International Journal of Technology

Jyoti Prakash ¹, Kultaran Kumari ¹, Vinod Kumar ²

Affiliations
1 Department of Mathematics and Statistics, Himachal Pradesh University, Summer Hill, Shimla 171005, IN
2 Department of Physics, M.L.S.M. College, Sunder-Nagar, Distt. Mandi (H.P.), IN

Abstract

Linear stability of double diffusive convection in a binary viscoelastic fluid saturated anisotropic porous layer has been studied analytically. A sufficient condition for the occurrence of stationary convection has been derived in terms of the parameters of the system alone. It is further proved the above result is uniformly valid for any combination of the bounding surfaces.

Keywords

Double-Diffusive Convection, Viscoelastic Fluid, The Principle of the Exchange of Stabilities, Porous Medium.

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Jyoti Prakash ¹, Virender Singh ¹, Shweta Manan ¹, Vinod Kumar ²

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

Abstract

The paper mathematically establishes that the complex growth rate (p_r,p_i ) 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 (p_r,p_i)-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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