We present a reduced order model for describing the transient diffusion and convection in monolith channels with diffusion, adsorption, desorption and reaction in the porous washcoat layer. Unlike the traditional two-phase or the 1(axial)+1(washcoat) dimensional models whose validity may be limited for transient reacting flows, the present multi-mode model is accurate to first order in the transverse diffusion time (t(D)) and hence is valid over a much wider range of operating conditions and kinetics. We provide a physical interpretation of the various effective coefficients appearing in the reduced order model. For the case of inert and non-reacting solutes, we obtain effective transport coefficients and relate them to experimental observations. For the steady-state reacting case, we present a multi-mode form of the model with intra- and interphase mass transfer coefficients. In the general transient case, we show that the traditional external mass transfer coefficient concept is not applicable as the solid-fluid interfacial flux cannot be expressed in terms of concentration differences even to leading order in t(D). We also show that for transient reacting flows, the widely used two-phase and 1+1 dimensional models may lead to errors of order unity in the solid-fluid interfacial flux and order tp in the exit concentration or moments. Finally, we apply the reduced order model to the chromatographic method to relate the first and second moments to the effective diffusivities and kinetic parameters and compare the results with those obtained from the traditional two-phase models. (C) 2014 Elsevier B.V. All rights reserved.