Effects of non-uniform heating on a variable viscosity Rayleigh–Bénard problem

Abstract

This study presents a natural convection problem with a temperature-dependent viscosity fluid, driven by buoyancy and influenced by horizontal temperature gradients. A numerical linear stability analysis of the stationary solutions is studied. The horizontal temperature gradients tend to localize motion near the warmer zones and favour pattern formation in the direction perpendicular to the gradient. In fact, the problem is almost 2D in the uniform heating case, but becomes totally 3D in the non-uniform heating case.