Particle-resolved direct numerical simulation (PR-DNS) of flow past a particle cluster is conducted to analyze the influence of heterogeneous particle distribution on the gas–solid heat transfer calculation. Then, the heat transfer rates calculated using Gunn's correlation are systematically compared with the DNS results for virtual computational fluid dynamics-discrete element method (CFD-DEM) grids with different levels of heterogeneity. The results show that, for a grid located at the interface between the dense cluster region and dilute region, Gunn's correlation significantly overestimates the heat transfer rate, especially at small Reynolds numbers. This is caused by the large temperature difference between the dense and dilute regions in the heterogeneous CFD-DEM grid. The value calculated by Gunn's correlation can be up to ten times the DNS result. For a homogeneous grid inside a dense region, the conventional Nusselt correlation fails to capture the rapid increase in the fluid temperature gradient around the near-interface particles when the grid approaches the cluster–fluid interface. Furthermore, even if the size of the CFD-DEM grid is reduced to twice the particle diameter, the heterogeneous particle distribution still leads to a remarkable error in the heat transfer calculation. Finally, modifications to Gunn's correlation are proposed for three typical cross-interface cases, which can well reflect the influence of the heterogeneous distribution of particles and yield a heat transfer rate close to the PR-DNS results. The mean relative deviations of the three fitted correlations are 5.8%, 14.3%, and 22.4%, respectively.
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