Stability analysis on the convection of a variable viscosity fluid in an infinite vertical slot

Abstract

Stability of convective motion in a variable-viscosity fluid contained in an infinite vertical slot generated by a lateral temperature difference was studied by means of linear stability analysis. The viscosity of the fluid was assumed to be an exponential function of the temperature. The undisturbed steady-state motion was assumed to consist of purely vertical motion with a linear temperature distribution across the slot. The linear stability equations were solved by the Galerkin method. The results show that (i) the onset of instability is in the oscillatory, or traveling wave, mode in fluids whose mean Prandtl number is greater than 25, and (ii) the variable-viscosity fluid is less stable than the constant-viscosity fluid at the same mean Prandtl number when it exceeds 100.