In this work, the melting process of a polymeric material is numerically investigated. In general, the heat required for melting plastics is obtained throughout electrical resistances or by burning fossil fuels. The heat transfer mechanisms of these common practices correspond to conduction and convection, respectively. This work explores the feasibility of using radiation as the primary mechanism of energy supply, which has not been widely studied. The energy to achieve the phase change from solid to liquid can be obtained by concentrated solar energy radiation. The total energy required is calculated solving the energy equation using the enthalpy formulation.  An explicit formulation with an enthalpy linearization was implemented in the Mathematica programming language and compared with the solution in the commercial softwares Ansys Fluent and COMSOL Multiphysics showing a good agreement. Based upon numerical predictions, it is examined the effects of the relevant parameters, such as incident radiation and convective heat transfer coefficient, on the melting process. It is observed that under weather conditions commonly attained in different cities worldwide, with a radiation of 1000 W/m$^2$ and low convective losses with $h=8$ W/m$^2\cdot$K, the melting process of a cylindrical rod of 3/4 inches diameter can be carried out in around 2 hours.