Assessment of heat transfer in <i>n</i>-immiscible coating layers on heated wire using linearly viscous fluid

Understanding the mechanics of n-immiscible coating layers on electrical wires can improve efficiency, design, and practical applications by optimizing their performance. This paper theoretically analyzes the flow and heat transfer of n-immiscible coating layers on a wire in an annulus die. A mathematical model of n-immiscible coating layers is developed. Formulated sets of linear ordinary differential equations are solved for closed-form solutions. The dynamic viscosity μk, Brinkman number Brk, and thermal conductivity ratio χ emerged as flow control parameters. The effects of the parameters involved in the velocity, temperature, coating thickness, and shear stress of five-immiscible coating layers are observed. It is delineated that internal resistance to flow increases with an increase in dynamic viscosity, thus affecting momentum transfer. This, in turn, reduces shear stress and alters temperature, velocity distribution, and coating thickness. The temperature rise is primarily due to viscous dissipation, while thermal diffusion works to lower it. Furthermore, improved thermal conductivity also contributes to a reduction in temperature. The analysis of five-immiscible coating layers provides insights and knowledge applicable to a coating system with a desired number of coating layers by utilizing the expressions derived for n-immiscible coating layers.