F. Pahuamba-Valdez, E. Mayoral-Villa, C. E. Alvarado-Rodriguez, J. Klapp, A. M. Goomez-Torres, E. Del Valle-Gallegos. Numerical modeling simulations and the use of high-performance computing are fundamental for detailed safety analysis, control and operation of a nuclear reactor, allowing the study and analysis of problems related to thermal-hydraulics, neutronic, and the dynamic of fluids that are involved in these systems. In this work, we introduce the basis for the implementation of the smoothed particle hydrodynamics (SPH) approach to analyze heat transfer in a nuclear reactor core. Heat transfer by means of convection is of great importance in many engineering applications and especially in the analysis of heat transfer in nuclear reactors. As a first approach, the natural convection in the gap (space that exists between the fuel rod and the cladding) can be analyzed helping to reduce uncertainty in such calculations that usually relies on empirical correlations while using other numerical tools. The numerical method developed in this work was validated while comparing the results obtained in previous numerical simulations and experimental data reported in the literature showing that our implementation is suitable for the study of heat transfer in nuclear reactors. Numerical simulations were done with the DualSPHysics open source code that allows performing parallel calculations using different numbers of cores. The current implementation is a version written in CUDA (Compute Unified Device Architecture) that allows also the use of GPU processors (Graphics Processor Unit) to accelerate the calculations in parallel using a large number of cores contained in the GPU. This makes it possible to analyze large systems using a reasonable computer time. The obtained results verified and validated our method and allowed us to have a strong solver for future applications of heat transfer in nuclear reactors fuel inside the reactor cores.