on the onsetof thermal instability in a low prandtl number nanofluid layer in a porous medium

Thermal instability in a low prandtl number nanofluid in a porous medium is investigated by using galerkin weighted residuals method for free-free boundaries. for porous medium, brinkman-darcy modelis applied. the model used for the nanofluid describes the effects of brownian motion and thermophoresis. linear stability theory based upon normal mode analysis is employed to find the expression for stationary and oscillatory convection. the effects of prandtl- number, darcy number, lewis number and modified diffusivity ratio on the stationary convection are investigated both analytically and graphically. the results indicated that the prandtl and darcy numbers have a destabilizing effect while the lewis number and modified diffusivity ratio have a stabilizing effect for the stationary convection.