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 ¯ in a cylindrical tube of length L and radius R, n ( r , x ) = n max ( x ) f ( r ) = C exp ( − λ β x ) [ 1 − 1 11 ( 18 r 2 − 9 r 4 + 2 r 6 ) ] wherein C=1.477 and λ=3.659 are fit constants to the numerical solution of the convection–diffusion equation for β x = DLx / u ¯ R 2 ≥ 0.2 , i.e. for fully developed concentration profile.