The Temperature Profiles in a Packed Bed

Thus far we have only considered the PFTR with gradients in the axial direction. The heat transfer to the wall at temperature Tj, was handled through a heat transfer coefficient U. The complete equations are 

If we assume that the reactor is in steady state and that in the z direction the reactor is still in plug flow, then the equations for a first-order irreversible reaction become 

We need to solve these equations with inlet conditions 

The notable feature of the wall-cooled tubular reactor is that there can exist a hot spot near the center of the reactor and near the entrance. We saw this for the lumped model, which allowed only for variations in the direction, but when radial variations are allowed, the effect can become even more severe as both temperature and concentration vary radially. 

We used the wall temperature in the boundary condition, and this may be different from the coolant temperature T. There may be temperature variations across the wall as well as through the coolant. These are described through the overall heat transfer coefficient U, but in practice all these effects must be considered for a detailed description of the wall-cooled tubular reactor. 

---