Fluid film squeezed between two rotating disks in the presence of a magnetic field

Abstract

A similarity solution is obtained for the flow of an electrically conducting viscous fluid film squeezed between two rotating disks which at time t are spaced a distance

D(1−αt)12 apart. The flow is under the influence of an external applied magnetic field H, which will give rise to an induced magnetic field B(r,z,t) with components Br, Bφ and Bz between the two disks. The combined effects of vertical motion of the upper disk, the rotational motion of the two disks, the magnetic forces on the velocity profiles, the magnetic field distributions in the fluid, the load capacity and the torques that the fluid exerts on the disks are studied. In general, the results show that the rotational motion of the lower disk described by ω1 (or R1) and the axial component of the magnetic force described by R3 have opposite effects on the load capacity and the torque exerted on the lower disk. It is established that the torque exerted on the two disks reaches its maximum absolute value when the two disks rotate in opposite directions with the same angular velocity (S = −1). It is found that the axial magnetic force R3 increases the azimuthal velocity of the fluid while the angular velocity of the upper disk ω2 for S>0 disperses the axial and azimuthal components of the induced magnetic field.