It is well known that many materials do not solidify at their nominal phase-change temperature. Rather, nucleation occurs in them at a lower temperature. This phenomenon is usually termed "supercooling" or "subcooling" in the literature. Understanding, prediction and, if possible, prevention,.or at least reduction, of supercooling are very important specifically to latent heat thermal energy storage (LHTES) systems, because the temperature differences in them must be small in order to achieve higher efficiency. In the present study, a novel mathematical model of solidification with supercooling and heat transfer is developed. For the first time, it is multidimensional in space. The model encompasses all possible stages of the process, namely, single-phase liquid cooling from the initial state to the nucleation temperature, kinetic nucleation accompanied by a rapid temperature rise to the nominal phase-change temperature, regular solidification and finally cooling of the solid phase. The kinetic solidification speed, based on the activation energy, is temperature- and, as a result, time-dependent. The model ensures a smooth, physically meaningful transition from the kinetic to regular solidification. Local and overall energy balance preservation at all stages of the process is ensured. The model is based on the enthalpy formulation, resolved using an in-house numerical code based on finite volumes. For the single phase cooling, it is validated using the well-known solutions from the literature. The model is then compared to experimental results of solidification of supercooled gallium in a vertical cylindrical mold. Accordingly, heat transfer in the mold is also included. It is shown that the model reflects the experimental results fairly well, in particular when predicting temperatures at various locations inside the material. Also, physically sound solidification patterns are obtained. (C) 2016 Elsevier Ltd. All rights reserved.