Unsteady MHD film flow over a rotating infinite disk

Abstract

The unsteady MHD flow and heat transfer of a fluid which is spread by a rotating infinite disk have been studied. The unsteady Navier–Stokes equations along with the energy equation taking into account the effect of the axial magnetic field governing the flow are reduced to a system of ordinary differential equations by using similarity transformations. For a given disk rotation, there exist two solutions which depend on the magnetic field. One is the thin film solution and the other is the thick film solution which represents the situation where a stagnant fluid layer is on the top of a flowing fluid near the rotating disk. No solution exists when the disk rotation exceeds a certain value λ 0 ( λ 0=0.5885 in the absence of the magnetic field). This value decreases with increasing magnetic field. Approximate solution for thin film and small acceleration is obtained which is found to be in good agreement with that of the numerical solution. For thick film with low acceleration, the solution tends to the magnetic counterpart of the von Kármán flow. For a fixed magnetic field, the surface shear stresses in the radial and tangential directions and the film thickness increase with the accelerating disk, but the heat transfer decreases. Similarly, for a prescribed disk rotation rate, the surface shear stress in the radial direction and the heat transfer decrease with increasing magnetic field, but the surface shear stress in the tangential direction and the film thickness increase.