CFD testing of the pointwise use of the Zehner–Schlünder formulas for fixed-bed stagnant thermal conductivity

For the conduction mode of heat transfer in a fixed bed, we have carried out an evaluation of whether the most widely-used equations for the overall stagnant bed effective thermal conductivity ke0, the Zehner–Schlünder cell model, can be used on a pointwise basis to obtain local values of ke0(r) using the local bed voidage, ε(r). A three-dimensional computational fluid dynamics (CFD) model of an annular test bed of spheres with tube-to-particle diameter ratio equal to four was constructed to obtain the local void fraction, and solved for the radial temperature profiles. Comparisons to a one-dimensional pseudo-continuum model with ke0(r) gave good agreement for a range of values of solid thermal conductivity, establishing that the Zehner–Schlünder cell model can be used in local models of fixed-bed heat transfer.