Thermal convection thresholds in a Oldroyd magnetic fluid

We report theoretical and numerical results on convection for a magnetic fluid in a viscoelastic carrier liquid. The viscoelastic properties is given by the Oldroyd model. We obtain explicit expressions for the convective thresholds in terms of the parameters of the system in the case of idealized boundary conditions. We also calculate numerically the convective thresholds for the case of realistic boundary conditions. The effect of the Kelvin force and of the rheology on instability thresholds for a diluted suspensions are emphasized. ►We study the linear analysis of the convection in magnetic fluids. ►The Rheological properties are given by the Oldroyd model. ►The numerical results are performed by the Spectral method.