Coupled multi-physics simulations play a crucial role in the design and operation of nuclear reactors, particularly in assessing the behavior of used nuclear fuel. This study focuses on exploring the efficacy of coupled calculations for used nuclear fuel through the integration of neutron transport and thermal-hydraulics codes. Neutronics calculations were conducted using the Monte Carlo code Serpent, while thermal-hydraulic calculations utilized the Computational Fluid Dynamics (CFD) software OpenFOAM. The investigation was focused on a VVER-440 fuel pin situated in a hexagonal coolant flow area. Three computational grids were generated, containing 0.15 million, 0.39 million, and 1.1 million computational cells, along with three variants of axial material refinement featuring 42, 21, and 10 material layers. The purpose was to analyze the impact of spatial refinement on key parameters such as multiplication factor, power flux, and temperature fields. Several relaxation factors in Picard iterations were systematically compared to enhance the convergence speed of the coupling procedure. Notably, simulations without relaxation (α = 1) resulted in oscillations in predicted results, while a low value of α led to slow convergence. The investigation revealed that employing a stochastic approximation with a varying relaxation factor coupled with a varying number of simulated particles demonstrated superior performance compared to cases with a constant relaxation factor α or a stochastic approximation with a constant number of simulated particles. Furthermore, it was observed that the resolution of axial fuel segmentation significantly influenced predicted multiplication factor kinf and temperature profiles. Interestingly, the spatial resolution of the computational grid exhibited minimal impact on the predicted results. •CFD code OpenFOAM and Monte Carlo neutron transport code Serpent were coupled.•Relaxation of power flux improved the simulation convergence.•The stochastic approximation converged faster than the fixed number of neutrons case.•Axial segmentation of material input had a significant effect on predicted results.