Analytical approximation to the fully developed concentration profile of diffusive aerosol particles in laminar flow in a circular tube

An analytical approximation is presented for the dimensionless concentration profile n(r,x) of aerosol particles of diffusion coefficient D flowing with mean axial velocity (u) over bar in a cylindrical tube of length L and radius R, n(r,x) = n(max)(x)f(r)=C exp(-lambda beta x)[1- 1/11(18r(2)-9r(4)+2r(6))] wherein C=1.477 and lambda=3.659 are fit constants to the numerical solution of the convection-diffusion equation for beta x = DLx/(u) over barR(2) >= 0.2, i.e. for fully developed concentration profile. (C) 2010 Elsevier Ltd. All rights reserved.