Steady state, laminar flow transport in a tube with a first order sink at the wall involves two dimensions-radial and axial. In this paper, a novel iterative technique has been proposed for reducing such a two-dimensional model to an equivalent one-dimensional dispersed plug flow model. The latter yields an analytical expression for the equivalent axial dispersion and a simple, closed form, but approximate, analytical solution of the original two-dimensional problem. The operating range in which this analytical solution is useful has been investigated for a system with mass transfer at the wall.