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The Onset of Convection in a Layer of Cellular Porous Material: Effect of Temperature-Dependent Conductivity Arising From Radiative Transfer

[+] Author and Article Information
D. A. Nield

Department of Engineering Science, University of Auckland, Private Bag 92019, Auckland 1142, New Zealandd.nield@auckland.ac.nz

A. V. Kuznetsov

Department of Mechanical and Aerospace Engineering, North Carolina State University, Campus Box 7910, Raleigh, NC 27695-7910avkuznet@eos.ncsu.edu

J. Heat Transfer 132(7), 074503 (May 05, 2010) (4 pages) doi:10.1115/1.4001125 History: Received September 27, 2009; Revised January 03, 2010; Published May 05, 2010; Online May 05, 2010

The onset of convection in a horizontal layer of a cellular porous material heated from below is investigated. The problem is formulated as a combined conductive-convective-radiative problem in which radiative heat transfer is treated as a diffusion process. The problem is relevant to cellular foams formed from plastics, ceramics, and metals. It is shown that the variation of conductivity with temperature above that of the cold boundary leads to an increase in the critical Rayleigh number (based on the conductivity of the fluid at that boundary temperature) and an increase in the critical wave number. On the other hand, the critical Rayleigh number based on the conductivity at the mean temperature decreases with increase in the thermal variation parameter if the radiative contribution to the effective conductivity is sufficiently large compared with the nonradiative component.

Copyright © 2010 by American Society of Mechanical Engineers
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