Shorter Commumcabons 2349 with and this IS the case of dlffus1on and zeroth-order reaction m an mtlmte cylinder wrth reactants dlffusmg through the curved part of the surface only It IS clear from the above discussion that the two characteristic lengths RO and HO can be approximated by the solutions of the corresponding onedrmenaonal boundary value problems of an mfimte cylinder and a slab, respectively The error m the approximation of &, decreases as the aspect rauo H/R increases and the error m the approximatron of HO decreases as the aspect ratio decreases The error 1n the approximation of both HO and R. IS small for large $ because 1n this case the zero concentration contours are very close to the bcundanes and therefore the ratios HdR and RdH are very small The above results are verdled by the contours of F@s 2 For 4 = 10, the errors involved 1n the approximauon of Ho and RO from the solutions of the correspondmg oned1mens1onal problems 1s of the same order with the error of the numerical calculations For smaller values of 4, the above approximauon IS not so accurate The effectiveness factor for a zeroth order reaction wdl be the rat10 of the volume of the pellet where reaction occurs by the total volume of the pellet In view of the almost rectangular shape of the unutihzed part of the pellet which IS obtamed for large values of 4, an eshmate of the effectiveness factor would be with HO and R,, calculated, as functions of the Th1eie modulus, from eqns (11) and @a), respectively