Hydromagnetic combined convection flow in a vertical lid-driven cavity with internal heat generation or absorption

The problem of unsteady, laminar, combined forced-free convection flow in a square cavity in the presence of internal heat generation or absorption and a magnetic field is formulated. Both the top and bottom horizontal walls of the cavity are insulated while the left and right vertical walls are kept at constant and different temperatures. The left vertical wall is moving in its own plane at a constant speed while all other walls are fixed. A uniform magnetic field is applied in the horizontal direction normal to the moving wall. A temperature-dependent heat source or sink is assumed to exist within the cavity. The governing equations and conditions are solved numerically by the finite-volume approach along with the alternating direct implicit (ADI) procedure. Two cases of thermal boundary conditions corresponding to aiding and opposing flows are considered. Comparisons with previously published work are performed and the results are found to be in excellent agreement. A parametric study is conducted and a set of representative graphical results is presented and discussed to illustrate the influence of the physical parameters on the solution.