Volume No. :   3

Issue No. :  2

Year :  2012

ISSN Print :  0976-2973

ISSN Online :  2321-581X


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The Onset of Thermal Instability in a Triply Diffusive Three Dimensional Fluid Layer in Porous Medium



Address:   Veena Sharma*, Priti Bala, Sumit Gupta and Radhe Shyam
Department of Mathematics and Statistics, H.P. University, Shimla-5.
*Corresponding Author
DOI No:

ABSTRACT:
An investigation is made on the onset of thermal instability in a triply diffusive three dimensional fluid layer in porous medium , since there are important fluid mechanical systems in which the density depends on three or more stratifying agencies having different diffusivities, in which the onset of convective instability in isothermal ternary and non-isothermal ternary fluids is termed as triple diffusion. Special attention is given to systems with , and , where is the molecular diffusivity of the ith component and is the thermal Prandtl number. The perturbation equations are analyzed in terms of normal modes after linearizing the relevant set of hydrodynamic equations to derive a characteristic equation. For the stationary convection, the stable solute gradients are found to have stabilizing effects on the system, due to which the onset of instability is postponed and the medium permeability parameter has a destabilizing effect on the system..The presence of stable solute gradients and medium permeability parameter also introduce oscillatory modes which were non- existent in their absence. The case of overstability (with increasing amplitude of perturbations) is also considered and the sufficient conditions for the non existence of stable solutions are derivedr. These analytical results are confirmed numerically and the effects of various parameters on the stability analysis for both the cases of stationary convection and overstability are depicted graphically using the software Mathematica version 2007.
KEYWORDS:
Thermal instability, ,Thermal Prandtl number, Solute Rayleigh numbers, medium permeability.
Cite:
Veena Sharma, Priti Bala, Sumit Gupta , Radhe Shyam. The Onset of Thermal Instability in a Triply Diffusive Three Dimensional Fluid Layer in Porous Medium. Research J. Engineering and Tech. 3(2): April-June 2012 page152-160.
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