Instability in Walters B’ Viscoelastic Dusty Fluid through Porous Medium

A detailed account of the theoretical and experimental study of thermal instability (Bénard convection) in Newtonian fluids, under varying assumptions of hydrodynamics and hydromagnetics, has been treated in detail by Chandrasekhar [1]. The use of Boussinesq approximation has been made throughout, which states that the density may be treated as a constant in all the terms in the equations of motion except the external force term. Chandra [2] observed that in an air layer, convection occurred at much lower gradients than predicted if the layer depth was less than 7mm, and called this motion “Columnar instability”. However, a Bénard -type cellular convection was observed for layers deeper than 10 mm. Chandra [2] added an aerosol to mark the flow pattern. Thus there is a decades-old contradiction between the theory and the experiment. Scanlon & Segel [3] have considered the effect of suspended particles on the onset of Bénard convection and found that the critical Rayleigh number was reduced solely because the heat capacity of the pure fluid was supplemented by that of the particles. The effect of suspended particles was thus found to destabilize the layer. Palaniswamy & Purushotham [4] have considered the stability of shear flow of stratified fluids with fine dust and have found the effect of fine dust to increase the region of instability. The medium has been considered to be non-porous and the fluid to be Newtonian in all the above studies.