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 ...