Effective thermal conductivities of a single species and a binary mixture of granular materials

The effective thermal conductivity is developed by employing the dense-gas kinetic theory. The free path used in the theory varies with the particle velocity. The analytical results can be used for the whole range of the product of Biot number and Fourier number provided that the Biot number is less than 0.1. For the very small Biot–Fourier numbers, the conductivities are found to increase with the particle diameters and the square root of granular temperatures. For the limit of very large Biot–Fourier numbers, the effective thermal conductivity is found to be linearly proportional to the granular temperature. The effective thermal conductivities for the binary mixtures are also derived. The influences of the species concentration, the total solid fraction and the Biot–Fourier number on the thermal conductivity are investigated. Increasing the concentration of the smaller particles or reducing the size of the smaller species can increase the thermal conduction in the binary mixture system.