MHD effect on double diffusive mixed convection in a lid driven trapezoidal enclousure for unsteady flow

Abstract

The effect of magnetic field on unsteady double diffusive mixed convection in a lid driven trapezoidal enclosure with uniformly (case-1) and non-uniformly (case-2) heated and concentrated bottom wall has been explored numerically. Both side walls are adiabatic but the top wall is kept at a constant low temperature and concentration and moves with a uniform velocity. The magnetic field is applied along the negative x-axis direction. The enclosure is filled with eclectically conducting fluid so that the magnetic field affect is noticeable. The physical problem is presented mathematically by different set of governing equations along with the corresponding initial and boundary conditions. Using a class of appropriate transformations, the governing equations along with the corresponding initial and boundary conditions are transformed into non-dimensional form, which are then solved by employing a finite element method based on the Galerkin weighted residual technique. Numerical calculation is carried out for different parameters namely, Hartmann number (Ha = 0.0-50), Lewis number (Le = 0.1-50), Buoyancy ratio (Br = -10 to 10) and Richardson’s number (Ri = 0.1-100) at time τ = 1. The velocity profile as streamlines, temperature distribution as isotherm lines, mass distribution as iso-concentration lines, the heat and mass transfer rate in terms of average Nusselt and Sherwood number inside the cavity is shown graphically. Higher heat and mass is transferred for uniformly heated and concentrated bottom wall than the non-uniformly heated and concentrated bottom wall.