Thermocapillary thin film flow upon a porous heated stretchable cylinder

Abstract

AbstractEarlier research work related to the unsteady flow of thin liquid film on a heated stretching cylinder has considered the boundary‐layer approximation under the assumption that the film thickness is thick. In this article, we have considered the full set of Navier–Stokes equations to study the unsteady film development over a porous heated stretching cylinder with the assumption that film height either coincides or lies within the boundary‐layer thickness. The effects of magnetic field, suction/injection, and cooling or heating of the cylinder have been considered for investigation. The governing set of coupled nonlinear partial differential equations is solved numerically by the implicit finite difference scheme (Crank–Nicolson). It was found that the film thinning rate diminishes with rising values of the porosity parameter and Hartmann number. It is also noted that the film thickness is enhanced for injection whereas opposite results are observed for suction through the porous cylinder. The thermocapillary effect showed that the thinning rate of the liquid film decreases or increases according to the surface of the cylinder being heated or cooled. It is observed that continuously increasing the stretching speed of the cylinder produces faster thinning of the liquid film. The temperature of the liquid film is the maximum at the surface of the cylinder and it decreases toward the free surface when the cylinder is heated. But the opposite phenomenon occurs when the cylinder is cooled.