Effect of ring-source release on dispersion process in Poiseuille flow with wall absorption

The analysis of Taylor dispersion in a fluid flowing through a narrow pipe is of considerable interest among the scientific community. Most of the studies on dispersion primarily considered a transversely uniform release of contaminant at the initial moment, while only a few have addressed the influence of the initial condition on the dispersion process in a tube flow. The present work investigates the transient dispersion process with a ring-source release of solute by means of an unsteady two-dimensional transport model. An irreversible absorptive type of a first-order reaction is also considered. The transport model is solved using the series expansion technique of W. N. Gill [ "A note on the solution of transient dispersion problems, " Proc. R. Soc. A 298, 335 (1967)], known as the generalized dispersion technique. The whole transport model is explained using the transport coefficients obtained from the first four terms of Gill's series expansion. Meanwhile, the concept of statistical moments is also used for finding the transport coefficients. The study outcomes are well established, satisfying the result of existing literature under limiting conditions. The inclusion of the ring-source release of solute in the study of dispersion has a significant effect at the initial time. In addition, the view of the cross-sectional distribution of solute concentration gives more detailed information on solute scattering under the proposed model.