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Dufour-Soret Driven Double-Diffusive Convection in Nonreactive Binary Fluids with Temperature Dependent Viscosity


Affiliations
1 Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005, India
2 UIIT, Himachal Pradesh University, Summerhill, Shimla-171005, India
     

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The aim of the present paper is to investigate the effects of temperature dependent viscosity on the stability of Dufour-Soret driven double-diffusive convection in nonreactive binary fluids, for general boundary conditions. Some analytical results concerning the stability of oscillatory motions and otherwise the complex growth rate of oscillatory motions are derived for this general problem. The expressions for Rayleigh numbers, when instability sets in as stationary modes, for each combination of rigid(slip free) and dynamically free(stress free) boundary conditions are derived numerically using Galerkin's method. The effects of linear and exponential temperature dependent viscosity on the onset stationary convection are studied and computed numerically. Various consequences of the obtained results for different convective problems have been worked out, as special cases.

Keywords

Binary Fluids, Dufour-Soret Effects, Double-Diffusive Convection, Principle of Exchange of Stabilities, Galerkin's Technique, Rayleigh Number.
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  • Dufour-Soret Driven Double-Diffusive Convection in Nonreactive Binary Fluids with Temperature Dependent Viscosity

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Authors

Joginder S. Dhiman
Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005, India
Praveen K. Sharma
UIIT, Himachal Pradesh University, Summerhill, Shimla-171005, India
Poonam Sharma
Department of Mathematics, Himachal Pradesh University, Summerhill, Shimla-171005, India

Abstract


The aim of the present paper is to investigate the effects of temperature dependent viscosity on the stability of Dufour-Soret driven double-diffusive convection in nonreactive binary fluids, for general boundary conditions. Some analytical results concerning the stability of oscillatory motions and otherwise the complex growth rate of oscillatory motions are derived for this general problem. The expressions for Rayleigh numbers, when instability sets in as stationary modes, for each combination of rigid(slip free) and dynamically free(stress free) boundary conditions are derived numerically using Galerkin's method. The effects of linear and exponential temperature dependent viscosity on the onset stationary convection are studied and computed numerically. Various consequences of the obtained results for different convective problems have been worked out, as special cases.

Keywords


Binary Fluids, Dufour-Soret Effects, Double-Diffusive Convection, Principle of Exchange of Stabilities, Galerkin's Technique, Rayleigh Number.