Weakly non-linear magneto-convection in a viscoelastic fluid saturating a porous medium

In this paper the effect of magnetic field on linear and non-linear thermal instability in an anisotropic porous medium saturated with viscoelastic fluid is considered. Normal mode technique is used to investigate the linear stability analysis, while non-linear stability has been done using minimal representation of truncated Fourier series involving only two terms. Extended Darcy model, which includes the time derivative and magnetic field terms has been employed in the momentum equation. The criteria for both stationary and oscillatory convection are derived analytically. The effect of magnetic field is found to inhibit the onset of convection in both stationary and oscillatory modes. Thermal Nusselt number is defined in weakly non-linear stability analysis. Steady and transient behavior of the thermal Nusselt number is obtained by solving the finite amplitude equations using Runge-Kutta method. The nature of streamlines, Isotherms and Magnetic stream functions also has been investigated. The results have been presented graphically and discussed in detail.