Journal of Fluid Mechanics

Stability of free-convection flows of variable-viscosity fluids in vertical and inclined slots

Yen-Ming  Chen a1 and Arne J.  Pearlstein a1
a1 Department of Aerospace and Mechanical Engineering, University of Arizona, Tucson, AZ 85721, USA

Article author query
chen ym   [Google Scholar] 
pearlstein aj   [Google Scholar] 


The stability of the buoyancy-driven parallel shear flow of a variable-viscosity Newtonian fluid between vertical or inclined plates maintained at different temperatures is studied theoretically. The analysis is capable of dealing with arbitrary viscosity-temperature relations. Depending on the Prandtl number, angle of inclination, and form of the viscosity-temperature variation, the flow may become unstable with respect to two-dimensional longitudinal or transverse disturbances. Outstanding questions arising in previous investigations of the stability of parallel free-convection flows of constant-viscosity fluids in inclined slots and of variable-viscosity fluids in vertical slots are discussed. We find that, in a variable-viscosity fluid, non-monotonic dependence of the critical Rayleigh number on the inclination angle can occur at significantly higher Prandtl numbers than is possible in the constant-viscosity case. Results are also presented for the stability of the free-convection flow of several glycerol-water solutions in an inclined slot.

(Published Online April 21 2006)
(Received November 3 1987)
(Revised July 5 1988)