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On a Heterogeneous Viscoelastic Fluid Heated from Below in Porous Medium

Commun. Math. Anal.
Volume 13, Number 1 (2012), 23 - 34

On a Heterogeneous Viscoelastic Fluid Heated from Below in Porous Medium

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Abstract

An attempt has been made to investigate the thermal convection of a heterogeneous Walters B' viscoelastic fluid layer through porous medium under linear stability theory. It is found that medium permeability and viscoelastic parameter have destabilizing effect while density distribution and Prandtl number have stabilizing effect on the fluid layer. The sufficient conditions depending upon the monotonic behaviour of $f\left(z\right)\; \left[\frac{df}{dz} \; \rangle \; 0\; or\; \lt \; 0\right]$ for the non-existence of overstability are also derived. It is shown that the sufficient conditions for the validity of principle of exchange of stabilities for the present problem are $\frac{df}{dz} \lt 0$ and $F\lt \frac{P_{1} }{\varepsilon }$. Further, it has been found that the complex growth rate of an arbitrary oscillatory modes lies inside a circle in the $\sigma _{r} -\sigma _{i}$ plane, whose centre is at the origin and radius is $\frac{a}{p_{1} } \sqrt{\frac{\left|R_{2} \right|P_{1} }{E} }$.