RK4 and HAM Solutions of Eyring–Powell Fluid Coating Material with Temperature-Dependent-Viscosity Impact of Porous Matrix on Wire Coating Filled in Coating Die: Cylindrical Co-ordinates

In this work, we studied the impacts of transmitting light, nonlinear thermal, and micropolar fluid mechanics on a wire surface coating utilizing non-Newtonian viscoelastic flow. Models with temperature-dependent variable viscosity were used. The boundary layer equations governing the flow and heat transport processes were solved using the Runge–Kutta fourth order method. A distinguished constituent of this study was the use of a porous matrix that acted as an insulator to reduce heat loss. In this paper we discuss the effects of numerous development parameters, including [Formula: see text] , [Formula: see text] , and [Formula: see text] (non-Newtonian parameter, heat-producing parameter, viscosity parameter, variable viscosity parameter, porosity parameter, and Brinkman number, respectively). Furthermore, the effects of two other parameters, D and M, are also discussed as they relate to velocity and temperature distributions. We observed that the velocity profiles decreased with increasing values of [Formula: see text]. Fluid velocity increased as the values of [Formula: see text] , and [Formula: see text] increased, while it decreased when the values of [Formula: see text] , [Formula: see text] and [Formula: see text] increased. For increasing values of [Formula: see text] , the temperature profile showed increasing behavior, while [Formula: see text] showed decreasing behavior. Furthermore, the present work is validated by comparison with HAM and previously published work, with good results.