In this research, nanofluid unsteady heat transfer process (solidification) under the impact of thermal radiation is reported. In order to simulate this problem, Finite element method with adaptive mesh is employed. CuO-water nanofluid is utilized and Brownian motion effect on thermal conductivity is taken into consideration. Total energy, average temperature, isotherm and solid fraction contours are reported as results. Results demonstrate that total energy reduces with increase of radiation parameter and solidification process is completed in lower time in presence of thermal radiation. Also, it can be understand that using Nano-enhanced phase change material (NEPCM) instead of pure PCM leads to higher heat transfer rate. (C) 2018 Elsevier Ltd. All rights reserved.