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Jyoti Prakash ¹, Renu Bala ¹, Kultaran Kumari ¹

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

Abstract

In the present paper it is mathematically established that the linear growth rate of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude in a triply diffusive fluid layer (with one of the component as heat with diffusivity κ) must lie inside a semicircle in the right half of the (P_r, P_i􀀅) - plane whose centre is at the origin and radius equals 􀀇√(|R􀀉| + R₁􀀋)􀀌 where R and R1 are the thermal Rayleigh number and concentration Rayleigh number with diffusivities κ and κ_1. Further, it is proved that this result is uniformly valid for quite general nature of the bounding surfaces.

Keywords

Triply Diffusive Convection, Oscillatory Motions, Complex Growth Rate, Concentration Rayleigh Number.

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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.

Full Text

     

Jyoti Prakash ¹, Kultaran Kumari ¹

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

Abstract

In the present paper it is mathematically established that the linear growth rate of an arbitrary neutral or unstable oscillatory perturbation of growing amplitude in a double diffusive binary viscoelastic fluid saturated anisotropic porous layer heated from below must lie inside a semicircle in the right half of the (P_r, P_i)-plane whose centre is at the origin and radius equals λ₁Pr_DRa_T+√P_rD(λ₁²Ra_T²Pr_D+4Ra_s)/2, where Ra_T and Ra_s are the Darcy -Rayleigh number and the solute Rayleigh number respectively. Further, it is proved that this result is uniformly valid for quite general nature of the bounding surfaces.

Keywords

Double-Diffusive Convection, Viscoelastic Fluid, Porous Medium, Complex Growth Rate, Solute Rayleigh Number.

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