Convective heat transfer coefficient for the side-wall in a fixed bed

Fixed beds are widely used in the chemical and process industry due to their relatively simple yet effective performance. Determining the radial heat transfer at the wall in a fixed bed is crucial to predict the performance of columns. Heat transfer parameters often need to be obtained experimentally. Various Nusselt Nuw versus Reynolds Rep correlations in literature show considerable scatter and discrepancies. The tube-to-particle diameter ratio D-t/D-p and boundary conditions on the particle surface have been understood to affect heat transfer near the wall by virtue of influence on the near-wall porosity and mixing. In this work, a fixed bed consisting of mono-disperse particles is generated via gravity-forced sedimentation modelling utilizing the discrete element method for a D-t/D-p ratio of 3.3. The system is meshed and imported in a computational fluid dynamics (CFD) solver. Fluid inlet velocity is varied to get Re-p is an element of [1,1500] corresponding to the laminar and turbulent flow regimes. The particles are treated as boundaries with Dirichlet, Neumann, and Robin boundary conditions applied for the closure of energy balance. Another set of simulations is run with particles modelled as solids with varying thermal conductivities (k(s)/k(f)). The heat flux and volume-averaged fluid temperature calculated during post- processing are used to determine the wall heat transfer coefficient and, subsequently, the wall Nu number. Fifteen Nu(w) versus Re-p correlations are compiled and analyzed. A new semi-empirical correlation for the wall Nusselt number has been developed for a fixed bed packed with monodisperse spheres for D-t/D-p = 3.3 and results compared with data published in literature. Additionally, the impact of buoyancy effect on the wall Nusselt number has been studied.