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Research Papers: Porous Media

Transient Aspects of Heat Flux Bifurcation in Porous Media: An Exact Solution

[+] Author and Article Information
Kun Yang

School of Energy and Power Engineering, Huazhong University of Science and Technology, Wuhan 430074, PR China; Department of Mechanical Engineering, University of California, Riverside, Riverside, CA 92521-0425

Kambiz Vafai1

Department of Mechanical Engineering, University of California, Riverside, Riverside, CA 92521-0425vafai@engr.ucr.edu

1

Corresponding author.

J. Heat Transfer 133(5), 052602 (Feb 04, 2011) (12 pages) doi:10.1115/1.4003047 History: Received September 07, 2010; Revised October 31, 2010; Published February 04, 2011; Online February 04, 2011

The transient thermal response of a packed bed is investigated analytically. A local thermal nonequilibrium model is used to represent the energy transport within the porous medium. The heat flux bifurcation phenomenon in porous media is investigated for temporal conditions and two primary types of heat flux bifurcations in porous media are established. Exact solutions are derived for both the fluid and solid temperature distributions for the constant temperature boundary condition. The fluid, solid, and total Nusselt numbers during transient process are analyzed. A heat exchange ratio is introduced to estimate the influence of interactions between the solid and fluid phases through thermal conduction at the wall within the heat flux bifurcation region. A region where the heat transfer can be described without considering the convection contribution in the fluid phase is found. The two-dimensional thermal behavior for the solid and fluid phases is also analyzed. The temporal temperature differential between the solid and fluid is investigated to determine the domain over which the local thermal equilibrium model is valid. In addition, the characteristic time for reaching steady state conditions is evaluated.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 8

Nusselt number distributions for fluid and solid phases for k=0.1, β=0.02, η1=5, and θin=−0.4

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Figure 1

Schematic diagram for transport through a channel filled with a porous medium and the corresponding coordinate system

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Figure 2

Dimensionless temperature distributions for fluid and solid phases for k=0.1, β=0.02, η1=5, ξ=2, and θin=−0.4: (a) τ=0.2, (b) τ=1.0, (c) τ=2.2, (d) τ=3.0, (e) τ=5.0, and (f) steady state

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Figure 3

Bifurcation region variations as a function of pertinent parameters β, k, and θin

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Figure 4

Dimensionless transverse average temperature distributions for fluid and solid phases for k=0.1, β=0.02, η1=5, and θin=−0.4

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Figure 5

Variations of the transient component of the average temperature for fluid and solid phases for k=0.1, β=0.02, η1=5, and θin=−0.4

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Figure 6

Spatial and temporal variations of the average temperature difference between the solid and fluid phases for k=0.1, β=0.02, η1=10, and θin=−0.4

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Figure 7

Characteristic time variations of the solid and fluid phases as a function of pertinent parameters k, β, η1, and θin

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Figure 9

Dimensionless total heat flux at the wall for k=0.1, β=0.02, η1=5, and θin=−0.4

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Figure 10

An example of the requirement to change the imposed heat flux direction at the wall, due to the bifurcation effect, to obtain a constant temperature condition

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Figure 11

Heat exchange ratio variations as a function of pertinent parameters η1, k, θin, and β for qw=0

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Figure 12

Heat exchange ratio for k=0.1, β=0.02, η1=5, θin=−0.4, and qw≠0

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Figure 13

Dimensional characteristic time variations of the solid and fluid phases at different Rep for sandstone

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