Model of thermal conductivity in powder beds

Heat transfer between contacting solid particles in gas is localized about the points of contact because of the low thermal conductivity of gas. This suggests the model of a network of discrete thermal resistances. Thermal interaction of two particles in the zone of contact between them includes thermal conductivity in the solid phase as well as heat transfer through a gas gap between the particles, where the conductive heat transfer at higher distances from the center of the contact changes to the transition transfer and free molecular transfer near the contact center. In the framework of this approach the effective thermal conductivity depends on three dimensionless morphological parameters: the volume fraction of solid phase, the mean coordination number, and the ratio of the size of necks between particles to the size of particles. The physical properties of the phases are specified by the thermal conductivities of the solid and the gas, the adiabatic exponent of the gas, and the Knudsen number. The proposed model agrees with the experimental S curves of the effective thermal conductivity versus the logarithm of gas pressure. It also describes the experimental tendencies of increasing the effective thermal conductivity with the particle size and the volume fraction of solid. The model can be applied to powder beds with micron-sized particles as well as to packed beds with millimeter-sized particles in gas. Free molecular and transient regimes of heat transfer in the gas filling pores can be important even for millimeter-sized particles at atmospheric pressure when the Knudsen number is as low as 10(-5). These rarefied gas phenomena are responsible for such a complicated behavior of the considered heterogeneous media. Their quantitative description gives the model, which does not contain fitting parameters.