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

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

Influence of tube and particle diameter on heat transport in packed beds

Influence of the tube and particle diameter and shape, as well as their ratio, on the radial heat transport in packed beds has been studied. Heat transport experiments were performed with four different packings in three wall-cooled tubes, which differed in inner diameter only. Experimental values for the effective radial heat conductivity and wall heat-transfer coefficient for the pseudo-homogeneous two-dimensional model and the overall heat-transfer coefficient for the one-dimensional model are presented. Values were obtained for glass spheres, alumina cylinders, and alumina Raschig rings. The effective radial heat conductivity and wall heat-transfer coefficient can both be correlated as a linear function of the gas flow rate. The Bodenstein number for heat at fully developed turbulent flow is influenced strongly by the shape of the packing: 10.9 for glass spheres, 7.6 for alumina cylinders, and 4.2 for alumina Raschig rings. For the same packing, no significant influence is found of the tube diameter on the effective radial heat conductivity or on the wall heat-transfer coefficient. The overall heat-transfer coefficient can be described very well by the so-called lump equation, which gives the relations among the overall heat-transfer coefficient, effective radial heat conductivity, and wall heat-transfer coefficient. The lump factor, as used in the lump equation, has a best-fit experimental value of 7.4

Significance of the radial porosity profile for the description of heat transport in wall-cooled packed beds

The influence of a radial porosity and velocity profile on the predicted temperature and concentration profiles in wall-cooled packed beds is studied, with and without an exothermic first-order chemical reaction, on the basis of literature correlations for the effective transport coefficients. Furthermore, values for the effective heat transport coefficients are obtained from ¿cold-flow¿ experiments by means of model fitting, with and without taking the radial velocity profile into account. The radial porosity and velocity profiles are approximately by step-function, which is referred to as the ¿two-region model¿. It is shown that the effective radial heat conductivity can be taken constant over the radius, despite the wall effect. Nevertheless, the influence of a radial superficial velocity profile can be significant through the convective term in the heat balance, especially for low tube-to-particle diameter ratios. The predicted NTU can increase the order of 20% for high values of the Reynolds number and up to 100% for low values. This is confirmed by the results obtained from the model fitting. In case of a first-order exothermic reaction, significantly higher values for the hot-spot temperatures are predicted, if a radial porosity and velocity profile is incorporated in the heat and mass balances. This is found to be mainly caused by the non-uniform distribution of active catalyst over the radius, due to the porosity profile