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Non‐linear stability for convection with quadratic temperature dependent viscosity
Author(s) -
Vaidya Ashwin,
Wulandana Rachmadian
Publication year - 2006
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.742
Subject(s) - mathematics , rayleigh number , newtonian fluid , viscosity , thermodynamics , convection , stability (learning theory) , quadratic equation , mechanics , mathematical analysis , natural convection , physics , geometry , machine learning , computer science
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.