Numerical and Analytical Study of Heat Transfer in the Wire Coating Process Using Carreau–Yasuda Fluid Model

In this article, we present a non-isothermal study of the wire coating process using the Carreau-Yasuda fluid model. Our aim is to explore how the Carreau-Yasuda fluid model parameters are linked to key operational factors in the wire coating process. These factors encompass the radius of the coated wire, the volumetric flow rate, and the force needed to pull the wire. The equations that depict the flow and heat transfer within the die are solved: (a) analytically using the perturbation method to get the analytical expression for velocity, temperature distribution, and relevant engineering quantities; (b) numerically using shooting method with the "Runge-Kutta-Fehlberg algorithm." The physical effects of the Weissenberg number (We), power law index (n), pressure gradient (A), and Brinkman number (Br) on the velocity profile, temperature distribution, and engineering quantities are discussed with the help of different graphs. Our findings reveal that, in the case of shear thinning (n < 1) with a constant pressure gradient, as compared to the Newtonian scenario, both the thickness of the coated wire and the force required to pull the wire decrease with an increase in the Weissenberg number (We). Moreover, the force required to pull the wire also decreases with an increase in the values of the pressure gradient parameter.