TY - JOUR
T1 - Non-linear stability for convection with quadratic temperature dependent viscosity
AU - Vaidya, Ashwin
AU - Wulandana, Rachmadian
PY - 2006/9/10
Y1 - 2006/9/10
N2 - 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.
AB - 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.
KW - Convection
KW - Energy stability
KW - Navier-Stokes
KW - Temperature dependent viscosity
UR - http://www.scopus.com/inward/record.url?scp=33747114467&partnerID=8YFLogxK
U2 - 10.1002/mma.742
DO - 10.1002/mma.742
M3 - Article
AN - SCOPUS:33747114467
SN - 0170-4214
VL - 29
SP - 1555
EP - 1561
JO - Mathematical Methods in the Applied Sciences
JF - Mathematical Methods in the Applied Sciences
IS - 13
ER -