Analysis of mixed convection in an air filled square cavity.

Abstract

A steady state two-dimensional mixed convection problem in an air filled square unit cavity has been numerically investigated. Two different cases of heating are investigated and compared. In the first case, the bottom wall was uniformly heated, the side walls were linearly heated and the top moving wall was heated sinusoidally. The second case differed from the first in that the side walls were instead uniformly cooled. This investigation is an extension of the work by Basak et al. [6, 7] who investigated mixed convection in a square cavity with similar boundary conditions to the cases listed above with the exception of the top wall which was well insulated. In this dissertation, their work is extended to include a sinusoidally heated top wall. The nonlinear coupled equations are solved using the Penalty Galerkin Finite Element Method. Stream function and isotherm results are found for various values of the Reynolds number and the Grashof number. The strength of the circulation is seen to increase with increasing Grashof number and to decrease with increasing Reynolds number for both cases of heating. A comparison is made between the stream function and isotherm results for the two cases. The results for the rate of heat transfer in terms of the Nusselt number are discussed. Both local and average Nusselt number results are presented and discussed. The average Nusselt number is found using Simpson's 1/3rd rule. The rate of heat transfer is found to be higher at all four walls for the case of cooled side walls than that of linearly heated side walls.