MHD mixed convection in an inclined lid-driven cavity with opposing thermal buoyancy force: Effect of non-uniform heating on both side walls

A numerical study of laminar magnetohydrodynamic mixed convection in an inclined lid-driven square cavity with opposing temperature gradients is presented. The vertical sidewalls are assumed to have non-uniform temperature variation while the top and bottom walls are kept insulated with the top surface moving at a constant speed. The transport equations are given in terms of the stream functions-vorticity formulation and are non-dimensionalized and then solved numerically by an accurate finite-volume method. The computation is carried out for wide ranges of the inclination angle (0 ≤ γ ≤ π/2), the Richardson number (0.01 ≤ Ri ≤ 100), the Hartmann number (0 ≤ Ha ≤ 100), the amplitude ratio (0 ≤ ɛ ≤ 1) and the phase deviation (0 ≤ ϕ ≤ π). The results indicate that the rate of heat transfer along the heated walls is enhanced on increasing either Hartmann number or inclination angle. Average Nusselt number is also, increased with increasing of the amplitude ratio for all values of the phase deviation. The non-uniform heating on both walls provides higher heat transfer rate than non-uniform heating of one wall.