Stability analysis of the Rayleigh–Bénard convection for a fluid with temperature and pressure dependent viscosity Academic Article uri icon

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-Bénard convection. We show that the principle of exchange of stability holds and the Rayleigh numbers for the linear and non-linear stability coincide. © 2009 Birkhäuser Verlag, Basel.

author list (cited authors)

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

citation count

  • 23

publication date

  • March 2009