CONVECTION IN A DIFFERENTIALLY-HEATED SQUARE CAVITY WITH A TORSIONALLY-OSCILLATING LID

Abstract

Numerical studies are made of the flow of a viscous thermally-stratified fluid in a square container. The flow is driven by the top lid of the container, which executes torsional oscillations. A stabilizing vertical temperature difference (T(H)-T(C)) is applied on the horizontal boundary walls; the two vertical side walls are thermally insulated. Numerical solutions are secured to the time-dependent Navier-Stokes equations under the Boussinesq-fluid approximation. Details of unsteady flow and thermal fields are exhibited over broad ranges of three principal parameters, i.e. the Reynolds number Re, the Grashof number Gr, and the frequency ratio omega'. Of particular interest is the possibility of resonance; this gives rise to intensification of flows in the interior and associated augmentation of convective heat transport. Systematically-organized computational results indicate that the existence of resonance is verified, and the enhancement of heat transfer is demonstrated at particular values of omega'.