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Non-linear stability for convection with quadratic temperature dependent viscosity

✍ Scribed by Ashwin Vaidya; Rachmadian Wulandana

Publisher
John Wiley and Sons
Year
2006
Tongue
English
Weight
84 KB
Volume
29
Category
Article
ISSN
0170-4214

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✦ Synopsis

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, 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. Copyright © 2006 John Wiley & Sons, Ltd.

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