Modelling of effective thermal conductivity of a packed bed of steel bars with the use of chosen literature models

Transport phenomena of heat in porous media have been focus of many investigations. Most studies deal with low-porosity granular media. A specific example of such a medium are steel bars heated during heat treatment in the form of cylindrically shaped bundles. The intensity of heating is determined by the processes of heat transfer which occur in the radial direction of the bundle, in which the considered charge is characterized by the lack of continuity of the solid phase. Therefore, the ability of the bundles to transfer heat is expressed by effective thermal conductivity kef. Knowing this coefficient is necessary to optimize heat treatment processes of bar bundles. The article presents the results of calculations of the kef for packed beds of round and square steel bars obtained for a few selected analytical models. The quality of the results was verified on the basis of experimental measurements performed in a guarded hot plate apparatus. The results indicate that simple models are not suitable for determining thermal properties of bundles. The kef values obtained with their use significantly vary from the measured values. Complex models are much more valuable in this respect. The best results were obtained for the Zehner-Bauer-Schlunder model.