Interaction between conduction and radiation during the phase-change process within multidimensional participating media was numerically investigated. The solutions were based on the reproducing kernel particle method (RKPM). Test cases were analyzed and compared to results from analytical solutions and other studies to examine the performance of RKPM. Comparisons indicate that the RKPM is stable and accurate. The effect of thermo-optics effect on the phase-change process was carried out with the refractive index increases/decreases linearly with the temperature. The solidification process involving radiation was studied in a 2D enclosure. The effects of different parameters, i.e., extinction coefficients, scattering albedos, conduction-radiation parameters, and latent heat, on the temperature profiles were investigated, and the results show the parameters have significant effects on the solidification process. In addition, the solidification process during convection-radiation cooling was analyzed in a cuboid enclosure with the effect of various phase transition temperature ranges. (C) 2017 Elsevier Ltd. All rights reserved.