Abstract
The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow. The Ellis model is adopted to describe the fluid rheology. Both horizontal boundaries are assumed to be impermeable. A uniform heat flux is supplied through the lower boundary, while the upper boundary is kept at a uniform temperature. Such an asymmetric setup of the thermal boundary conditions is analysed via a numerical solution of the linear stability eigenvalue problem. The linear stability analysis is developed for three–dimensional normal modes of perturbation showing that the transverse modes are the most unstable. The destabilising effect of the non–Newtonian shear–thinning character of the fluid is also demonstrated as compared to the behaviour displayed, for the same flow configuration, by a Newtonian fluid.
Highlights
The emergence of convection Rayleigh–Bénard cells in a fluid saturated porous medium heated from below is a cornerstone topic in the research on convection heat transfer in porous solids
The onset of the thermal instability is investigated in a porous channel with plane parallel boundaries saturated by a non–Newtonian shear–thinning fluid and subject to a horizontal throughflow
Except for a minor part of the papers available in the literature regarding the Darcy–Bénard instability, most investigators have focussed their attention on the Newtonian fluids saturating a porous medium
Summary
The emergence of convection Rayleigh–Bénard cells in a fluid saturated porous medium heated from below is a cornerstone topic in the research on convection heat transfer in porous solids. The usual setup envisaged in the studies on the onset of Darcy–Bénard instability in a saturated porous layer is one where the plane parallel boundaries are considered as isothermal with different temperatures. The temperature boundary conditions are modified, with respect to the study developed by Celli et al [14], by assuming a uniform heat flux on the lower boundary of the layer. Such a modification is accompanied by a numerical solution of the stability eigenvalue problem, whereas an analytical dispersion relation is available with isothermal boundary conditions [14]. A basic uniform throughflow is imposed along the horizontal x direction
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