A modelling of a metallic bath heating with a transferred arc has been developed using the EDF's research code "Melodie". The computational tests are based on a pilot furnace of 200kW - 2000A, 300kg of iron on which an experimental study is in progress. The two-dimensional axi-symmetrical model considers turbulent or laminar flows, temperature and electromagnetic fields both in the arc and the bath. In the arc chamber the influence of the iron vapour on the plasma properties and the radiative loss are taken into account. A one-dimensional subgrid model is used to describe the anodic layer on the bath surface. Concerning the bath domain, both the solid and liquid regions are treated. Arc and bath domains are computed separately and linked by a coupling procedure through the boundary conditions. This paper presents recent results with an emphasize on those concerning the near-bath surface region.