Spinning of a liquid film from a rotating disc in the presence of a magnetic field - a numerical solution

A numerical solution is obtained for the development of a conducting fluid film on the surface of a spinning disc, in the presence of a magnetic field applied perpendicular to the disc. A finite-difference method is employed to obtain the solution of Navier-Stokes equations modified to include magne tic forces due to MHD interactions. The combined effects of film inertia, a cceleration of the disc and magnetic forces are analysed. The numerical res ults reveal that the rate of thinning of the fluid film is strongly influen ced by the inertial and magnetic forces when the Reynolds number is large a nd that the existing asymptotic theory by Ray and Dandapat [24] is inadequa te for predicting transient film thickness. When the disc has a finite acce leration at the start-up, the magnetic and inertia effects are important ev en at low Reynolds numbers and the thinning rate is reduced. It is observed that for both low and high Reynolds number flows, the film thickness incre ases with Hartmann number M for a fixed time and the rate of depletion is l ess for large M than for small M.