Abstract
In this article, we study the effect of variable viscosity on the flow and vortex instability of non-Darcian free convection boundary layer flow on a horizontal surface in a saturated porous medium. The wall temperature is a power function of the distance from the origin. The variation of viscosity is expressed as an exponential function of temperature. The transformed boundary layer equations, which are developed using a non similar solution approach, are solved by means of a finite difference method. The analysis of the disturbance flow is based on linear stability theory. The local Nusselt number, critical Rayleigh number and the associated wave number at the onset of vortex instability are presented over a wide range of wall to ambient viscosity ratio parameters μ*= μ w /μ∞. The variable viscosity effect is found to enhance the heat transfer rate and destabilize the flow for liquid heating, while the opposite trend is true for gas heating.
Highlights
The problems of the vortex mode of instability in free and mixed convection flows over horizontal and inclined heated surfaces in saturated porous media have received considerable attention
The effect of variable viscosity on non-Darcy, free or mixed convection flow on a horizontal surface in a saturated porous medium is studied by Kumari [16]
Afify [18] studied the effects of non-Darcy, variable viscosity and Hartmann-Darcy number on free convective heat transfer from an impermeable vertical plate embedded in a thermally stratified, fluid saturated porous medium for the case of power-law variation in the wall temperature
Summary
The problems of the vortex mode of instability in free and mixed convection flows over horizontal and inclined heated surfaces in saturated porous media have received considerable attention (see [1,2,3,4,5,6,7,8,9,10,11]). The effect of variable viscosity on non-Darcy, free or mixed convection flow on a horizontal surface in a saturated porous medium is studied by Kumari [16]. Afify [18] studied the effects of non-Darcy, variable viscosity and Hartmann-Darcy number on free convective heat transfer from an impermeable vertical plate embedded in a thermally stratified, fluid saturated porous medium for the case of power-law variation in the wall temperature. In [15,16,17,18], the viscosity of the fluid is assumed to vary as an inverse linear function of temperature, whereas in [19], the variation of viscosity with temperature is represented by an exponential function
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