Thermal convection thresholds in an Oldroyd magnetic fluid in porous media

We have exploited the Oldroyd-B model to explain the appearance of stationary and oscillatory convection in a viscoelastic magnetic fluid saturating a porous horizontal layer heated from below. The analytical expressions of the Rayleigh number corresponding to each convection are determined as a function of dimensionless parameters. We note that the appearance of steady convection does not depend on the viscoelastic properties of the fluid. Using numerical simulations, we analysed the stabilising effect of each dimensionless parameter on the evolution of the convection and on the size of the convection cells formed. We note that in the oscillatory convection case, the values of the Darcy number, the parameter characterising the permeability of the medium, are low compared to those of stationary convection. The behaviour of the critical frequency for oscillatory convection is studied. The possibility of co-dimension-2 bifurcation is discussed and the boundary between the oscillatory and stationary convections is found.