Transient MHD rotating flow over a rotating sphere in the vicinity of the equator

Abstract

Transient rotating flow of a laminar incompressible viscous electrically conducting fluid over a rotating sphere in the vicinity of the equator has been investigated. We have considered the situation where prior to the time t=0 both the fluid and the sphere are at rest and at time t=0 they are impulsively rotated with different angular velocities either in the same direction or in opposite directions and subsequently maintained at the same angular velocities. The effects of surface suction and the magnetic field are considered in the analysis. The nonlinear coupled parabolic partial differential equations governing the boundary layer flow have been solved by using an implicit finite-difference method. The computation has been carried out starting from time t=0 to t→∞ when the steady-state is reached. For large suction and magnetic field, analytical solutions have been obtained for the steady state case. Also the asymptotic behaviour of the steady-state equations for large independent variable η (η→∞) has been examined. The early flow development is governed by the Rayleigh type of equations and the steady state is governed by the Bodewadt type of equations and there is a smooth transition from the early flow development to the steady-state flow. The surface shear stresses in the meridional and rotational directions decrease with increasing time until the steady state is reached. The surface shear stress in the rotational direction is found to increase with magnetic field and suction, but the surface shear stress in the meridional direction decreases.