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Research Papers: Porous Media

Exact Solutions for a Thermal Nonequilibrium Model of Fluid Saturated Porous Media Based on an Effective Porosity

[+] Author and Article Information
F. Kuwahara1

Department of Mechanical Engineering,  Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu 432-8561, Japan e-mail: tmfkuwa@ipc.shizuoka.ac.jpDepartment of Mechanical Engineering,  Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu 432-8561, Japan; School of Energy and Power Engineering,  Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China Research Division, Nitto Kogyo Corporation, 2201 Kanihara, Nagakute-Cho, Aichi-Gun, Aichi 480-1189, JapanDepartment of Mechanical Engineering,  Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu 432-8561, Japan; School of Civil Engineering and Architecture,  Wuhan Polytechnic University, Wuhan, Hubei 430023, China

C. Yang, K. Ando, A. Nakayama

Department of Mechanical Engineering,  Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu 432-8561, Japan e-mail: tmfkuwa@ipc.shizuoka.ac.jpDepartment of Mechanical Engineering,  Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu 432-8561, Japan; School of Energy and Power Engineering,  Huazhong University of Science and Technology, Wuhan, Hubei 430074, P. R. China Research Division, Nitto Kogyo Corporation, 2201 Kanihara, Nagakute-Cho, Aichi-Gun, Aichi 480-1189, JapanDepartment of Mechanical Engineering,  Shizuoka University, 3-5-1 Johoku, Naka-Ku, Hamamatsu 432-8561, Japan; School of Civil Engineering and Architecture,  Wuhan Polytechnic University, Wuhan, Hubei 430023, China

1

Corresponding author.

J. Heat Transfer 133(11), 112602 (Sep 19, 2011) (9 pages) doi:10.1115/1.4004354 History: Received January 27, 2011; Revised May 16, 2011; Published September 19, 2011; Online September 19, 2011

An effective porosity concept has been introduced to account for the effects of tortuosity and thermal dispersion on the individual effective thermal conductivities of the solid and fluid phases in a fluid-saturated porous medium. Using this effective porosity concept, a thermal nonequilibrium model has been proposed to attack locally thermal nonequilibrium problems associated with convection within a fluid-saturated porous medium. Exact solutions are obtained, assuming a plug flow, for the two cases of thermally fully developed convective flows through a channel, namely, the case of isothermal hot and cold walls and the case of constant heat flux walls. These exact solutions for the cases of metal foam and air combination reveal that the local thermal equilibrium assumption may hold for the case of isothermal hot and cold walls, but may fail for the case of constant heat flux walls.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

Various expressions for stagnant thermal conductivity of aluminum metal foam saturated with air

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Figure 2

Thermal conductivities of the fluid and solid phases in aluminum foam and air combination

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Figure 3

Heat transfer in a channel filled with a metal foam bounded by isothermal walls

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Figure 4

Fluid and solid temperature profiles in a metal foam channel with isothermal walls

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Figure 5

The Nusselt number for a metal foam channel with isothermal walls

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Figure 6

Heat transfer in a channel filled with a metal foam bounded by constant heat flux walls

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Figure 7

Fluid and solid temperature profiles in a metal foam channel with constant heat flux: (a) local thermal equilibrium walls (ΔT = 0) and (b) local uniform heat flux walls

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Figure 8

The Nusselt number for a metal foam channel with constant heat flux walls

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