Numerical modeling of Marangoni convection in the presence of external magnetic field

The present numerical study has been conducted to explore on the effects of external magnetic field at different angle of inclination on the flow driven by the combined mechanism of buoyancy and thermo-capillary flow in an open enclosure. The enclosure is provided with localized heating from below and symmetric cooling is assumed from sides. Along the free surface on the top of the enclosure, the surface tension varies with temperature difference which is known as the Marangoni effect and also called the thermo-capillary effect. The governing equation of the system (i.e. mass, momentum and energy) are presented in the non-dimensional form along with necessary boundary conditions and hence been solved numerically by Galerkin finite element method (FEM) with triangular discretization system. The effect of pertinent parameters such as Hartmann number (0 < Ha < 100), angle of inclination of the magnetic field (0° < ϕ < 90°), Grashof number (103 < Gr < 106), Marangoni number (-100 < Ma < 100) and Prandtl number (0.7 < Pr < 7) on the isotherms, streamlines inside the enclosure as well the heat transfer performance of the system have been explored for various parametric conditions of the system. One key observation is flow field changes drastically with angle of inclination in the presence of the Marangoni effect. And also the heat transfer increases at higher Prandtl number and Grashof number.