Heat Transfer Coefficient Between Spherical Particles in Low-Conducting Fluid

Calculation of heat transfer in granular materials is an important task for many applications, from thermal management in electronics to exploring celestial soils. Usually, an effective thermal-conductivity model is employed to predict heat flux in unstructured granular media, such as a packed bed. However, a more advanced approach, the discrete element method (DEM), can capture the complex effects of mechanical loading and material mixtures on thermal transport coefficients, which traditional models struggle with. Pivotal for this approach is knowing the heat transfer coefficient between two adjacent particles. Currently, in most DEM-capable software, only particles in direct surface contact are considered to have non-zero heat conduction. We propose considering particles that are close to each other but don’t have a contact area with a non-zero surface area. We perform numerical modeling of the conductive heat transfer coefficient between equal spherical particles separated by media, assuming the fluid’s thermal conductivity is at least an order of magnitude lower. We use numerical solutions of differential equations to account for both thermal resistance within particles and through the gap between them. We found a simple generalized correlation for the heat transfer coefficient between particles and a general formula for the angular distribution of heat flux density across the particle surface. By employing a non-dimensional approach, the obtained formulas are constructed using non-dimensional parameters: the ratio of the particle’s thermal conductivity to that of the medium, and the ratio of the gap width between particles to their radius. The resulting formula is simple and convenient for DEM heat transfer calculations in packed and fluidized beds.