We utilize the recently developed concept of internal or intraphase mass transfer coefficient to simplify the problem of diffusion and reaction in more than one spatial dimension for a washcoated monolith of arbitrary shape. We determine the dependence of the dimensionless internal mass transfer coefficient (Sh(i)) on washcoat and channel geometric shapes, reaction kinetics, catalyst loading and activity profile. It is also reasoned that the concept of intraphase transfer coefficient is more useful and fundamental than the classical effectiveness factor concept. The intraphase transfer coefficient can be combined with the traditional external mass transfer coefficient (Sh(e)) to obtain an overall mass transfer coefficient (Sh(app)) which is an experimentally measurable quantity depending on various geometric and transport properties as well as kinetics. We present examples demonstrating the use of Sh(app) in obtaining accurate macro-scale low-dimensional models of catalytic reactors by solving the full 3-D convection-diffusion-reaction problem for a washcoated monolith and comparing the solution with that of the simplified model using the internal mass transfer coefficient concept. (C) 2009 Elsevier Ltd. All rights reserved.