Numerical Investigation of Damped Wave Type MHD Flow with Time-Varied External Magnetic Field

Abstract

In recent years, the MHD flow problems has received a significant attention as the behavior of the flow changes when the Lorentz force (electromagnetic force) acts on the fluid. The aim of this study is to observe numerically the behavior of damped wave-type magnetohydrodynamic (MHD) flow in a sufficiently long rectangular channel having time-varied oblique magnetic field. The mathematical model of the considered problem is coupled convection-diffusion heat-type for the velocity of the fluid and convection-diffusion wave-like for the induced magnetic field. To obtain the numerical simulation, we have used the finite difference method for the discretization of the temporal variable and we also have considered the Galerkin finite element method for the discretization of the spatial variable. In the numerical investigation procedure, the time-varied oblique magnetic field has been considered several functions of the time as polynomial, exponential, and trigonometric e.t.c. We have also considered the several values of the Hartmann number and several directions of the induced magnetic field. In literature, there are many studies about numerical solution of steady and unsteady magnetohydrodynamic flow problems using finite element method, boundary element method and finite difference method e.t.c. For all that, it is the first time in the literature, the damped wave type MHD flow has been considered numerically in this study. The numerical results show Hartmann layer occurs for the high Hartmann numbers in accordance with the nature of the MHD flow. We have obtained numerical results in good agreement with the numerical results available in the literature. The acquired numerical results have been presented by the contour plots.