Differential Transform Method Approach to the Study of an MHD Flow of a Third Grade Fluid with Reynolds’ Model Viscosity and Joule Heating

Abstract

In this research, the Differential Transform Method (DTM) approach was utilized to analyze a third-grade fluid, a non-Newtonian substance, flowing within a circular duct subjected to magnetic force and joule heating, while incorporating Reynolds' model viscosity. When both the joule heating parameter (J) and the magnetic parameter (M) are zero (J = M = 0), the midpoint temperature (θ(0)) results demonstrate that DTM converges faster compared to the Adomian decomposition method (ADM), with a difference of about 10−2 between the two methods. Graphical representations of the fluid's velocity and temperature reveal that an increase in magnetic force decreases both velocity and temperature, whereas higher values of the joule heating factor lead to an increase in flow velocity and a reduction in the fluid's temperature at the midpoint of the duct.