Projection operator theoretical approach to unsteady convective diffusion phenomena.

Abstract

A systematic method is proposed to derive the dispersion equation in a cylindrical channel, based on the projection operator technique originated by Nakajima and Zwanzig. Under the general condition that the axial flow velocity and the diffusion coefficient are arbitrarily dependent on the radial distance, an analytical expression of the Taylor-type dispersion equation is obtained. In the classical Taylor problem, this expression coincides with the result of Gill and Sankarasubramanian. The sufficient condition, under which the approximate dispersion equation is valid, is explicitly presented. The transient term dependent on the radial concentration heterogeneity in the initial condition can be also accounted for. The present result can be applied to various problems of dispersion phenomena, such as unsteady mass or heat transfer in tubular mass or heat exchangers. Because the projection operator technique is a general method to treat dynamic systems with many degrees of freedom, this method can be applied systematically to various problems in transport phenomena.