Onset of convection in a viscoelastic-fluid-saturated sparsely packed porous layer using a thermal nonequilibrium model

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Shivakumara, I.S. and Malashetty, M.S. and Chavaraddi, K.B. (2006) Onset of convection in a viscoelastic-fluid-saturated sparsely packed porous layer using a thermal nonequilibrium model. Canadian journal of physics, 84 (11). pp. 973-990. ISSN 00084204

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Official URL: https://doi.org/10.1139/P06-085

Abstract

A linear stability analysis is carried out to study viscoelastic fluid convection in a sparsely packed horizontal porous layer heated from below. The viscoelastic fluid flow in the porous medium is modeled by using a modified Brinkman-Lapwood-extended Darcy model with the fluid viscosity different from the effective viscosity, which accounts for the viscoelastic properties and friction due to macroscopic shear. Besides, a two-field model for temperature each representing the solid and fluid phases separately is employed. The conditions for the occurrence of direct and Hopf bifurcations of the thermal convective instability are obtained analytically. It is shown that Hopf bifurcation occurs only if the retardation to relaxation-time ratio, A, is less than unity and the elasticity parameter, Πexceeds a threshold. Further, the effects of the viscoelastic parameters and the thermal nonequilibrium on the onset of convection are analyzed in detail. © 2006 NRC.

Item Type: Article
Additional Information: cited By 14
Uncontrolled Keywords: Bifurcation (mathematics); Flow of fluids; Linear stability analysis; Porous materials; Saturation (materials composition); Viscoelasticity; Viscosity, Fluid phases; Hopf bifurcations; Porous layer; Thermal nonequilibrium model, Heat convection
Subjects: Faculty of Science > Pure Sciences > Mathematics
Divisions: Jnana Bharathi / Central College Campus > Department of Mathematics
Depositing User: Mr. Kirana Kumar D
Date Deposited: 22 Feb 2016 10:39
Last Modified: 03 Mar 2016 10:11
URI: http://eprints-bangaloreuniversity.in/id/eprint/1380

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