Lie symmetry analysis of heat transfer in a liquid film over an unsteady stretching surface with viscous dissipation and external magnetic field

Abstract

Fluid flow and heat transfer in thin films over unsteady stretching sheets are studied and analyzed by employing similarity transformations and analytical or numerical solution schemes. We derive Lie point symmetries for system of partial differential equations describing the flow and heat transfer in a thin liquid film on an unsteady stretching surface with viscous dissipation in the presence of external magnetic field. We deduce a 5-dimensional Lie point symmetry algebra. We use a couple of the admitted Lie point symmetry generators to construct new similarity transformations for the considered model, through associated invariants. These transformations enable reductions of the model to nonlinear ordinary differential equations. We construct analytic solutions for this system using the Homotopy analysis method to study the considered MHD flow and heat transfer. These results are presented in the form of tables and figures to reflect variations in fluid velocity, film thickness and heat transfer with the magnetic parameter, Prandtl number, Eckert number and unsteadiness parameter. We show that these variations in the velocity and temperature profiles are different from those reported earlier for the flow and heat transfer within a thin film under the effects of viscous dissipation and external magnetic field.