Circulating fluidized beds wall region

Derive the radial profile of the particle convective heat transfer coefficient in a circulating fluidized bed of fine particles using the information given in 10.4.2, and simplify the expression for the center region and the near-wall region, respectively. 

Contrary to dense-phase fluidized beds, the radial and axial distributions of voidage, particle velocity, and gas velocity in a circulating fluidized bed are considerably nonuniform, resulting in a nonuniform heat transfer coefficient profile. Since the particle concentration decreases in the axial direction, the heat transfer also decreases. In the radial direction the heat transfer coefficient exhibits a steep profile near the wall, but is almost constant in the center region. The overall heat transfer coefficient increases with suspension density and particle circulation rate. 

Circulating Beds These fluidized beds operate at higher velocities, and virtually all the solids are elutriated from the furnace. The majority of the elutriated sohds, still at combustion temperature, are captured by reverse-flow cyclone(s) and recirculated to the foot of the combustor. The foot of the combustor is a potentially very erosive region, as it contains large particles not elutriated from the bed, and they are being fluidized at high velocity. Consequently the lower reaches of the combustor do not contain heat-transfer tubes and the water walls are protected with refractory. Some combustors have... 

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