Modeling Effective Thermal Conductivity of Randomly Distributed Loads of Mono-Sized Parts of Arbitrary Geometry

Abstract A new model of the effective thermal conductivity of randomly distributed loads of mono-sized metal parts of arbitrary geometry heated under natural convective and radiation heat transfer has been developed. A series of transient heating experiments has been performed in a batch-type furnace using loads comprised of parts of various geometries, sizes, steel grades, and void fractions and at various furnace set point temperatures. Experimental results showed a strong dependency of the load effective thermal conductivity on: (1) load void fraction, (2) internal radiation between parts, and (3) external radiation between parts and furnace enclosure. An assessment of a number of effective thermal conductivity models reported in the literature and developed for packed beds and porous media has been carried out. This assessment led to the development of the present model, which incorporates a new additional temperature difference term that accounts for external radiation and a new generalized characteristic length scale that can be used for parts of any arbitrary geometry. All thermophysical properties of solid and gaseous phases have been considered as functions of the parts temperature. The proposed model is in good agreement, within ±25 %, with the experimental data obtained for the various part geometries, load void fractions, and the surrounding temperatures considered in this investigation.