Magnetohydrodynamics Flow Over Spherical Body

Abstract

The magnetohydrodynamics flow of electrically conducting Newtonian fluid around an approximate sphere has been discussed in different situations. The motion is slow, steady and axisymmetric which typically happens at very low Reynolds numbers. The governing equations in fluid region are derived by neglecting the inertial terms from the momentum equation in presence of Lorentz force. The equation of motion in porous is governed by Darcy s law and Brinkman equation with magnetic force. Equation of continuity for incompressible fluid is combined together with momentum equation. To determine the coefficients in general solution, the appropriate boundary conditions are applied. The choice of boundary conditions depends on the physical situation. The common boundary conditions include impenetrability, no slip, free slip, far field conditions, continuity of velocity and stress at interface boundary. These conditions insure the uniqueness and physical relevance of the solution. The separation of variable technique is used to solve the partial differential equation arising in magnetohydrodynamics flow problem. By separating the variables, the original partial differential equation is reduced to a set of ordinary differential equation and solved each resulting ordinary differential equation separately. The stream function and#968; in axisymmetric magnetohydrodynamics flow around approximate sphere is derived from the continuity equation. The stream function in axisymmetric flow provides a powerful way to describe the velocity field and simplify the analysis of fluid flow problems. Stream function describes the axisymmetric magnetohydrodynamics flow and ensure that the velocity components satisfy the continuity equation. The stream function solution is the sum of separated solution that satisfies the boundary conditions. The variables and parameters of governing equations are transformed into dimensionless form. newline