Unsteady two-layer film flow on a non-uniform rotating disk in presence of uniform transverse magnetic field

Two-layer film flow over a non-uniformly rotating disk in presence of uniform transverse magnetic field is studied numerically under the assumption of planar interface. von Kármán's type similarity variables are used to transform the Navier-Stokes equations into a set of coupled unsteady non-linear partial differential equations. These guiding equations are solved with help of finite difference method. It is found that the lower layer thins faster than the upper layer at the initial stage, later on, upper layer thins faster in all three different type of rotations. Further it is shown that the thinning rate for both the layers slowdown with increasing value of either Ekman or Hartmann number.