Integral method of analysis for chemical reaction in a nonisothermal finite cylindrical catalyst pellet-II. Robin problem

The problem of diffusion and reaction on a porous nonisothermal finite cylindrical catalyst pellet in the presence of external heat and mass-transfer resistances is solved by the integral equation method. The modified Green's function method developed previously (Mukkavilli et al., 1987, Chem. Engng Sci., 42, 27-33) is extended to transform the partial differential equation into a Fredholm integral equation and to accelerate the convergence of the partial eigen series by an order of two. The Prater relation, expressing the pellet temperature as a linear function of concentration, is used under two simplifying assumptions: (i) the Nusselt and Sherwood numbers are equal; or (ii) the surface concentration is invariant. The resulting integral equation is solved to obtain effectiveness factors for various nonlinear reaction rate forms. This is the first study to report effectiveness factors for the commonly used finite cylindrical catalyst pellet geometry for the important case of internal and external resistances.