Numerical correlation for thermal conduction in packed beds

The numerical conduction of heat in packed beds of particles is investigated, including the effects of inter‐particle microasperity gaps and deformation contacts. A detailed numerical model of two half spheres in contact with interstitial fluid is constructed, including asperity (roughness) gaps and deformation contacts on the respective orders of 5 μm and 100 μm for 1 mm particle diameters. The resulting heat flux distributions at the diametrical planes of the particles are integrated to yield the overall thermal conductance, K , or resistance, R = 1/ K , between the two diametrical planes. The results show K to be strongly dependent on the interstitial fluid gap and the deformation contact diameter, as well as on fluid and solid conductivities. The effective bed conductivity, k e , is determined as a function of K and the void fraction, and correlated in terms of bed parameters. The resulting k e correlation agrees well with published experimental data over a wide range of substances and temperatures.