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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

Figures

Grahic Jump Location
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)
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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)
Grahic Jump Location
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)
Grahic Jump Location
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)
Grahic Jump Location
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
Grahic Jump Location
Schematic diagram of the free surface front and the corresponding coordinate system
Grahic Jump Location
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
Grahic Jump Location
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
Grahic Jump Location
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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