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On the Characterization of Nonoscillatory Motions in Triply Diffusiveconvection in Porous Medium


Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
     

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The present paper mathematically establishes that 'the principle of the exchange of stabilities' for triply diffusive convection in porous medium (Darcy model) is valid in the regime (R_1 σ)/(2〖ι_1〗^2 π^4 )+(R_2 σ)/(2〖ι_2〗^2 π^4)≤1, where R_1 and R_2 are the Rayleigh numbers for the two concentration components, ι_1 and ι_2 are the Lewis numbers for the two concentration components and σ is the thermal Prandtl number. It is further proved that the above result is uniformly valid for any combination of rigid and free boundaries.


Keywords

Triply Diffusive Convection, Nonoscillatory Motions, Principle of the Exchange of Stabilities, Concentration Rayleigh Number, Porous Medium, Darcy Model.
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  • On the Characterization of Nonoscillatory Motions in Triply Diffusiveconvection in Porous Medium

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Authors

Jyoti Prakash
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
Shweta Manan
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
Virender Singh
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India

Abstract


The present paper mathematically establishes that 'the principle of the exchange of stabilities' for triply diffusive convection in porous medium (Darcy model) is valid in the regime (R_1 σ)/(2〖ι_1〗^2 π^4 )+(R_2 σ)/(2〖ι_2〗^2 π^4)≤1, where R_1 and R_2 are the Rayleigh numbers for the two concentration components, ι_1 and ι_2 are the Lewis numbers for the two concentration components and σ is the thermal Prandtl number. It is further proved that the above result is uniformly valid for any combination of rigid and free boundaries.


Keywords


Triply Diffusive Convection, Nonoscillatory Motions, Principle of the Exchange of Stabilities, Concentration Rayleigh Number, Porous Medium, Darcy Model.