Unsteady compressible boundary layer flow at the stagnation point of a rotating sphere with an applied magnetic field

Abstract

The paper is concerned with the unsteady compressible boundary layer flow near the forward stagnation point of a rotating sphere in a uniform axial stream of conducting fluid, with magnetic field normal to the surface. The unsteadiness in the flow is created by (i) giving a sudden change in the wall temperature (enthalpy) as the impulsive motion has started, (ii) impulsive change of the rotation of the sphere, and (iii) sudden changing of the free stream velocity. The motion is governed by a coupled set of three nonlinear time-dependent partial differential equations which are solved accurately by Newton's linearization technique and an implicit finite difference scheme. Attention is given to the transient phenomenon from the initial flow to the final steady state solution. The numerical results show changes in the flow pattern with time, rotation and strength of the magnetic field, and are in good agreement with earlier theoretical results. The calculated skin friction, heat transfer, displacement thickness and enthalpy thickness show interesting dependence on time and the physical parameters, which are quite similar to the earlier investigations, and the mechanism of dependence is closely examined.