The lumping of heat transfer parameters in cooled packed beds: effect of the bed entry

The lumping of the heat transfer parameters of the one- and the two-dimensional pseudo-homogeneous model of a cooled fixed bed were compared. It appeared that the lumping of the two-dimensional parameters, being the effective radial conductivity h-eff and the heat transfer coefficient at the wall (alpha)w, into the one-dimensional overall heat transfer coefficient U results in a length dependence of U. It is shown that the ratio (alpha)w/U develops from unity at the bed inlet to a final value. The magnitude of this final value depends on the Biot number, whereas the length of this transition section is affected by the Peclet number. A new relation to lump the effective conductivity and the heat transfer coefficient at the wall into an overall heat transfer coefficient which depends on the values of the Biot number and the Peclet number is presented. This relation accounts for both the magnitude and the transition length of the ratio (alpha)w/U.