Stability of thermal convection between non-uniformly heated plates

Abstract

The effect of horizontal as well as vertical temperature gradients on the stability of natural convection in a thin horizontal layer of viscous, incompressible fluid is studied on the basis of linear theory. The boundaries are taken to be rigid, perfectly thermally conducting, having prescribed temperatures and the horizontal temperature gradient is assumed to be small. It is found that for Prandtl number greater than 0.13, the critical Rayleigh number is always larger than that for the corresponding Benard problem. The preferred mode of disturbance is stationary and will be a transverse roll (having axes normal to the basic flow) or a longitudinal roll (having axes aligned in the direction of the basic flow) depending on whether the Prandtl number is less or larger than 1.7. Finally, it is shown that the instability is of thermal origin.