Computational analysis of magnetohydrodynamic mixed convection in a lid-driven rectangular cavity with wavy bottom wall

Abstract

Magnetohydrodynamic mixed convection in a lid-driven rectangular cavity with wavy bottom wall is studied numerically in the present thesis. The left and right walls of the cavity are maintained at low temperature whereas the wavy bottom wall is supposed to be high temperature while the remaining wall is kept adiabatic. The left and right cold walls are allowed to move with constant velocity from downward to upward direction in its own plane. A uniform magnetic field of strength is applied perpendicular to the cavity. The Physical problem is presented mathematically by a set of governing equations (such as mass, momentum and energy equations) along with the corresponding initial and boundary conditions. By using appropriate transformations, the governing equations along with the boundary conditions are transformed into non-dimensional form, which are then solved by employing a finite-element scheme based on the Galerkin method of weighted residuals. The investigations is reported for a wide range of dimensionless parameters such as Richardson number, Hartmann number, Prandtl number, Reynolds number and the physical parameter namely number of undulations. These results are also presented graphically in the form of streamlines, isotherms contours, and average Nusselt number along the heated section of the wavy bottom wall at the three values of Richardson number. Comparisons with previously published work are conducted and the results are found to be in excellent agreement. The fluid flow and thermal field inside the cavity depends on strength of the magnetic field, Richardson number and the number of undulations. In addition, heat transfer rate influenced noticiably with the variation of governing parameters.