RESEARCH PAPERS: Natural Convection

Three-Dimensional Free Convection in a Long Rotating Porous Box: Analytical Solution

[+] Author and Article Information
P. Vadasz

Department of Mechanical Engineering, University of Durban-Westville, Durban, 4000 South Africa

J. Heat Transfer 115(3), 639-644 (Aug 01, 1993) (6 pages) doi:10.1115/1.2910734 History: Received September 01, 1991; Revised December 01, 1992; Online May 23, 2008


A three-dimensional analytical solution to the steady-state free convection problem in a long rotating porous box is presented for large values of the porous media Ekman number. The convection results from differential heating of the horizontal walls leading to temperature gradients orthogonal to the centrifugal body force. The solution to the nonlinear set of partial differential equations was obtained through an asymptotic expansion of the dependent variables in terms of two small parameters representing the reciprocal Ekman number in porous media and the aspect ratio of the domain. The results are focused towards the Coriolis effect on the flow. Secondary circulation was obtained in a plane orthogonal to the leading free convection plane. The results show that the Coriolis effect on free convection is controlled by a combined dimensionless group representing the ratio of the centrifugal Rayleigh number to the porous media Ekman number.

Copyright © 1993 by The American Society of Mechanical Engineers
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