Similarity analysis of magnetohydrodynamic flows with viscous stress relaxation

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Abstract
A novel similarity solution in terms of a hyperelliptic integral is given for a magnetohydrodynamic flow across an azimuthal magnetic field in a diverging duct, under consideration of viscous stress relaxation. Velocity profiles and the critical duct angle for flow separation are calculated as a function of the Reynolds number and the Hartmann number. It is shown that viscous stress relaxation modifies the velocity distribution and reduces considerably the critical duct angle for flow separation at low Reynolds numbers. At large Reynolds numbers, viscous stress relaxation is less important, and the results approach asymptotically those of ordinary magnetofluiddynamics, which is based on a static relation between viscous stresses and the velocity component gradients.