Finite element analysis of thin film flows in non-Newtonian third grade Sisko fluid for lifting and drainage applications

Abstract

The study of thin film-like flow has emerged as a critical area in fluid dynamics, driven by its relevance to numerous applications in industries such as semiconductor manufacturing, food processing, irrigation systems, surface coating, and oil refining. This study presents a finite element method to investigate the behavior of third-grade non-Newtonian Sisko fluids in lifting and drainage scenarios. By extending the formulations of third-grade fluids, Galerkin�s finite element method is particularly developed to derive solutions and conduct a comprehensive analysis. The analysis focuses on the impact of various parameters, including film thickness, liquid velocity profile, volumetric flux, viscosity, shear stress, gravitational effects, density, and boundary conditions. The reliability, consistency, and accuracy of the results are assessed by evaluating residuals for different scenarios. The accuracy of the results obtained by the proposed framework is higher than the previous studies as the residuals of proposed Galerkin�s FEM is found as low as 10 ? 17 , whereas traditional semi-analytical techniques stay around 10 ? 6 to 10 ? 2 . Results also reveal that the gravitational parameter inversely affects the velocity profile during lifting, while the material constant exhibits a direct relationship. Conversely, in the drainage scenario, the material constant has an inverse effect on the velocity profile. To the best of our knowledge, the thin film flow of third-grade fluid in both lifting and drainage scenarios has not been attempted using Galerkin�s FEM so far.