Thin film flow of Casson liquid over a nonlinear stretching sheet in the presence of a uniform transverse magnetic field

Thin film flow of Casson liquid over a nonlinear stretching sheet is studied in the presence of a transverse uniform magnetic field. The evolution equation for the film thickness is derived using the long-wave approximation for thin liquid film and this nonlinear partial differential equation is solved numerically by using the Newton-Kantorovich method. Four different types of nonlinear stretching velocities are considered to study the effects of Casson parameter and Hartmann number on film thinning rate and the corresponding film thinning patterns are analyzed. It is observed that the Casson parameter exerts resistance on film thinning. Further it is also found that all types of stretching generate film thinning, but non-monotonic stretching provides faster thinning at small distances from the origin.