In evaluating effective reaction rates in catalysts subject to heat and mass transport limitations, the size of the catalytic body is best defined by the so-called characteristic length l, the ratio between catalyst volume and its external surface area, l = V-p/S-p. This result follows from the limiting behaviour at very high reaction rates, when the effective reaction rates are proportional to 1/l (e.g., Aris [R. Aris, The Mathematical Theory of Diffusion and Reaction in Permeable Catalysts, Oxford University Press, London, 1975]) or, in dimensionless form, to the inverse of the Thiele modulus Phi. It is further known from simple geometrical shapes that a series solution can be written in terms of powers of (1/Phi) and that the second order term [in(1/Phi)(2)] depends on the shape of the catalytic body. It is the aim of this paper to develop expressions of such second order term for 2D or 3D catalytic bodies showing arbitrary smooth external surfaces. In a similar way as the first order term allows to define the proper size of a catalyst, the second order term provides a characterization for the catalyst shape. This and other applications of the second order term are discussed. (c) 2005 Elsevier B.V. All rights reserved.