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On mixed convection in a cavity with sinusoidally heated moving lid and uniformly heated and cooled side walls

Deborah S Ducasse and Precious Sibanda*

Author Affiliations

School of Mathematics, Statistics and Computer Science, University of KwaZulu-Natal, Private Bag X01 Scottsville, Pietermaritzburg, 3209, South Africa

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Boundary Value Problems 2013, 2013:83  doi:10.1186/1687-2770-2013-83

Published: 10 April 2013

Abstract

In this study a steady state two-dimensional mixed convection problem in an air filled cavity is investigated. The effects of linearly heated and uniformly cooled walls on flow and heat transfer characteristics within the cavity are determined. The strength of the fluid circulation within the cavity is found for both heated and cooled walls for different Reynolds and Grashof numbers. The nonlinear coupled equations are solved numerically using the penalty-Galerkin finite element method. Stream function and isotherm results are obtained for different Reynolds and Grashof numbers. The results for the heat transfer rate are presented in terms of both the local and the average Nusselt number. In general, the strength of the circulation is stronger for the case of cooled walls, and the anti-clockwise circulation is significantly stronger for cooled walls, while the clockwise circulation is only slightly stronger for the cooled walls and the difference in strength decreases both with increasing Reynolds and Grashof numbers. Both the local and average Nusselt numbers are generally higher for the case of cooled side walls than that for heated side walls.

MSC: 34B15, 65N30, 76M20.