Onset of convection in the Rayleigh-Bénard flow with temperature dependent viscosity: An asymptotic approach

Abstract.

In this study it is investigated how variable viscosity affects the onset f instability in the Rayleigh-Bénard convection. An asymptotic approach provides results that are independent of specific property laws. They are compared to those of other studies and to direct solutions of the non-expanded stability equations for particular property laws. It is demonstrated that one can also get the asymptotic results from solutions of the non-expanded equations by use of a so-called combined method. The asymptotic results are general in nature and hold for all Newtonian fluids and all (small) heat transfer rates.