Analysis of thin film flows of Pseudo-Plastic and Oldroyd 6-constant fluids using modified residual power series algorithm

Abstract

This manuscript presents the detailed analysis of thin film flows of two non-Newtonian fluid models by proposing a new modification of residual power series method (RPSM). The numerical algorithm is extended to boundary value problems (BVPs) in the current scenario. Major advantage of RPSM is its direct usage with discretization, linearization or perturbation. Convergence analysis of the proposed algorithm is also performed for the implication of RPSM to thin film phenomena. The governing equations of Pseudo-Plastic and Oldroyd 6-constant fluids leads to highly nonlinear ordinary differential equations (ODEs) in lifting and drainage cases. Due to highly nonlinear nature of the modeled problems, exact solutions do not exist. As a result, validity of the obtained solutions is confirmed by computing residuals in each case. Furthermore, detailed graphical analysis is performed to check the effects of different fluid parameters on the velocity profile in lifting and drainage situations. It is observed that magnetic parameter and non-Newtonian parameter have similar, while stokes number has opposite effects on the velocity in lifting and drainage of thin film of Pseudo-Plastic fluid. On the other hand, in case of Oldroyd 6-Constant fluid, gravitational parameter and involved material constants are showing opposite behavior on the velocity profile in lifting and drainage. Analysis of the numerical solutions and errors reveals that proposed modification ensure reliable solutions and hence may be used for more advanced problems in science and engineering.