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Upper Limits to the Complex Growth Rates in Triply Diffusive Convection in Porous Medium


Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
2 Department of Physics, MLSM College, Sundernagar, H.P., India
     

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The paper mathematically establishes that the complex growth rate (pr,pi ) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer in porous medium (Darcy Model) with one of the components as heat with diffusivity , must lie inside a semicircle in the right- half of the (pr,pi)-plane whose centre is origin and radius equals √(R1+<R2)σ where R1 and R2 are the Raleigh numbers for the two concentration components with diffusivities k1 and k2 (with no loss of generality, k > k1> k2 ) and is the Prandtl number. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.

Keywords

Triply Diffusive Convection, Oscillatory Motions, Complex Growth Rate, Porous Medium.
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  • Upper Limits to the Complex Growth Rates in Triply Diffusive Convection in Porous Medium

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Authors

Jyoti Prakash
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
Shweta Manan
Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla-171005, India
Vinod Kumar
Department of Physics, MLSM College, Sundernagar, H.P., India

Abstract


The paper mathematically establishes that the complex growth rate (pr,pi ) of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude, in a triply diffusive fluid layer in porous medium (Darcy Model) with one of the components as heat with diffusivity , must lie inside a semicircle in the right- half of the (pr,pi)-plane whose centre is origin and radius equals √(R1+<R2)σ where R1 and R2 are the Raleigh numbers for the two concentration components with diffusivities k1 and k2 (with no loss of generality, k > k1> k2 ) and is the Prandtl number. Further, it is proved that above result is uniformly valid for quite general nature of the bounding surfaces.

Keywords


Triply Diffusive Convection, Oscillatory Motions, Complex Growth Rate, Porous Medium.