An analysis based on a three-energy equation model for forced convective heat transfer in bi-disperse packed bed channels and tubes

A three-energy equation model was utilized to analyze forced convective heat transfer in bi-disperse packed bed channels and circular tubes. The fluid phase energy equation was coupled and solved with two distinct heat conduction equations, accounting for both large and small particles. An exact solution was obtained for hydrodynamically and thermally fully developed Darcy flows in a bi-disperse packed bed channel under constant wall heat flux conditions. Additionally, highly accurate approximate solutions based on an integral method were developed for plane and axisymmetric forced convective flows, for which exact solutions are unavailable. The Nusselt numbers for conduits filled with a bi-disperse packed bed were found to be significantly higher than those for conduits filled with a mono-disperse packed bed. Since the Nusselt number remains insensitive to the filler diameter under fixed porosity conditions, employing fillers with comparatively larger diameters is advisable to mitigate excessive pressure drop.