Author(s)

S. J. D. D’Alessio & K. A. Ogden

Abstract

This study investigates the effects of a sinusoidally varying temperature distribution and rotation on free convection between two rigid plates. The domain is assumed to be much larger in the horizontal direction than in the vertical direction, which naturally introduces a small parameter. An approximate analytical solution for the steady-state flow is derived by expanding the flow variables in the small parameter. The steady-state solution was also determined numerically using the commercial CFD software package CFX. A comparison of the results shows that the form of the steady-state flow pattern is indeed captured by the approximate analytical solution. Unsteady numerical calculations are also carried out for various sets of parameters to determine when the flow destabilizes, how the modulated temperature boundary condition and rotation affect the critical Rayleigh number, and also to illustrate the flow pattern that develops when the flow becomes unstable. Keywords: Bénard convection, rotation, sinusoidally varying boundary condition, shallow flow, analytical, numerical. 1 Introduction The problem of free convection within a long, rotating rectangular domain driven by a sinusoidally varying bottom temperature is studied. This problem is an extension of traditional Bénard convection to account for both rotation and a periodic temperature distribution along the bottom plate. Numerous studies have been devoted to Bénard convection. One previous related study is the work by Pascal and D’Alessio [1], which addresses the stability of the flow with rotation and a quadratic equation of state. Schmitz and Zimmerman [2] studied the effects of a spatially varying temperature condition together with wavy boundaries, but

Keywords

Bénard convection, rotation, sinusoidally varying boundary condition, shallow flow, analytical, numerical.