Free surface film flow of an unsteady second grade fluid over a stretching sheet with surface tension linearly varies with temperature

In this investigation, the work of Noor and Hashim (2010) is explored in a more advance form by considering the effectiveness of the second grade boundary layer equations with the adjust of pressure term in the presence of transverse magnetic field. The conducted unsteady momentum equations in xy-plane attached with energy equation are shifted into a group of two ODEs involving the important physical parameters, having effective results for the constructive progress. These parameters are second grade non-dimensional parameter, surface tension parameter(thermocapillary number), temperature Grashof number, sheet thickness, magnetic parameter(Hartmann number), Prandtl number and non-dimensional parameter of unsteadiness. The same system give local free surface temperature, heat transfer(heat flux) normal to the flow surface and local surface skin friction. All observations are possible by the use of Homotopy Analysis Method called HAM. Graphs and Tables are made to see the physical properties of the fluid flow by varying arbitrary parameters. Error analysis is a part of this study which define the validity of the HAM method. Further, comparison of the methods(HAM and BVP4C) are done in a table for the validity of the solution.