Amplitude equation for stationary convection in a viscoelastic magnetic fluid

We report theoretical and numerical results on convection for a magnetic fluid in a viscoelastic carrier liquid. We focus on the stationary convection for idealized boundary conditions. We obtain explicit expressions of convective thresholds in terms of the control parameters of the system. Close to bifurcation, the coefficients of the corresponding amplitude equation are determined analytically. The effect of the rheology and Kelvin force are emphasized and, finally, the nature of the bifurcation is discussed.