Transfer of Heat through a Thin Liquid Film

Abstract

The present work discusses heat transfer in thin liquid films past a stretching surface in the presence of Joule heating, radiation, viscous dissipation, and magnetic effects. Using a suitable similarity transformation, the nonlinear coupled partial differential equations are reduced to nonlinear ordinary differential equations. The coupled nonlinear ordinary differential equations are then solved by using the shooting method. The physical quantities, such as the unsteadiness parameter, the Prandtl number, the magnetic field parameter, the radiation parameter, and the viscous dissipation parameter on temperature distributions, are depicted graphically. It is observed that the effects of Prandtl and Eckert numbers are same over the temperature distribution. Furthermore, it is also evident that the increasing values of the unsteadiness parameter enhance the thermal conductivity of the fluid.