Influence of magnetic field on Marangoni convection: An investigation with mixed hydrodynamic and thermal boundaries

The effect of a unvarying vertical magnetic field, counteracting gravity, on the initiation of Marangoni convection in a horizontal layer of electrically conducting liquid is systematically examined using linear stability analysis. In this setup, the upper surface of the liquid layer is free, with surface tension gradients arising due to temperature variations, while the lower boundary is permeable, each subject to mixed thermal conditions. Using the Fourier series method, the eigenvalue equation is derived analytically to shed light on how this system behaves. Numerical values of the critical Marangoni number and wave number at the onset of Marangoni convection are calculated for prescribed values of the other parameters involved in the problem. Interestingly, it is observed that the limiting cases of the permeable parameter encompass scenarios where the lower boundary is either dynamically free or rigid, and the thermal boundary conditions are considered special cases-each worthy of its own investigation. The asymptotic behavior of the Marangoni number at high Chandrasekhar number is also further explored. A detailed analysis of the marginal stability curves offers a clear picture of the impact of the magnetic field on the onset of convection.