Taylor diffusion for a natural convective flow through a vertical channel

The dispersion of a solute in a naturally convecting laminar flow through a vertical channel with uniform wall temperature variation is investigated. For the case of the steady fully developed flow of a viscous incompressible fluid between two vertical plane parallel walls under a constant pressure gradient, an expression is obtained for solute concentration as a function of time and vertical and radial positions. It is observed that for small and moderate values of the Rayleigh number, the Taylor diffusion coefficient oscillates with increasing Rayleigh number up to about 3, then increases gradually.