A model of a partially ionized, high pressure plasma in stagnation flow as it melts a nonhomogeneous solid is presented. It encompasses both the analysis of the multi-fluid plasma to ascertain its bulk temperature and the heat flux profile, as well as its interaction with a receding melt interface in and around the stagnation domain. The model examined in this study couples the plasma motion, bulk energy, electron and ion densities and temperatures, with impinging jet theory to determine the amount of heat transfer into the particular substrate material — soil. “Multi-fluid” equations are derived for an axially symmetric plasma from the Boltzmann equations for Maxwellian velocity distributions. By examining the dominant effects, the equations are scaled and the roles of the driving dimensionless parameters are established. For specified values of these parameters, various numerical methods are used to couple and solve the two distinct models. The first one, to ascertain the moving boundary phase change heat transfer characteristics, is developed by adopting a form of the enthalpy method. The second model, characterizing the plasma jet is solved via and adaptation of the commercially available code, CHEMKIN, developed by the Sandia National Laboratories. A parametric study is performed, leading to evaluation of such important torch characteristics including mass flow rate of the Argon gas, temperature of the plasma bulk, and proximity of the plasma torch to the surface, as it influences the substrate melt zone. The extremely high temperatures produced by the plasma irreversilby changes the material structure of the sample. This new structure, when cooled, forms a predominantly glassy product. Such a vitrification process has been proven to improve the construction properties of the soil and to reduce a toxic sample of the soil into a leachable solid. From the calculations of solid/liquid interfacial location, radii of the melt zones, and depths of the melt zones an overall perspective of the vitrification process is assessed.