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

Published online by Cambridge University Press:  21 April 2006

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

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.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 198 , January 1989 , pp. 513 - 541
Copyright
1989 Cambridge University Press

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