Nusselt number correlation for convective heat transfer in dual core-ring packed beds

Core-ring packed beds have been proposed to redistribute flow and mitigate hot spots in strongly exothermic reactors. These beds consist of two concentric zones, core and ring, each filled with pellets of different diameters. One-dimensional models for those reactors currently lack a closure for convective heat coefficient between zones, which limits systematic research and predictive design. A Nusselt number and heat transfer coefficient are formulated from the radial heat flux across the core-ring interface. The coefficient is obtained from an axisymmetric porous-media computational model using a Darcy-Forchheimer formulation and a volumetric heat source to mimic reaction heat release. Analyzed inlet Reynolds number (Re_in), based on tube diameter, spans from 100 to 10000, core size from 25 % to 75 %, and core and ring pellet diameter ratios from 0.5 to 1.5. Results indicate that the inter-zone Nusselt number decreases at a pellet diameter ratio of unity, shows a V-shaped dependence on pellet diameter ratio, and displays a bell-shaped trend with core fraction. At high bed Reynolds number (10000), the velocity field becomes more uniform and inter-zone convection decreases to slightly above laminar conditions. These findings support the development of a power-law correlation that incorporates an effective particle Reynolds number (Re‾_p) weighted by the core–ring flow split, together with the Prandtl number, pellet-size ratio, core fraction, and a measure of the velocity difference across the interface. The correlation shows strong agreement with the results and provides closure for one-dimensional reactor models.