An analytical model for the three-dimensional thermal resistance of particles considering internal heat conduction based on the generalized thermal resistance concept

An analytical model for the three-dimensional thermal resistance of particles considering internal heat conduction based on the generalized thermal resistance concept

A novel model for thermal resistance within particles, applicable to three-dimensional systems and based on a heat flux-weighted temperature difference definition, has been proposed through analytical solution derivation. The proposed model is suitable for calculating thermal resistance under arbitrary heat flux density boundary conditions on the surfaces of spherical particles and can be applied to modeling the internal conduction of particles in a pebble bed. The analysis was conducted to determine the appropriate number of series terms to be selected when using the model. Additionally, the model was validated against results obtained from the finite volume method, showing a good agreement. A parameter sensitivity analysis was conducted to examine the influences of contact area, particle radius, and the angle between contact surfaces on the internal thermal resistance of particles. It was found that changes in the contact area are particularly sensitive to variations in the distance between two critical contact surfaces. Increasing the angle between contact surfaces raises thermal resistance, especially at smaller angles. Additionally, as the particle radius increases, thermal resistance decreases, although the rate of decrease becomes progressively slower. Specific analytical solutions for the internal thermal resistance and effective thermal conductivity of pebble beds are also provided for simple packing arrangements, including simple cubic, body-centered cubic, and face-centered cubic configurations. When the relative contact radius is 10−5 and the material's thermal conductivity is 1 W/(m∙K), the effective thermal conductivities calculated for simple cubic, body-centered cubic, and face-centered cubic packing are 0.04858, 0.0847, and 0.1369 W/(m∙K), respectively.