The use of materials such as paraffin is widespread in modern energy industries. The ability to absorb a large amount of energy during a phase transition at a constant temperature conditions allows to store and transport the heat. The intensity of melting is related to the thermophysical characteristics of the material and the geometric parameters of the system. Heat transfer inside the system is carried out due to the heat conduction, while in the melt the convective heat transfer intensifies the process. In this paper, a numerical study of heat transfer inside a domain filled with paraffin with nanoparticles and heated from a source of constant volumetric heat generation is performed. A two-dimensional model of the melting process has been formulated in the dimensionless variables "stream function-vorticity temperature", taking into account the natural convective heat transfer occurring in the melt. The system of partial differential equations has been solved using the finite difference method. The simulation has been carried out at different inclination angles of the considered system. Local and integral characteristics of the melting process at different heating levels of the system have been obtained. (C) 2019 Elsevier Ltd. All rights reserved.