Open Access Research

Thermal instability in a non-Darcy porous medium saturated with a nanofluid and with a convective boundary condition

Sachin Shaw and Precious Sibanda*

Author Affiliations

School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X01, Scottsville, Pietermaritzburg, 3209, South Africa

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Boundary Value Problems 2013, 2013:186  doi:10.1186/1687-2770-2013-186

Published: 20 August 2013

Abstract

In this paper, we investigate the effect of vertical throughflow on the onset of convection in a horizontal layer of a non-Darcy porous medium saturated with a nanofluid. A normal mode analysis is used to find solutions for the fluid layer confined between parallel plates with free-rigid boundaries. The criterion for the onset of stationary and oscillatory convection is derived. The analysis incorporates the effects of Brownian motion, thermophoresis and a convective boundary condition. The effects of the concentration Rayleigh number, Lewis number, Darcy number and modified diffusivity ratio on the stability of the system are investigated.

Keywords:
throughflow; convective boundary condition; oscillatory convection; linear stability analysis