Preface ........................................................ v
Dual-Phase-Lagging and Porous-Medium Heat Conduction
Processes ....................................................... 1
Liqiu Wang, Mingtian Xu, and Xiaohao Wei
1. Introduction ................................................. 1
2. Well-Posedness ............................................... 3
2.1. Existence ............................................... 4
2.2. Inequality .............................................. 6
2.3. Uniqueness .............................................. 7
2.4. Stability ............................................... 9
3. Solution Structure .......................................... 13
4. Thermal Oscillation and Resonance ........................... 17
4.1. Thermal Oscillation .................................... 17
4.2. Resonance .............................................. 25
5. Equivalence Between Dual-Phase-Lagging and Porous-Medium
Heat Conduction Processes ................................... 27
6. Concluding Remarks .......................................... 35
References .................................................. 36
Heat Transfer Analysis Under Local Thermal Non-equilibrium
Conditions ..................................................... 39
A. Haji-Sheikh and W.J. Minkowycz
1. Introduction ................................................ 39
2. Theoretical Model ........................................... 40
2.1. Energy Equation ........................................ 40
2.2. Physical Interpretation of Relaxation Times ............ 43
3. Temperature Field with Stationary Fluids .................... 45
3.1. Temperature Solutions .................................. 46
4. Temperature Field with Moving Fluid ......................... 55
5. Remarks and Discussions ..................................... 58
References .................................................. 61
General Heterogeneity Effects on the Onset of Convection
in a Porous Medium ............................................. 63
D.A. Nield
1. Introduction ................................................ 63
2. Analysis .................................................... 65
3. Results and Discussion ...................................... 70
3.1. Thermal Convection in a Square Enclosure ............... 70
3.2. Thermal Convection in a Tall Rectangular Enclosure ..... 71
3.3. Double Diffusive Convection in a Square Enclosure ...... 71
4. Non-Uniform Basic Temperature Gradient ...................... 73
5. Bidisperse Porous Medium .................................... 75
6. Enclosure of Variable Width ................................. 77
7. Strong Heterogeneity ........................................ 81
8. Concluding Remarks .......................................... 83
References .................................................. 83
The Instability of Unsteady Boundary Layers in Porous Media .... 85
D.A.S. Rees, A. Selim, and J.P. Ennis-King
1. Introduction ................................................ 85
2. Background .................................................. 86
3. Governing Equations ......................................... 87
4. Linearised Stability Equations .............................. 89
5. Comparison of the Methods Used .............................. 90
5.1. Quasi-Static Analyses .................................. 90
5.2. Local Rayleigh Number Analysis ......................... 92
5.3. Energy Stability Analysis .............................. 94
5.4. Amplitude Theory ....................................... 94
5.5. Discussion ............................................. 98
6. Isolated Small-Amplitude Disturbances ....................... 98
7. Other Linear Systems ....................................... 100
7.1. Anisotropy ............................................ 100
7.2. Ramped Heating ........................................ 100
7.3. Internal Heat Sources ................................. 101
7.4. Local Thermal Nonequilibrium .......................... 101
8. Nonlinear Studies .......................................... 101
9. Conclusion ................................................. 108
References ................................................. 109
Analytical Transition to Weak Turbulence and Chaotic Natural
Convection in Porous Media .................................... 1ll
Peter Vadasz
1. Introduction ............................................... 11l
2. Problem Formulation and Reduced Set of Equations ........... 113
3. Analytical Solution ........................................ 117
4. Computational and Numerical Solutions ...................... 121
5. Compatible Initial Conditions .............................. 122
6. Results and Discussion ..................................... 124
7. Conclusions ................................................ 130
References ................................................. 130
Natural Convection in Gravity-Modulated Porous Layers ......... 133
Saneshan Govender
1. Introduction ............................................... 133
2. Problem Formulation ........................................ 134
3. Linear Stability Analysis .................................. 136
4. Weak Non-linear Anlaysis ................................... 140
5. Pendulum Analogy ........................................... 144
6. Conclusion ................................................. 147
References ................................................. 147
Thermal Vibrational Convection in a Porous Medium Saturated
by a Pure or Binary Fluid ..................................... 149
Yazdan Pedramrazi, Marie-Catherine Charrier-Mojtabi and
Abdelkader Mojtabi
1. Introduction ............................................... 149
1.1. What is Thermal Vibration? ............................ 149
1.2. A Brief History of Thermal Vibration in Porous
Media: Suppression of Motion and Generation of
Motion ................................................ 150
2. The Effect of Vibration in Horizontal Porous Layer
Saturated by a Pure Fluid .................................. 151
2.1. Infinite Horizontal Porous Layer ...................... 151
2.2. Confined Cavity ....................................... 163
2.3. Some Key Results ...................................... 166
3. Influence of Mechanical Vibration on a Porous Media
