Analytical generalized thermal resistance model for conductive heat transfer in pebble beds based on heat flux weighted temperature difference

A novel model for inter-particle contact thermal resistance based on analytical solutions is proposed. By applying the concept of heat flux weighted temperature difference in thermal resistance modeling for the first time, this model offers greater physical significance than traditional thermal resistance models. It effectively describes the dissipation in the heat transfer process and the influence of particle radius on thermal resistance, making it a generalized thermal resistance model suitable for multi-dimensional systems. The impact of applying different levels of uniform heat flux boundary conditions on thermal resistance is analyzed from the perspective of energy dissipation, revealing that a more uniform heat flux input results in lower thermal resistance. The effects of contact radius and particle size on the dimensionless generalized thermal resistance of inter-particle contact were studied, showing that the dimensionless resistance increases with larger particle contact radius and smaller particle size. Using the thermal discrete element method, the thermal resistance model with uniform heat flux density boundary conditions was applied to calculate the effective thermal conductivity of the pebble bed. Considering the distribution of contact radius, differences in effective thermal conductivity at various heights of the pebble bed due to different contact radii were examined and compared with the traditional fixed-coefficient contact resistance model. It was found that the difference between the two models decreases as the contact radius decreases. Finally, multiple sets of fixed contact radii were established under three different particle sizes, revealing that as the contact radius increases, the deviation between the new generalized resistance model and the traditional fixed-coefficient model rises from 8.18 % to 14.64 % for different particle radii.