Creeping axisymmetric MHD flow about a sphere translating parallel with a uniform ambient magnetic field

This work investigates the slow viscous MHD axisymmetric flow about a solid sphere with a radius a translating parallel to a uniform magnetic field with a magnitude B > 0 in a quiescent conducting Newtonian liquid with a uniform viscosity μ and a conductivity σ > 0. The advocated treament exploits two fundamental axisymmetric MHD flows recently obtained elsewhere and holds by essence whatever the Hartmann number Ha = αB/√μ/σ. It consists in determining the surface traction at the sphere boundary by inverting there a boundary-integral equation and then getting the flow velocity and pressure in the liquid by appealing to integral representations of those quantities solely in terms of the surface traction. As a result, the drag experienced by the translating sphere and the MHD flow patterns about it are given for different values of Ha. Not surprisingly, the MHD flow about the sphere is found to be very sensitive to the Hartmann number Ha.