Cylindrical reactor

Similarly, for infinite cylindrical

$$\ {\frac{1}{r}}\ {\frac{d}{dr}}\left( r{\frac{d\varphi}{dr}}\right) +B^{2}\varphi(r)=0$$ (4.37)

where the solution is

$$\varphi(r)=AJ_{0}(Br)$$

with J₀ is the ordinary Bessel function of order 0. J₀(BR)=0. This condition is fulfilled for a number of values, the smallest beeing BR=2.405