Investigation of Wire Coating Using Hydromagnetic Third-Grade Liquid for Coating along with Hall Current and Porous Medium

In this research study, we investigated and performed coating analysis of wire by using MHD convective third-order fluid in the presence of a permeable matrix taking into account the Hall current. The equations that control the motion of fluid in the chamber are first modeled and then numerically solved by using 4th order Runge–Kutta–Fehlberg technique. The Runge–Kutta–Fehlberg method is a powerful tool used in this article to attain a numerical solution for a system of nonlinear ordinary differential equations describing the problem of fluid flow. The impact of governing parameters on velocity and temperature profiles is investigated graphically. It is noticed that the velocity profiles ur rise as the value of viscoelastic parameter β increases and slow down when the permeability parameter K and the Hartmann number M increase. Also, the temperature profiles θr enhance as the Brinkman number Br, permeability parameter K, magnetic parameter M, and non-Newtonian parameter β increase. For the sake of validation, the proposed method is also compared with BVPh2, and good agreement is found. Furthermore, a comparison is also done with the published work as a limiting case.