Refractory linings of electric arc furnaces are subjected to intense thermal loads, leading to occasional failure of the insulating bricks. A numerical model that simulates the phenomena of arcing, scrap melting, and the transient thermal evolution in the refractory lining of a laboratory‐scale direct current‐electric arc furnace (DC‐EAF) is developed. The rise in the temperature of the refractory lining depends on many factors, including the duration of the melting operation, the intensity and duration of arcing, the design of the furnace, thermophysical properties, and the thickness of the lining. Continuum formulation‐based equations for the transport of momentum, energy, and species, auxiliary models of phase changes associated with scrap melting and evaporation of metal under the arc and Maxwell's equations are solved in a conjugate domain to model the progress of the melting of the scarp and temperature evolution in the refractory lining. Combining experimental data from lab‐scale DC‐EAF, the model is enhanced to represent the laboratory experiment. Scrap with high porosity needs more time for melting, and thermal damage of refractory lining is linked to prolonged arcing coupled with the poor quality of refractory materials.