A stochastic simulation was devised in order to obtain a more correct solution of the phenomenon of convection combined with axial and radial diffusion, which is also called Taylor's dispersion, as it could occur in the pulmonary tract. The fit with Aris' moments which can be deemed as a reference since they are obtained analytically without approximation, was quite good. On the other hand, Taylor's solution usually led to large discrepancies with these moments. Taylor's stipulation that his solution be used only under certain conditions was therefore confirmed. This solution is not applicable in the lungs.