Solid energy balance, cross-flow

A number of fluidized bed reactor model versions are based on the cross sectional averaged two-phase transport equations as presented in sect 3.4.7. Bue to the vigorous particle flow the fluidized beds are essentially isothermal, so no energy balance is generally required . In addition, the necessary species mass (mole) balance can be deduced from (3.498). The solids are considered... 

One of the simplified heat transfer models of two-phase flows is the pseudocontinuum one-phase flow model, in which it is assumed that (1) local thermal equilibrium between the two phases exists (2) particles are evenly distributed (3) flow is uniform and (4) heat conduction is dominant in the cross-stream direction. Therefore, the heat balance leads to a single-phase energy equation which is based on effective gas-solid properties and averaged temperatures and velocities. For an axisymmetric flow heated by a cylindrical heating surface at rw, the heat balance equation can be written as... 

In a typical slurry pipeline design situation, the flowrates and solids concentrations are fixed by process material balances and equipment performance specifications. In these circumstances, a primary goal in design is selection of the optimum pipe diameter. For slurries in turbulent flow, the optimum transport condition almost invariably occurs when all the particles are suspended but moving at the lowest possible mean velocity. By operating the pipeline at the slurry deposition velocity, the frictional energy losses and wear are minimized and the whole of the pipe cross-section is available for flow. 

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