Darcy–Benard–Marangoni convection in porous media

The onset of coupled Darcy–Benard–Marangoni convection in a liquid saturated porous layer of high permeability of practical importance is investigated by employing the Brinkman–Forchheimer– Lapwood-extended Darcy flow model with fluid viscosity different from effective viscosity. The lower boundary is taken to be rigid and insulating to temperature perturbations, while the upper surface is open to atmosphere and subject to a general thermal condition. The critical eigenvalues are obtained numerically, in general, using Galerkin method. However, closed form solution is also obtained using regular perturbation technique for insulated boundaries. Besides, the eigenvalue problem is solved exactly for pure Darcy–Marangoni convection. The numerical and analytical results are found to be in excellent agreement with each other. It is observed that the effect of buoyancy is destabilizing, while an increase in the permeability parameter is to delay the onset of convection. The Biot number and the ratio of effective viscosity to fluid viscosity are found to increase the critical conditions. Some known results are recovered as special cases.