Non-linear stability for convection with quadratic temperature dependent viscosity

Ashwin Vaidya, Rachmadian Wulandana

Research output: Contribution to journalArticle

4 Scopus citations

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.

Original languageEnglish
Pages (from-to)1555-1561
Number of pages7
JournalMathematical Methods in the Applied Sciences
Volume29
Issue number13
DOIs
StatePublished - 10 Sep 2006

Keywords

  • Convection
  • Energy stability
  • Navier-Stokes
  • Temperature dependent viscosity

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