Dissolution of steel scrap in molten iron is studied by using analytical as well as numerical approaches for the case of a heat transfer-controlled process. The approaches used are Green's function approach, quasi-static approach, integral profile method (IPM) (with parabolic profile), and finite difference methods (FDM). Application of FDM explicit and FDM implicit with fixed grid and variable grid is described. Accuracy of all the approaches is compared in terms of total dissolution time evaluated from overall heat balance criterion. The selection rule of time step and deciding the suitable approach for achieving minimum error for different operating conditions, represented by nondimensional Biot number, are described in this paper.