Radial Temperature and Concentration Gradients in a Packed Bed Reactor

Here are the dimensionless equations of a packed bed reactor with radial temperature and concentration gradients, assuming constant physical properties, plug flow, and first-order kinetics:

1) ,

2) ,

with the boundary conditions

3) at ,

4) , at ,

and the initial conditions

5) , at .

Reference: B. A. Finlayson, "Packed Bed Reactor Analysis by Orthogonal Collocation," Chemical Engineering Science, 26(7), 1971 pp. 1081–1091.