EFFECT OF TIME VARYING THERMAL BOUNDARY CONDITIONS ON OSCILLATORY NATURAL CONVECTION OF A LOW-PRANDTL-NUMBER FLUID

Abstract

Numerical simulations, based on a control-volume-based finite difference method with central differencing and semi-implicit time marching, are performed for natural convection of liquid metals within a square cavity. All calculations are made with the Prandtl number held constant at 0.005, while Grashof numbers of 3 × 10⁶ and 10⁷ are considered with both steady and time varying sidewall temperatures. With steady boundary conditions and the assumption of two-dimensional convection, periodic and quasi-periodic conditions, respectively, are predicted for Gr equals 3 × 10⁶ and 10⁷, and the oscillatory states are related to the transport of thermal energy and vorticity. The effects of small and large cooling rates on predicted convection are considered. It is found that the small cooling rates have a negligible effect on the dynamic behavior of the system, while large cooling rates cause transitions to more complex flow structures and enhance mixing.

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Notes on contributors

Craig M. Cless

Address correspondence to Professor Patrick J. Prescott, Department of Mechanical Engineering, Pennsylvania State University, 137 Reber Building, University Park, PA 16802-1412, USA.