	p. 40
2.2 Physical Interpretation of Relaxation Times	p. 43
3 Temperature Field with Stationary Fluids	p. 45
3.1 Temperature Solutions	p. 46
4 Temperature Field with Moving Fluid	p. 55
5 Remarks and Discussions	p. 58
References	p. 61
General Heterogeneity Effects on the Onset of Convection in a Porous Medium	p. 63
1 Introduction	p. 63
2 Analysis	p. 65
3 Results and Discussion	p. 70
3.1 Thermal Convection in a Square Enclosure	p. 70
3.2 Thermal Convection in a Tall Rectangular Enclosure	p. 71
3.3 Double Diffusive Convection in a Square Enclosure	p. 71
4 Non-Uniform Basic Temperature Gradient	p. 73
5 Bidisperse Porous Medium	p. 75
6 Enclosure of Variable Width	p. 77
7 Strong Heterogeneity	p. 81
8 Concluding Remarks	p. 83
References	p. 83
The Instability of Unsteady Boundary Layers in Porous Media	p. 85
1 Introduction	p. 85
2 Background	p. 86
3 Governing Equations	p. 87
4 Linearised Stability Equations	p. 89
5 Comparison of the Methods Used	p. 90
5.1 Quasi-Static Analyses	p. 90
5.2 Local Rayleigh Number Analysis	p. 92
5.3 Energy Stability Analysis	p. 94
5.4 Amplitude Theory	p. 94
5.5 Discussion	p. 98
6 Isolated Small-Amplitude Disturbances	p. 98
7 Other Linear Systems	p. 100
7.1 Anisotropy	p. 100
7.2 Ramped Heating	p. 100
7.3 Internal Heat Sources	p. 101
7.4 Local Thermal Nonequilibrium	p. 101
8 Nonlinear Studies	p. 101
9 Conclusion	p. 108
References	p. 109
Analytical Transition to Weak Turbulence and Chaotic Natural Convection in Porous Media	p. 111
1 Introduction	p. 111
2 Problem Formulation and Reduced Set of Equations	p. 113
3 Analytical Solution	p. 117
4 Computational and Numerical Solutions	p. 121
5 Compatible Initial Conditions	p. 122
6 Results and Discussion	p. 124
7 Conclusions	p. 130
References	p. 130
Natural Convection in Gravity-Modulated Porous Layers	p. 133
1 Introduction	p. 133
2 Problem Formulation	p. 134
3 Linear Stability Analysis	p. 136
4 Weak Non-linear Anlaysis	p. 140
5 Pendulum Analogy	p. 144
6 Conclusion	p. 147
References	p. 147
Thermal Vibrational Convection in a Porous Medium Saturated by a Pure or Binary Fluid	p. 149
1 Introduction	p. 149
1.1 What is Thermal Vibration?	p. 149
1.2 A Brief History of Thermal Vibration in Porous Media: Suppression of Motion and Generation of Motion	p. 150
2 The Effect of Vibration in Horizontal Porous Layer Saturated by a Pure Fluid	p. 151
2.1 Infinite Horizontal Porous Layer	p. 151
2.2 Confined Cavity	p. 163
2.3 Some Key Results	p. 166
3 Influence of Mechanical Vibration on a Porous Media Saturated by a Binary Mixture	p. 167
3.1 Problem Description	p. 168
3.2 Linear Stability Analysis	p. 169
3.3 Numerical Simulations in a Confined Cavity (A = 1 and A = 10)	p. 172
3.4 Conclusions	p. 176
References	p. 178
New Developments in Bioconvection in Porous Media: Bioconvection Plumes, Bio-Thermal Convection, and Effects of Vertical Vibration	p. 181
1 Introduction	p. 181
2 Numerical Modeling of a Falling Plume in a Suspension of Oxytactic Microorganisms	p. 183
2.1 Problem Description	p. 183
2.2 Governing Equations	p. 184
2.3 Numerical Results	p. 185
3 The Onset of Bio-thermal Convection in a Porous Medium	p. 186
3.1 The Onset of Bio-thermal Convection in a Suspension of Gyrotactic Microorganisms	p. 189
3.2 The Onset of Bio-thermal Convection in a Suspension of Oxytactic Microorganisms	p. 197
4 Effect of Vertical Vibration on the Onset of Bioconvection in a Horizontal Porous Layer of Finite Depth	p. 206
4.1 Problem Description	p. 206
4.2 Governing Equations	p. 206
4.3 Boundary Conditions	p. 208
4.4 Basic State	p. 209
4.5 Linear Stability Analysis	p. 209
4.6 Numerical Results	p. 212
References	p. 215
Macromolecular Transport in Arterial Walls: Current and Future Directions	p. 219
1 Introduction	p. 219
2 Mathematical Models	p. 220
2.1 Wall-Free Model	p. 220
2.2 Fluid-Wall Model	p. 221
2.3 Multi-Layers Model	p. 223
2.4 Other Models	p. 224
3 Physiological Parameters	p. 225
3.1 Endothelium and Internal Elastic Lamina	p. 226
3.2 Intima and Media	p. 226
4 Mathematical Model of Macromolecule Transport with the Arterial Wall	p. 227
4.1 Lumen	p. 227
4.2 Endothelium and Internal Elastic Lamina	p. 228
4.3 Intima and Media	p. 229
5 Future Directions	p. 232
References	p. 233
Flow and Heat Transfer in Biological Tissues: Application of Porous Media Theory	p. 237
1 Brain Aneurysm	p. 237
1.1 Introduction	p. 237
1.2 Clinical and Experimental Studies Associated with the Treatment of Aneurysms Using Stent Implantation and Coil Placement	p. 238
1.3 Computational Studies Associated with Combined Use of Stents and Coils for the Treatment of Cerebral Aneurysms	p. 239
1.4 Mathematical Formulation	p. 241
2 Flow and Heat Transfer in Biological Tissues	p. 242
2.1 Introduction	p. 242
2.2 Thermal Models for Blood Perfused Tissues	p. 244
2.3 Mathematical Modeling of Bioheat Equation Using Porous Media Theory	p. 249
3 Tissue Engineering	p. 251
3.1 Introduction	p. 251
3.2 Porous Scaffolds for Tissue Engineering	p. 251
References	p. 256
Metal Foams as Passive Thermal Control Systems	p. 261
1 Introduction	p. 261
2 Mathematical Formulation and Numerical Modeling	p. 263
3 Results and Discussion	p. 266
3.1 Melt Volume Fraction	p. 272
3.2 Wall Nusselt Number	p. 274
4 Summary	p. 278
References	p. 281
Nanofluid Suspensions and Bi-composite Media as Derivatives of Interface Heat Transfer Modeling in Porous Media	p. 283
1 Introduction	p. 283
2 Problem Formulation and the Apparent Paradox	p. 285
3 Solution by the Eigenvectors Method	p. 288
4 Solution by the Elimination Method	p. 292
5 Resolution of the Paradox	p. 295
6 Experimental Measurement of the Effective Thermal Conductivity of a Porous Medium via the Transient Hot Wire (THW) Method	p. 301
6.1 Background	p. 301
6.2 Concepts and Methods	p. 301
7 Application of the Heat Conduction in Porous Media to Nanofluid Suspensions	p. 314
7.1 Problem Formulation	p. 316
7.2 Solution and Correction of the THW Results	p. 318
7.3 Results, Discussion and Conclusions	p. 319
References	p. 323
Index	p. 327

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