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Cattaneo–LTNE porous ferroconvection

Ravisha M. (Department of Mathematics, Dr G. Shankar Government Women’s First Grade College and Post Graduate Study Centre, Udupi, India)
I.S. Shivakumara (Department of Mathematics, Bangalore University, Bengaluru, India)
Mamatha A.L. (Department of Mathematics, Smt. Rukmini Shedthi Memorial National Government First Grade College and PG Study Centre, Barkur, India)

Multidiscipline Modeling in Materials and Structures

ISSN: 1573-6105

Article publication date: 14 May 2019

Issue publication date: 14 June 2019

Abstract

Purpose

The onset of convection in a ferrofluid-saturated porous layer has been investigated using a local thermal nonequilibrium (LTNE) model by allowing the solid phase to transfer heat via a Cattaneo heat flux theory while the fluid phase to transfer heat via usual Fourier heat-transfer law. The flow in the porous medium is governed by modified Brinkman-extended Darcy model. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method. The presence of Cattaneo effect introduces oscillatory convection as the preferred mode of instability contrary to the occurrence of instability via stationary convection found in its absence. Besides, oscillatory ferroconvection is perceived when the solid thermal relaxation time parameter exceeds a threshold value and increase in its value is to hasten the oscillatory onset. The effect of different boundary conditions on the instability of the system is noted to be qualitatively same. The paper aims to discuss these issues.

Design/methodology/approach

The investigators would follow the procedure of Straughan (2013) to obtain the expression for Rayleigh number. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The investigators have used a Galerkin method to obtain the numerical results for rigid-ferromagnetic/paramagnetic boundaries, while the instability of the system is discussed exactly for stress-free boundaries.

Findings

The Cattaneo–LTNE porous ferroconvection has been analyzed for different velocity and magnetic boundary conditions. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system has been highlighted. The instability of the system is discussed exactly for stress-free boundaries, while for rigid-ferromagnetic/paramagnetic boundaries the results are obtained numerically using the Galerkin method.

Originality/value

The novelty of the present paper is to combine LTNE and second sound effects in solids on thermal instability of a ferrofluid-saturated porous layer by retaining the usual Fourier heat-transfer law in the ferrofluid. The Brinkman-extended Darcy model is used to describe the flow in a porous medium. The effect of different types of velocity and magnetic boundary conditions on the instability of the system is discussed.

Keywords

Citation

M., R., Shivakumara, I.S. and A.L., M. (2019), "Cattaneo–LTNE porous ferroconvection", Multidiscipline Modeling in Materials and Structures, Vol. 15 No. 4, pp. 779-799. https://doi.org/10.1108/MMMS-11-2018-0189

Publisher

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Emerald Publishing Limited

Copyright © 2019, Emerald Publishing Limited