This paper presents the advancements in developing a 2D-axisymmetric finite element method model for a pilot-scale furnace used in the production of manganese alloys. The model is specifically designed to simulate furnace runs and predict the production of both ferromanganese and silicomanganese alloys, along with acid and basic slags. The multiphysics model incorporates several intercoupled phenomena, including material flows, physical-chemical transformations, electrical conditions, and heat transfer. It enables the investigation of both steady and transient states through time-dependent simulations. The model provides valuable insights into the distribution of materials within the furnace, temperature profiles, current paths, energy balances, and the rates and compositions of alloy and slag production.