A Numerical Solution of MHD Heat Transfer in a Laminar Liquid Film on an Unsteady Flat Incompressible Stretching Surface with Viscous Dissipation and Internal Heating

Abstract

This study deals with the numerical solution of MHD flow and heat transfer to a laminar liquid film from a horizontal stretching surface. Similarity transformations are used to convert unsteady boundary layer equations to a system of non-linear ordinary differential equations. The resulting non-linear differential equations are solved numerically by using efficient numerical shooting technique with fourth order Runge–Kutta algorithm (see references [26] and [27]). The effect of  Prandtl number Pr, Eckert number Ec, Magnetic parameter Mn and temperature-dependent parameter on various flow parameters are shown with the aid of graphs. The important observation in this study is, for high values of unsteadiness parameter S reduces the surface temperature which is well in agreement with the earlier published works, under some limiting cases, and temperature-dependent heat absorption is one better suited for effective cooling purpose as temperature-dependent heat generation enhance the temperature in the boundary layer.