Analysis of modified second-grade fluids in thin film configurations employing the asymptotic homotopy perturbation method

Abstract

Abstract This article investigates the steady, incompressible and non-isothermal thin film flow of a modified second grade fluid under both conditions that is, lifting and drainage. The governing highly non-linear ordinary differential equations with appropriate boundary conditions have been solved and achieved approximate solutions employing the Asymptotic Homotopy Perturbation Method (AHPM). The velocity and temperature distributions have been obtained, moreover average velocity, shear stress and volume flow rate at the belt surface are presented graphically for both lifting and drainage configurations. Here it is worth mentioning that the flow of thin films are significantly influenced by $$m$$ (flow behavior index of modified second grade fluid), Brinkman number and Stokes number. The outcomes of this work are relevant to several industrial and engineering applications, comprising coating and drying technologies, polymer extrusion and processing, lubrication systems, chemical and food processing, and thermal control in thin-film transport processes. Additionally, graphical and numerical analyses have been provided to explain the impact of various parameters on the fluid behavior.