Homotopy analysis methods with applications to thin-film flow of a magnetohydrodynamic-modified second grade fluid

This study investigates thin film's drainage and lifting of a steady, non-isothermal-modified second-grade incompressible fluid. An approximate analytical technique The homotopy analysis method (HAM) is used to solve the developed governing equations for velocity and temperature fields together with boundary conditions. The expressions for velocity profile, average velocity, temperature distribution, shear stress, and volume flow rate are provided explicitly. The flow of the thin film is found to be substantially dependent on the flow behavior index m, magnetic field parameter, dimensionless numbers say stock number S-t, and Brinkman number B-r. The impact of the above-involved parameters on the fluid's temperature and velocity is depicted numerically as well as graphically.