Application of novel method to withdrawal of thin film flow of a magnetohydrodynamic third grade fluid

In this work, we examine thin film flow of a non-Newtonian third-grade fluid flowing on a vertical moving belt. The modelled differential equation is solved using the Homotopy perturbation method and the Optimal axillary functions method. The solutions obtained by the proposed methods are compared through graphs and tables. Results reveal the efficiency, reliability, and fast convergence of both methods as the obtained solutions are in close agreement. The effect of different flow parameters for velocity profile, flow rate, and shear stress on the belt is also investigated. HPM and OAFM are particularly effective in solving nonlinear differential equations compared to some traditional numerical methods. OAFM is specifically useful in solving nonlinear boundary value problems. Both methods offer a flexible and efficient approximate solution for complex systems described by nonlinear differential equations and have a wide range of applications in heat conduction, fluid dynamics and structural mechanics