Stream function annular flow

From the contours of the stream function and a closeup of the flow field near the shroud and top cover plate, we note that the shroud causes significant recirculation at the top end of the catalyst bed. Also, the downward velocity field in the annular region between catalyst bed and reactor shell is found not to be uniform. The comparative... 

Calculate the stream function for axisymmetric fully developed creeping viscous flow of an incompressible Newtonian fluid in the annular region between two concentric tubes. This problem is analogous to axial flow on the shell side of a double-pipe heat exchanger. It is not necessary to solve algebraically for all the integration constants. However, you must include all the boundary conditions that allow one to determine a unique solution for i/f. Express your answer for the stream function in terms of ... 

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