A new Adomian decomposition technique for a thermal analysis forced non-Newtonian magnetic Reiner-Rivlin viscoelastic fluid flow

This paper presents a new semi-analytical method, called the Adomian Decomposition Method (ADM), as well as Finite Element Methods, to study forced Reiner-Rivlin non-Newtonian Magnetohydrodynamic (MHD) fluid motion confined between two disks. The innovation presented in this paper is the utilization of both analytical and numerical methods, namely ADM and FEM, to solve coupled linear differential equations, which enables the calculation and examination of parameters such as heat transfer and fluid velocity between the two disks by simplifying these equations. This model incorporates the magnetic field, and the system of partial differential equations (PDEs) acts as the governing equation in this study, which are then transformed into a set of non-linear ordinary differential equations (ODEs) using von Karman analog variables. The Adomian decomposition method can be used to solve ODEs that are related to boundary conditions. The main findings of this article suggest that as the dimensionless force parameter increases, the displacement of the fluid velocity decreases, as the particles collide with each other, the temperature gradient around the disks decreases inversely. Moreover, when the stress tensor increases, the heat transfer rate reaches its maximum value, and the transverse velocity gradient between different disks decreases.