Saturated by a Binary Mixture .............................. 167
3.1. Problem Description ................................... 168
3.2. Linear Stability Analysis ............................. 169
3.3. Numerical Simulations in a Confined Cavity
(A = 1 and A = 10) .................................... 172
3.4. Conclusions ........................................... 176
References ................................................. 178
New Developments in Bioconvection in Porous Media:
Bioconvection Plumes, Bio-Thermal Convection, and
Effects of Vertical Vibration ................................. 181
A.V. Kuznetsov
1. Introduction ............................................... 181
2. Numerical Modeling of a Falling Plume in a Suspension of
Oxytactic Microorganisms ................................... 183
2.1. Problem Description ................................... 183
2.2. Governing Equations ................................... 184
2.3. Numerical Results ..................................... 185
3. The Onset of Bio-thermal Convection in a Porous Medium ..... 186
3.1. The Onset of Bio-thermal Convection in a Suspension
of Gyrotactic Microorganisms .......................... 189
3.2. The Onset of Bio-thermal Convection in a Suspension
of Oxytactic Microorganisms ........................... 197
4. Effect of Vertical Vibration on the Onset of
Bioconvection in a Horizontal Porous Layer of Finite
Depth ...................................................... 206
4.1. Problem Description ................................... 206
4.2. Governing Equations ................................... 206
4.3. Boundary Conditions ................................... 208
4.4. Basic State ........................................... 209
4.5. Linear Stability Analysis ............................. 209
4.6. Numerical Results ..................................... 212
References ................................................. 215
Macromolecular Transport in Arterial Walls: Current
and Future Directions ......................................... 219
K. Khanafer and K. Vafai
1. Introduction ............................................... 219
2. Mathematical Models ........................................ 220
2.1. Wall-Free Model ....................................... 220
2.2. Fluid-Wall Model ...................................... 221
2.3. Multi-Layers Model .................................... 223
2.4. Other Models .......................................... 224
3. Physiological Parameters ................................... 225
3.1. Endothelium and Internal Elastic Lamina ............... 226
3.2. Intima and Media ...................................... 226
4. Mathematical Model of Macromolecule Transport within the
Arterial Wall .............................................. 227
4.1. Lumen ................................................. 227
4.2. Endothelium and Internal Elastic Lamina ............... 228
4.3. Intima and Media ...................................... 229
5. Future Directions .......................................... 232
References ................................................. 233
Flow and Heat Transfer in Biological Tissues: Application
of Porous Media Theory ........................................ 237
Khalil Khanafer, Abdalla AlAmiri, loan Pop, and Joseph
L. Bull
1. Brain Aneurysm ............................................. 237
1.1. Introduction .......................................... 237
1.2. Clinical and Experimental Studies Associated with
the Treatment of Aneurysms Using Stent Implantation
and Coil Placement .................................... 238
1.3. Computational Studies Associated with Combined Use
of Stents and Coils for the Treatment of Cerebral
Aneurysms ............................................. 239
1.4. Mathematical Formulation .............................. 241
2. Flow and Heat Transfer in Biological Tissues ............... 242
2.1. Introduction .......................................... 242
2.2. Thermal Models for Blood Perfused Tissues ............. 244
2.3. Mathematical Modeling of Bioheat Equation Using
Porous Media Theory ................................... 249
3. Tissue Engineering ......................................... 251
3.1. Introduction .......................................... 251
3.2. Porous Scaffolds for Tissue Engineering ............... 251
References ................................................. 256
Metal Foams as Passive Thermal Control Systems ................ 261
Shankar Krishnan, Jayathi Y. Murthy, and Suresh
V. Garimella
1. Introduction ............................................... 261
2. Mathematical Formulation and Numerical Modeling ............ 263
3. Results and Discussion ..................................... 266
3.1. Melt Volume Fraction .................................. 272
3.2. Wall Nusselt Number ................................... 274
4. Summary .................................................... 278
References ................................................. 281
Nanofluid Suspensions and Bi-composite Media as Derivatives
of Interface Heat Transfer Modeling in Porous Media ........... 283
Peter Vadasz
1. Introduction ............................................... 283
2. Problem Formulation and the Apparent Paradox ............... 285
3. Solution by the Eigenvectors Method ........................ 288
4. Solution by the Elimination Method ......................... 292
5. Resolution of the Paradox .................................. 295
6. Experimental Measurement of the Effective Thermal
Conductivity of a Porous Medium via the Transient Hot
Wire (THW) Method .......................................... 301
6.1. Background ............................................ 301
6.2. Concepts and Methods .................................. 301
7. Application of the Heat Conduction in Porous Media
to Nanofluid Suspensions ................................... 314
7.1. Problem Formulation ................................... 316
7.2. Solution and Correction of the THW Results ............ 318
7.3. Results, Discussion and Conclusions ................... 319
References ................................................. 323
Index ......................................................... 327
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