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

Abstract

Abstract 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 − θ ′ ( 0 ) $-\theta'(0)$ , surface skin-friction coefficient f ″ ( 0 ) $f''(0)$ , free surface temperature θ ( 1 ) $\theta(1)$ for flow field, and heat transfer are studied in this article.

Keywords

• second grade fluid
• HAM
• magnetic field
• thin film
• free surface flow
• unsteady stretching surface