Non-linear stability for convection with quadratic temperature dependent viscosity

In this paper, we study the non-linear stability of convection for a Newtonian fluid heated from below, where the viscosity of the fluid depends upon temperature. We are able to show that for Rayleigh numbers below a certain critical value, Ra_c, the rest state of the fluid and the steady temperature distribution remains non-linearly stable, using the calculations of Diaz and Straughan (Continuum Mech. Thermodyn. 2004; 16:347-352). The central contribution of this paper lies in a simpler proof of non-linear stability, than the ones in the current literature, by use of a suitable maximum principle argument.