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# Analytical Solution of Nonequilibrium Heat Conduction in Porous Medium Incorporating a Variable Porosity Model With Heat Generation

[+] Author and Article Information
M. Nazari

School of Mechanical Engineering, Tehran University,P.O. Box 14395-515, Tehran, Iranmnazari@alum.sharif.edu

F. Kowsary

School of Mechanical Engineering, Tehran University,P.O. Box 14395-515, Tehran, Iranfkowsari@ut.ac.ir

J. Heat Transfer 131(1), 014503 (Oct 20, 2008) (4 pages) doi:10.1115/1.2977544 History: Received December 27, 2007; Revised June 18, 2008; Published October 20, 2008

## Abstract

This paper is concerned with the conduction heat transfer between two parallel plates filled with a porous medium with uniform heat generation under a nonequilibrium condition. Analytical solution is obtained for both fluid and solid temperature fields at constant porosity incorporating the effects of thermal conductivity ratio, porosity, and a nondimensional heat transfer coefficient at pore level. The two coupled energy equations for the case of variable porosity condition are transformed into a third order ordinary equation for each phase, which is solved numerically. This transformation is a valuable solution for heat conduction regime for any distribution of porosity in the channel. The effects of the variable porosity on temperature distribution are shown and compared with the constant porosity model. For the case of the exponential decaying porosity distribution, the numerical results lead to a correlation incorporating conductivity ratio and interstitial heat transfer coefficient.

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## Figures

Figure 1

Nondimensional temperature distribution in a porous channel with constant porosity (ε=0.5) at different conductivity ratios between solid and fluid for A=1

Figure 2

Nondimensional temperature distribution in a porous channel with constant porosity (ε=0.5) at different values of A for k=1∕2

Figure 3

Maximum temperature difference in a porous channel incorporating the limit values (ε=0.5)

Figure 4

Maximum temperature in a porous channel at different porosity and conductivity values (A=1)

Figure 5

Temperature distribution in a porous channel with variable porosity at different values of k for A=1

Figure 6

Maximum temperature of solid and fluid phases in a porous channel with variable porosity model

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