Linear and non-linear analyses of convection in a Rivlin-Ericksen fluid-saturated porous medium

Linear and non-linear analyses of convection in a second-order Boussinesquian fluid-saturated porous medium are made. The Rivlin-Ericksen constitutive equation is considered to effect a viscoelastic correction to the Brinkman momentum equation together with a single-phase heat transport equation. The linear and non-linear analyses are respectively based on the normal mode technique and the truncated representation of Fourier series. The linear theory reveals that the critical eigenvalue is independent of viscoelastic effects and the principle of exchange of stabilities holds. The non-linear study of cellular convection leads to an autonomous system of differential equations which is solved numerically. The finite amplitude disturbances are found to be independent of transient conditions and viscoelasticity is shown to stabilize the system. The Nusselt number is calculated for different values of the parameters arising in the problem. The possibility of chaotic motion and its similarity to the problem of magnetoconvection are discussed.