Effective conductivity computation of a packed bed using constriction resistance and contact angle effects

Effective conductivity computation is a major component in the study of conduction within a porous medium, consisting of packed spheres. For packings with porosity lower than 0.47, previous studies typically model the packed bed as an arrangement of cylinders with connecting webs. Not only does such system deviate from the actual structure, but its usage also requires empirically determined parameters. An alternative method is herein presented, and is valid for packed beds of porosity below 0.5, and where the conductivity of the sphere is much larger than that of the surrounding matrix. The present method approximates the packed bed as packed sphere systems consisting of different unit cells, and then using the presently computed relations to obtain the effective thermal conductivity. The relations were derived from constriction resistance relations, accounting for the angles formed between the contacting spheres. The results show for the first time, the necessity of properly accounting for these contact angles. Accounting for the contact angle, the effective thermal conductivity was computed for seven packed beds with porosities ranging from 0.18 to 0.47. The results were in excellent agreement with previous experimental and numerical work.