Significance of axial heat dispersion for the description of heat transport in wall‐cooled packed beds

Abstract

AbstractA two‐dimensional pseudo‐homogeneous model with axial dispersion of heat has been solved numerically with different boundary conditions at the inlet and outlet of the packed bed. The model solutions are fitted to experimental temperature profiles, determined in a wall‐cooled packed bed in which a hot gas is cooled down, and best fit values of the effective axial and radial thermal conductivities and the wall heat transfer coefficient are obtained. In the range of Reynolds numbers employed, Re > 50, the axial dispersion of heat is found to be of no significance for the description of heat transport in wall‐cooled packed beds without reaction, provided that the inlet boundary conditions are chosen appropriately. If a radially flat inlet temperature profile is assumed, while the actual profile is curved, an apparent improvement in the description of heat transport is observed when axial dispersion is incorporated into the heat balance and high effective axial thermal conductivities are obtained. If a Danckwerts type inlet boundary condition is used, assuming a flat temperature profile immediately in front of the inlet, an apparent improvement is also found on incorporation of axial dispersion of heat. This is caused by the temperature jump at the inlet, compensating for the overestimation of inlet temperature, in the case of cooling. The latter also explains why the inclusion of axial dispersion may eliminate the so‐called “length effect”, often related to the effective radial thermal conductivity and the wall heat transfer coefficient. It is shown for the outlet boundary condition that deletion of the axial dispersion term from the heat balance at the outlet is a convenient boundary condition for the model being solved numerically.