Instability of the Benard–Marangoni convection in a porous layer affected by a non-vertical magnetic field

The onset of the Benard–Marangoni convection in a horizontal porous layer permeated by a magnetohydrodynamic fluid with a nonlinear magnetic permeability is examined. The porous layer is assumed to be governed by the Brinkman model; it is bounded by a rigid surface from below and by a non-deformable free surface from above and subjected to a non-vertical magnetic field. The critical effective Marangoni number and the critical Rayleigh number are obtained for different values of the effective Darcy number, Biot number, Chandrasekhar number, nonlinear magnetic parameter, and angle from the vertical axis for the cases of stationary convection and overstability. The related eigenvalue problem is solved by using the first-order Chebyshev polynomial method.