The transient Stokes flow induced by a point source of electric current (Q1072413)

The development of the magnetohydrodynamic Stokes flow field due to the discharge of an electric current from a point into a viscous incompressible fluid bounded by a hemispherical bowl is investigated. We also discussed, as a special case, the flow induced for the case when the radius of the hemispherical bowl becomes infinitely large and showed that the time taken to establish the steady state flow in the interior of the hemisphere is reduced by a factor of ten compared with the situation where the flow takes place in a semi-infinite fluid. Our solution is analytic as compared with the existing numerical solution.