Instability of Convection and Heat Transfer of High Prandtl Number Fluids in a Vertical Slot

The stability of convective motion of high-Prandtl-number fluids, generated by a lateral temperature difference across a vertical slot with aspect ratio 15, is studied numerically. The Prandtl number range studied is from 50 to 2000. The nonlinear governing equations are solved by a finite difference method. The predicted flow patterns and critical values are in good agreement with the recent experimental results of Wakitani (1994). It is found that the vorticity distribution along the vertical centerline of the slot is a very sensitive indicator of the onset of multicellular flow. The critical Grashof number varies almost inversely with the Prandtl number; consequently, the critical Rayleigh number is essentially independent of the Prandtl number. Heat transfer results show good agreement with the experimentally correlated values, and they are independent of the Prandtl numbers and the flow patterns.