RESEARCH PAPERS: Natural Convection

Three-Dimensional Natural Convection in a Confined Fluid Overlying a Porous Layer

[+] Author and Article Information
A. K. Singh

Department of Civil and Agricultural Engineering, University of Melbourne, Parkville, Victoria, Australia-3052

E. Leonardi

School of Mechanical and Manufacturing Engineering, University of New South Wales, Kensington, NSW, Australia-2033

G. R. Thorpe

Department of Civil and Building Engineering, Victoria University of Technology, Footscray, Victoria, Australia-3011

J. Heat Transfer 115(3), 631-638 (Aug 01, 1993) (8 pages) doi:10.1115/1.2910733 History: Received February 01, 1992; Revised September 01, 1992; Online May 23, 2008


This paper presents a numerical study of three-dimensional, laminar natural convection in an enclosure containing a fluid layer overlying a porous layer saturated with the same fluid. The Brinkman-extended Darcy formulation is used to model fluid flow in the porous layer as this facilitates the imposition of a no-slip boundary condition at the fluid/porous layer interface. The enclosure is heated from one side wall and cooled from an opposite wall, while the remaining walls are adiabatic. The mathematical analysis is carried out in terms of a vorticity-vector potential formulation that ensures the conservation of mass. The governing equations in non-dimensional form are transformed into parabolic equations by means of a false transient method in order to facilitate a solution procedure by an alternating direction implicit method. Accuracy of the numerical solutions with respect to uniformly and nonuniformly spaced grid points has been tested by performing extensive numerical experiments. As expected, it is found that the intensity of free convection is much more profound in the fluid layer. The numerical results indicate that penetration of the fluid into the porous region depends strongly upon the Darcy and Rayleigh numbers. The effect of the ratio of thermal conductivities (porous to fluid regions) is to intensify the convection current in the fluid layer.

Copyright © 1993 by The American Society of Mechanical Engineers
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