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TECHNICAL PAPERS: Porous Media

Analysis of Variable Porosity, Thermal Dispersion, and Local Thermal Nonequilibrium on Free Surface Flows Through Porous Media

[+] Author and Article Information
Bader Alazmi

Department of Mechanical Engineering, Kuwait University, P.O. Box 5969, Safat 13060 Kuwait

Kambiz Vafai

University of California, Riverside, Department of Mechanical Engineering, A363 Bourns Hall, Riverside, CA 92521-0425

J. Heat Transfer 126(3), 389-399 (Jun 16, 2004) (11 pages) doi:10.1115/1.1723470 History: Received April 19, 2003; Revised January 21, 2004; Online June 16, 2004
Copyright © 2004 by ASME
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References

Muskat, M., 1937, The Flow of Homogeneous Fluids Through Porous Media, Edwards, Ann Arbor, MI.
Srinivasan,  V., and Vafai,  K., 1994, “Analysis of Linear Encroachment in Two-Immiscible Fluid Systems in a Porous Medium,” ASME J. Fluids Eng., 116, pp. 135–139.
Chen,  S. C., and Vafai,  K., 1996, “Analysis of Free Surface Momentum and Energy Transport in Porous Media,” Numer. Heat Transfer, Part A, 29, pp. 281–296.
Chen,  S. C., and Vafai,  K., 1997, “Non-Darcian Surface Tension Effects on Free Surface Transport in Porous Media,” Numer. Heat Transfer, Part A, 31, pp. 235–254.
Vafai,  K., 1984, “Convective Flow and Heat Transfer in Variable-Porosity Media,” J. Fluid Mech., 147, pp. 233–259.
Vafai,  K., 1986, “Analysis of the Channeling Effect in Variable Porosity Media,” ASME J. Energy Resour. Technol., 108, pp. 131–139.
Vafai,  K., Alkire,  R. L., and Tien,  C. L., 1985, “An Experimental Investigation of Heat Transfer in Variable Porosity Media,” ASME J. Heat Transfer, 107, pp. 642–647.
Amiri,  A., and Vafai,  K., 1994, “Analysis of Dispersion Effects and Non-Thermal Equilibrium, Non-Darcian, Variable Porosity, Incompressible Flow Through Porous Media,” Int. J. Heat Mass Transfer, 37, pp. 939–954.
Hwang,  G. J., Wu,  C. C., and Chao,  C. H., 1995, “Investigation of Non-Darcian Forced Convection in an Asymmetrically Heated Sintered Porous Channel,” ASME J. Heat Transfer, 117, pp. 725–732.
Lee,  D. Y., and Vafai,  K., 1999, “Analytical Characterization and Conceptual Assessment of Solid and Fluid Temperature Differentials in Porous Media,” Int. J. Heat Mass Transfer, 42, pp. 423–435.
Quintard,  M., and Whitaker,  S., 1995, “Local Thermal Equilibrium for Transient Heat Conduction: Theory and Comparison With Numerical Experiments,” Int. J. Heat Mass Transfer, 38, pp. 2779–2796.
Quintard,  M., Kaviany,  M., and Whitaker,  S., 1997, “Two-Medium Treatment of Heat Transfer in Porous Media: Numerical Results for Effective Properties,” Adv. Water Resour., 20, pp. 77–94.
Quintard,  M., and Whitaker,  S., 1995, “The Mass Flux Boundary Condition at a Moving Fluid-Fluid Interface,” Ind. Eng. Chem. Res., 34, pp. 3508–3513.
Quintard,  M., and Whitaker,  S., 1999, “Dissolution of an Immobile Phase During Flow in Porous Media,” Ind. Eng. Chem. Res., 38, pp. 833–844.
Vafai,  K., and Tien,  C. L., 1981, “Boundary and Inertia Effects on Flow and Heat Transfer in Porous Media,” Int. J. Heat Mass Transfer, 24, pp. 195–203.
Vafai,  K., and Kim,  S. J., 1989, “Forced Convection in a Channel Filled With a Porous Medium: An Exact Solution,” ASME J. Heat Transfer, 111, pp. 1103–1106.
Sharif,  N. H., and Wiberg,  N. E., 2002, “Adaptive ICT Procedure for Non-Linear Seepage Flows With Free Surface in Porous Media,” Commun. Numer. Methods Eng., 18, pp. 161–176.
Vafai,  K., and Alazmi,  B., 2003, “On the Line Encroachment in Two-Immiscible Fluid Systems in a Porous Medium,” ASME J. Fluids Eng., 125, pp. 738–739.

