This article describes the flow-induced axial dispersion of solutes in conduits of arbitrary cross-sections when the channel wall affects the process due to either adsorption or surface-reaction. The analysis uses a multiple time-scale technique to identify three transport coefficients which characterize the interplays between convection, diffusion and surface-interactions. One of these parameters is well-known diffusion constant recognized in the classical works of Taylor and Aris. In contrast, the other two indicate additional convection and overall slow temporal variation, respectively. Our general formulation obtains these three constants for different commonly seen vessels like the ones with circular, annular, rectangular and elliptical shapes. In case of annular vessels, we consider either inner or outer or both surfaces to be active. Similarly, for rectangle, we repeat the calculations for different numbers of sides involved in the surface interactions. The computed Taylor diffusivity matches with known values for circular and very narrow rectangular conduits. For limiting cases with other geometries, we either derive new exact results or devise novel asymptotic approach based on perturbation analysis yielding useful mathematical expressions for all three transport coefficients. Our computational results are independently verified by these analytical findings when the specific geometric conditions are satisfied. (C) 2015 Elsevier Ltd. All rights reserved.