Transient drainage of the thin film of linearly viscous MHD fluid on a slippery flat belt

Abstract

This paper considered the transient drainage of a linearly viscous magnetohydrodynamic (MHD) fluid down a vertical flat slippery belt. An inhomogeneous partial differential equation with an inhomogeneous boundary condition was developed. Exact solutions for the velocity distribution, flow rate, surface profile, and variable thickness were then computed. The effect of MHD and the slip parameter on the velocity, flow rate, and surface profile were then considered. The effect of the magnetic field on the derived flow properties was discussed and represented graphically. It was determined that the absence of the magnetic field and the assumption of no-slip boundary conditions reduced the problem to the well-known Jeffreys problem.