Figures

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Schematic diagram of the free surface front and the corresponding coordinate system
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Comparison between the present results and the numerical results in Chen and Vafai 3: (a) temporal free surface distribution using constant Darcy number; and (b) temperature contours for Rek=5.72×10−4,Da=1.0×10−6 at t=0.5 s
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Progress of the interfacial front for (a) constant porosity category with Da=1.0×10−6, ε=0.8, Λ=10.0, and Re=100; and (b) variable porosity category with ε=0.45,b=0.98,c=2.0, Re=100, and dP/H=0.05
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Effect of Darcy number for the constant porosity category using Λ=10.0, Re=100 and ε=0.8 on (a) the temporal free surface front; and (b) the total time to reach the channel exit (τmax)
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Effect of Inertia parameter for the constant porosity category using ε=0.8, Da=1.0×10−6 and Re=100: (a) On the temporal free surface front; and (b) On the total time to reach the channel exit (τmax)
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Effect of Reynolds number for the constant porosity category using ε=0.8, Da=1.0×10−6 and Λ=10.0: (a) the temporal free surface front; and (b) the total time to reach the channel exit (τmax)
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Effect of Reynolds number for the variable porosity category using ε=0.45,b=0.98,c=2.0, and dP/H=0.05 on (a) the temporal free surface front; and (b) the total time to reach the channel exit (τmax)
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Effect of particle diameter for the variable porosity category using ε=0.45,b=0.98,c=2.0, and Re=100 on (a) the temporal free surface front; and (b) the total time to reach the channel exit (τmax)
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Temporal dimensionless temperature profiles including thermal dispersion effects, ε=0.8, Da=10−6, Re=100, Λ=10, κ=15.0, and dP/H=0.05: (a) τ=0.25, (b) τ=0.5, and (c) τ=τmax
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Temporal dimensionless temperature profiles excluding thermal dispersion effects, ε=0.8, Da=10−6, Re=100, Λ=10, κ=15.0, and dP/H=0.05: (a) τ=0.25, (b) τ=0.5, and (c) τ=τmax
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Effect of porosity for the thermal dispersion category using Da=10−6, Re=100, Λ=10, κ=15.0, and dP/H=0.05 on (a) dimensionless temperature profiles using ε=0.7, (b) dimensionless temperature profiles using ε=0.9, and (c) total Nusselt number
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Effect of Darcy number for the thermal dispersion category using ε=0.8, Re=100, Λ=10, κ=15.0, and dP/H=0.05 on (a) dimensionless temperature profiles using Da=10−4, (b) dimensionless temperature profiles using Da=10−8, and (c) total Nusselt number
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Effect of Reynolds number for the thermal dispersion category using ε=0.8 Da=10−6, Λ=10, κ=15.0, and dP/H=0.05 on (a) dimensionless temperature profiles using Re=50, (b) dimensionless temperature profiles using Re=150, and (c) total Nusselt number
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Effect of particle diameter for the thermal dispersion category using ε=0.8 Da=10−6, Re=100, Λ=10, and κ=15.0 on (a) dimensionless temperature profiles using dP/H=0.01, (b) dimensionless temperature profiles using dP/H=0.1, and (c) total Nusselt number
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Effect of solid-to-fluid thermal conductivity ratio, κ, for the thermal dispersion category using ε=0.8 Da=10−6, Re=100, Λ=10, and dP/H=0.05 on (a) dimensionless temperature profiles using κ=5.0, (b) dimensionless temperature profiles using κ=30.0, and (c) total Nusselt number
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Dimensionless temperature profiles for the LTNE category using ε=0.8, Da=10−6, Re=100, Λ=10, κ=15.0, and dP/H=0.05: (a) fluid phase; and (b) solid phase
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Dimensionless temperature profiles for the LTNE category using ε=0.9, Da=10−8, Re=200, Λ=100, κ=5.0, and dP/H=0.1: (a) fluid phase; and (b) solid phase
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Effect of porosity on average Nusselt numbers for the LTNE category, Da=10−6, Re=100, Λ=10, κ=15.0, and dP/H=0.05: (a) excluding thermal dispersion effects; and (b) including thermal dispersion effects
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Effect of Darcy number on average Nusselt numbers for the LTNE category, ε=0.8, Re=100, Λ=10, κ=15.0, and dP/H=0.05: (a) excluding thermal dispersion effects; and (b) including thermal dispersion effects
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Effect of Inertia parameter on average Nusselt numbers for the LTNE category, ε=0.8, Da=10−6, Re=100, κ=15.0, and dP/H=0.05: (a) excluding thermal dispersion effects; and (b) including thermal dispersion effects

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