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THE PENETRATION OF UNSTEADY FREE CONVECTION FROM A HEATED AND COOLED VERTICAL FLAT SURFACE IN A POROUS MEDIUM

DOI: 10.1615/ICHMT.1997.IntSymLiqTwoPhaseFlowTranspPhenCHT.710
8 pages

R. Bradean
Department of Mathematics, Simon Fraser University, Burnaby, Canada

Derek B. Ingham
Centre for CFD, Department of Applied Mathematical Studies, The University of Leeds, Leeds, LS2 9JT, UK; Energy-2050, Faculty of Engineering, University of Sheffield, Sheffield, S10 2TN, UK

Peter J. Heggs
School of Chemical and Process Engineering, University of Leeds, Leeds, UK; Dept of Chem Eng, UMIST, Sackville St., Manchester, M60 1QD

Ioan Pop
Department of Applied Mathematics, Babes-Bolyai University, 400084 Cluj-Napoca, Romania

Resumo

Unsteady two-dimensional free convection is generated by an impulsively heated and cooled, in space, infinite vertical flat surface which is embedded in a stationary porous medium. The matched asymptotic expansions technique is used to obtain approximate analytical solutions for small values of time and these results are found to be in very good agreement with the finite-difference results for all the values of the Rayleigh number considered, namely 0 ≤ Ra ≤ 100. It is found that the flow consists of a row of counter rotating cells, each cell developing along the hot or cold regions of the surface. For values of Ra larger than about 40, and for small times, two recirculating regions develop at the point of collision of the two opposite streams which flow along the surface. At large values of time the unsteady numerical solution converge to the steady state results.

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