Salt-based phase-change materials (Salt-PCMs) are highly effective for high-temperature thermal energy storage, operating above 500 °C and enabling large absorption and release of thermal energy during solid–liquid phase transitions. In central-tower concentrated solar power (CSP) systems, molten salt is pumped from a cold storage tank to a solar receiver, where concentrated solar radiation heats it. The heated salt is then stored in a hot tank and discharged during periods of low or no solar input to ensure continuous energy supply. A major operational challenge in such systems is preventing salt solidification, which can severely affect performance and reliability. Conducting experimental investigations at these high temperatures is often labor-intensive, costly, and sometimes impractical. Consequently, numerical modeling represents a valuable alternative for analyzing system behavior and addressing key operational challenges. However, accurate numerical simulations require solving large systems of integro-differential equations, which are computationally demanding, particularly for three-dimensional configurations.\\ In this study, we develop a new class of reduced mathematical models to efficiently address radiative heat transfer in phase-change problems, considering configurations both with and without convection. The proposed methodology replaces the original integro-differential radiative transfer equations with a set of elliptic equations that are significantly easier to solve [1], while remaining efficiently coupled with the enthalpy formulation and, when convection is present, the Navier–Stokes equations [2]. A mixed finite element method is employed for spatial discretization, and a second-order implicit scheme is used for time integration [3]. The resulting nonlinear systems are solved using a Newton-based algorithm. Two- and three-dimensional melting problems of sodium chloride with finned geometries are investigated. The results demonstrate that thermal radiation accelerates the phase-change process and significantly reduces melting time in both convective and non-convective cases. Comparisons with existing results from the literature confirm the accuracy and efficiency of the proposed approach.