Dense-phase fluidized beds particle interaction

It is important to do the balance over the whole of the dense phase when this is, by assumption, uniform, failure to do this led to an erroneous result in an earlier paper of ours, Heat transfer in fluidized and moving beds (Proc. Symp. on Interactions between Fluids and Particles. 1962. pp 176-182. The error was ultimately corrected in 1990 see Manners makyth Modellers, Chem Eng Sci, 46 1535-44 (1991) and in Trans IChemE, 68 165-174 (1991). 

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