thin film flow over a heated nonlinear stretching sheet in presence of uniform transverse magnetic field

the unsteady flow of a thin viscous liquid film over a heated horizontal stretching surface permitted by uniform transverse magnetic field is studied by considering the stretching velocity and the temperature distribution in their general functional forms. an evolution equation for the film thickness is derived using long-wave approximation theory of thin liquid film and this nonlinear pde is solved numerically for some representative values of non-dimensional parameters. it is observed that the magnetic field resists the film thinning process for all types of velocity and temperature distribution. but thermocapillarity enhances the film thinning rate even in presence of magnetic field. further, effect of marangoni and prandtl numbers are explored in presence of magnetic field. physical explanations are provided to understand the different effects on film thinning.