Title

Non-Linear Stability for Convection with Quadratic Temperature Dependent Viscosity

Document Type

Article

Publication Date

9-10-2006

Abstract

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, Rac, 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.

DOI

10.1002/mma.742

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