Governing Equations for Cylindrical Coordinates

This section applies the method of lines to the equations for convective diffusion of mass and heat. It is convenient to replace r hy r = i Ar, i = 0. I, for coding 

Values at the wall, i = /, are determined from the wall boundary condition. Eor concentrations in any reactor with solid walls and for temperature in an adiabatic reactor, there is zero slope at the wall. It would be sufficient to set d/ = d/ i, but this is only a first-order approximation. Fitting a cubic to the points d/, d/ i, d/ 2, and d/ 3 and then forcing the slope to be zero at / = / give a smoother estimate that sometimes improves convergence  

The condition of radial symmetry is satisfied by setting d(-l, z) = d(l, z) at each axial step in the calculations. 

Equation 8.33 gives the method-of-lines equation for the diffusion of heat  

The simple boundary condition for temperature is 7/ = T waii(z), where T waii(z) is the external temperature, but see Appendix 8.2 for the case where there is external resistance to heat transfer. The simple boundary condition for adiabatic reactors is 

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