Melting Flow in Wire Coating of a Third Grade Fluid over a Die Using Reynolds’ and Vogel’s Models with Non-Linear Thermal Radiation and Joule Heating

Wire coatings are necessary to provide protection from the aggressive environment and to add mechanical strength to wires and cables. In this study, we investigated the effect of radiative linear as well as non-linear heat transfer on the wire coating in response to joule heating, using a third grade fluid as the coating material. For the temperature dependent viscosity, two models namely—Reynolds’ and Vogel’s—were used. The non-linear ordinary differential equations were solved analytically by the Homotropy Analysis Method (HAM). Numerical technique was also applied for comparison and good agreement was found. It is interesting to note that the temperature parameter had a remarkable effect on the temperature distribution and heat transfer characteristics in the flow region within the die. It was observed that the velocity of the fluid within the die decreased as the magnetic parameter increased, while the magnetic field had an accelerating effect on the temperature distribution. Near the surface of the wire, the velocity of the coating material accelerated as the temperature parameter and radiation parameter increased. Analysis also showed that the temperature of the coating material decreased with increasing radiation and temperature parameters.