General equation for a cylindrical reactor

The following equations describe transport of species, heat, and momentum in a cylindrical tubular reactor with laminar flow 

At the inlet, we have only axial velocity, and no radial or tangential variation in concentration or temperature  

We have no slip at the wall and no penetration of species, but heat transfer though the wall will occur  

The boundary conditions are not obvious they require detailed knowledge of the actual flow pattern, and, as discussed, the outlet conditions are questionable. 

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