Similarity analysis of MHD flow field and heat transfer of a second grade convection flow over an unsteady stretching sheet

Unsteady magnetohydrodynamic (MHD) flow of a second grade fluid over a stretching sheet is a focus of this steady. Surface tension is considered to be varies linearly with temperature. The stretching velocity is defined in (Liu and Andersson in Int. J. Therm. Sci. 47(6):766-772, 2008). Similarity transformation reported by Abbas et al. (Math. Comput. Model. 48:518-526, 2008) are used to develop nonlinear system of differential equations coupled in velocity and temperature fields. The system is solved by the homotopy-analysis method (HAM), while the effects of different parameters such as the unsteadiness parameter S, film thickness, Hartmann number Ma, Prandtl number Pr, Thermocapillary number M, heat flux \(-\theta'(0)\), surface skin-friction coefficient \(f''(0)\), free surface temperature \(\theta(1)\) for flow field, and heat transfer are studied in this article.