Heat transfer in MHD thin film flow with concentration using lie point symmetry approach

Heat and mass transfer in a viscous film on an unsteady stretching surface in the presence of a variable magnetic field is investigated using Lie symmetry analysis. Combination of translational and scaling Lie point symmetries is used to obtain invariants of the model. The deduced invariants provide a new generalized class of similarity transformations that have not been used before. These transformations restructure the governing problem in a system of eight-parameter nonlinear ordinary differential equations. Analytic series solutions are obtained for the resulting system of equations for different values of these parameters and are illustrated graphically. We found that coefficients of the translational symmetries do not have any effect on the solutions however, coefficients of the scaling symmetries significantly affect the variation of temperature and concentration distribution across the fluid film and help in controlling the heat and mass transfer rates. Also, increasing the value of unsteadiness and magnetic parameter decreases the film thickness and promotes a uniform temperature and concentration across film thickness. Furthermore, we found that at the lower values of Prandtl and Schmidt number, diffusion dominates the heat and mass transfer while at the higher values advection dominates the heat and mass transfer.