A two-dimensional advection-diffusion model accompanied with a parabolic velocity profile of Poiseuille flow is considered for the chemical species transport in a tube with a constant wall concentration. The Reynolds decomposition technique is applied to reduce it to an equivalent one-dimensional model for advective-dispersive transport in a tube through which the effective advection coefficient, the dispersion coefficient, and the effective Sherwood number are developed for the problem under study. The derived and the classical Taylor models are also compared in order to find the difference between the two arrangements. The reduced-order model for the transport equation shows that the effective advection coefficient increases, whereas the dispersion coefficient in the tube decreases as compared to the classical Taylor equation. The effective Sherwood number for the steady state form of the developed model is found to be only a function of the Peclet number, which varies in the range of 3.215Sh4. These results find application in design of experiments and improve our understanding of mass transfer in microfluidic devices.