MIXED CONVECTION IN A DRIVEN CAVITY WITH A STABLE VERTICAL TEMPERATURE-GRADIENT

Abstract

Extensive parametric studies are made of flow and heat transfer of a viscous fluid contained in a square cavity. Flow is generated by the top horizontal boundary wall, which slides in its own plane at constant speed. A stabilizing externally-applied vertical temperature gradient is imposed on the system boundaries; the top wall is maintained at a higher temperature than the botom wall. Numerical solutions to the Navier-Stokes equations are secured over broad ranges of the parameters, 0 less-than-or-equal-to Ra less-than-or-equal-to 10(6), 0 less-than-or-equal-to Re less-than-or-equal-to 3000, Pr approximately O(1), aspect ratio approximately O(1). Systematical evaluations of the numerical results are carried out to ascertain the relative importance of natural and forced convections. Representative plots illustrating the velocity and thermal fields are presented. These clearly identify the major dynamic elements in various regimes of the parameter spaces. When Gr/Re2 less-than-or-equal-to 1, the flow features are similar to those of a conventional driven-cavity of a non-stratified fluid. In the bulk of the interior, fluids are well mixed and temperature variations are small. When Gr/Re2 much greater than 1, much of the middle and bottom portions of the cavity interior is stagnant. In these regions, isotherms are nearly horizontal, and vertically-linear temperature distributions are seen. By inspecting separate plots of partial derivative T/partial derivative y and - Pr Re.vT, contributions to total heat transfer by conduction and by convection are assessed in a quantitative manner. The Nusselt number at the top wall is calculated, and these results indicate the intensification of heat transfer as Gr/Re2 much less than 1.