Comparative Analysis of Delta Perturbation Method and Homotopy Perturbation Method for Thin Film Flow of Third-Grade Fluid

Abstract

Thin film flow of non-Newtonian fluids has significant importance in coating processes, lubrication systems, polymer processing, food industries, chemical engineering, and other industrial applications where accurate prediction of flow and heat transfer behavior is required. In particular, third-grade fluids provide a more realistic model for complex fluids because they incorporate nonlinear stress–strain characteristics that cannot be fully described by Newtonian fluid models. This study presents a comparative analysis of the Delta Perturbation Method and the Homotopy Perturbation Method for the analytical approximation of thin film flow of an incompressible third-grade fluid under lift and drainage configurations. The governing nonlinear differential equations are derived from the continuity, momentum, and energy equations by considering suitable assumptions for steady, laminar, and incompressible flow. The effects of dynamic viscosity, fluid density, film thickness, third-grade material parameters β₂ and β₃, thermal conductivity, and inclination angle are examined on velocity and temperature profiles. The comparison between the two methods is based on convergence behavior, accuracy, closeness of approximate solutions, and physical interpretation of the obtained results. The expected findings indicate that both methods provide close approximate solutions for the velocity and temperature fields; however, the Delta Perturbation Method offers a systematic perturbation-based framework for treating nonlinear terms. The results are useful for understanding non-Newtonian thin film behavior in coating, lubrication, food processing, chemical engineering, and polymeric fluid applications.