Stability analysis of the Rayleigh-Benard convection for a fluid with temperature and pressure dependent viscosity

abstract

• The classical problem of thermal-convection involving the classical Navier-Stokes fluid with a constant or temperature dependent viscosity, within the context of the Oberbeck-Boussinesq approximation, is one of the most intensely studied problems in fluid mechanics. In this paper, we study thermal-convection in a fluid with a viscosity that depends on both the temperature and pressure, within the context of a generalization of the Oberbeck-Boussinesq approximation. Assuming that the viscosity is an analytic function of the temperature and pressure we study the linear as well as the nonlinear stability of the problem of Rayleigh-Bnard convection. We show that the principle of exchange of stability holds and the Rayleigh numbers for the linear and non-linear stability coincide. 2009 Birkhuser Verlag, Basel.

authors

• Rajagopal, Kumbakonam

published proceedings

• ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK

author list (cited authors)

• Rajagopal, K. R., Saccomandi, G., & Vergori, L.

citation count

• 25

complete list of authors

• Rajagopal, KR||Saccomandi, G||Vergori, L

publication date

• July 2009

publisher

• Springer Nature  Publisher

keywords

• Convection
• Exchange Of Stability
• Oberbeck-boussinesq Approximation
• Pressure Dependent Viscosity
• STABILITY

Digital Object Identifier (DOI)

• 10.1007/s00033-008-8062-6

start page

• 739

end page

• 755

volume

• 60

issue

• 4

URL

• http://dx.doi.org/10.1007/s00033-008-8062-6