Non-linear stability for convection with quadratic temperature dependent viscosity

Ashuwin Vaidya, Rachmadian Wulandana

Research output: Contribution to journalArticle

4 Citations (Scopus)

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

Fingerprint

Temperature-dependent Viscosity
Nonlinear Stability
Convection
Viscosity
Fluid
Fluids
Rayleigh number
Newtonian Fluid
Temperature Distribution
Maximum Principle
Critical value
Continuum
Maximum principle
Temperature
Temperature distribution

Keywords

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

Cite this

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Non-linear stability for convection with quadratic temperature dependent viscosity. / Vaidya, Ashuwin; Wulandana, Rachmadian.

In: Mathematical Methods in the Applied Sciences, Vol. 29, No. 13, 10.09.2006, p. 1555-1561.

Research output: Contribution to journalArticle

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