Self-similar solution of the unsteady flow in the stagnation point region of a rotating sphere with a magnetic field

The unsteady flow and heat transfer of a viscous incompressible electricall y conducting fluid in the forward stagnation point region of a rotating sph ere in the presence of a magnetic field are investigated in this study. The unsteadiness in the flow field is caused by the velocity at the edge of th e boundary layer and the angular velocity of the rotating sphere, both vary ing continuously with time. The system of ordinary differential equations g overning the flow is solved numerically. For some particular cases, an anal ytical solution is also obtained. It is found that the surface shear stress es in x- and y-directions and the surface heat transfer increase with the a cceleration, the magnetic and the rotation parameters whether the magnetic field is fixed relative to the fluid or body, except that the surface shear stress in x-direction and the surface heat transfer decrease with increasi ng the magnetic parameter when the magnetic field is fixed relative to the body. For a certain value of the acceleration parameter, the surface shear stress in the x-direction vanishes while the surface shear stress in the y- direction and the surface heat transfer remain finite. Also, below a certai n value of the acceleration parameter, reverse flow occurs in the x-compone nt of the velocity profile.