Convective instabilities in a viscoelastic-fluid-saturated porous medium with throughflow

Linear stability theory is used to investigate convective instability in a horizontal porous layer saturated with viscoelastic fluid of Oldroyd-B type in the presence of vertical throughflow. The flow in the porous medium is modelled using a modified Forchheimer - extended Darcy equation for viscoelastic fluids which takes into account the non-Darcy effects of inertia. The Galerkin method is used to obtain the eigenvalues under different hydrodynamic and temperature boundary conditions. The analysis reveals that there is competition between the processes of viscous relaxation and thermal diffusion that causes the first convective instability to be oscillatory rather than stationary. It is established that the oscillatory convection occurs only if Lambda, the ratio of retardation time to relaxation time, is less than unity and the elasticity parameter Gamma exceeds a threshold value which increases with throughflow strength. The effect of throughflow is to suppress the oscillatory convection independent of its direction when the velocity boundary conditions at the bounding surfaces of the porous layer are of the same type. In contrast to this, throughflow in one particular direction augments oscillatory convection if the velocity boundary conditions are not of the same type. It is observed that a decrease in the value of Gamma and an increase in the value of Lambda is found to delay the onset of convection, while the critical wavenumber decreases with both increasing Gamma and Lambda.