Efficient Expressions for Effectiveness Factor for a Finite Cylinder

Abstract

New efficient analytical expressions for steady-state concentration profile in an isothermal permeable two-dimensional finite cylindrical catalyst pellet with first-order irreversible chemical reaction are presented here. In the present approach, the particular solution is used to remove one non-homogeneous boundary condition from the original partial differential equation with two non-homogeneous boundary conditions so that the resulting problem becomes amenable to a solution by the separation of variable method. Two different particular solutions are used here, yielding two different final expressions for the concentration profile in the pellet. The first particular solution is the solution of the one-dimensional infinite cylinder problem while the second one is the solution of the one-dimensional disk problem. Effectiveness factors are evaluated for both cases. Both these expressions for effectiveness factor show much better convergence behaviour than others reported in the literature. While the first expression is especially suitable for cases where height-to-diameter (H/D) ratio of the cylindrical pellet exceeds unity, second one is superior for smaller H/D ratios. Moreover, the effectiveness factor is found to increase as the sphericity of the cylindrical catalyst pellet is decreased.