Bénard Convection With Rotation And APeriodic Temperature Distribution

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.