Analytical Manipulation of the Joint Integrodifferential Equations

Thus we have found the solution of the differential equation (4.47) to be 

In more simplified and reorganized form this becomes 

The analogy between the above equations and the CSTR model can be easily realized. From this analogy we can define the modified flow rate with the following physical significance  

Heat balance design equations for fluidized beds 

The heat balance equation applied to the dense phase gives us 

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