The aim of this project aims to develop a magnetohydrodynamics (MHD) numerical model applied in the metallurgy industries, mainly for submerged arc furnaces (SAFs) of Silicon/Ferrosilicon metal production. In the SAF, energy is re-leased by ohmic heating as the current passes through the furnace. This heat dissipation is split between an electric arc at temperatures 20000 K and releases heat that supports the last and most energy-intensive step of silicon production. To better understand the silicon production process, it is crucial to get an insight into the electric arc behavior in SAF. The phenomena in SAF are governed by chemistry and magnetohydrodynamics. This paper focuses on modeling MHD, considering the Lorentz forces, Ohmic heating, and radiation transport. In the present case, a vector potential method is applied to solve the electromagnetic equations coupled with fluid flow equations. Each physics problem is solved simultaneously. On the one hand, the main challenge is modeling the plasma arc. The physical properties of the plasma are one of the keys to modeling electric arc behavior. On the other hand, the realistic simulation of the electric arc phenome-non leads to enormous computation times. In the scope of this work, the vector potential electromagnetic equations are implemented in Ansys Fluent as user-defined scalars (UDS) transport equations. The implementation includes the standard approximations for arc modeling used in industry, such as material properties calculation in the LTE approximation implemented in the Ansys Fluent flow solver. Different electrical properties will be presented, such as arc current and voltage, including temperature and velocity distributions.