CONVECTIVE DIFFUSION IN A TUBE WITH NON-UNIFORM INLET CONDITIONS

• Published in: Journal of aerosol science Vol. 31; no. 8; pp. 959 - 968
• Main Authors: Housiadas, Christos, Larrodé, Francisco Ezquerra, Drossinos, Yannis
• Format: Journal Article
• Language: English
• Published: Elsevier Ltd 01.08.2000
• ISSN: 0021-8502; 1879-1964
• DOI: 10.1016/S0021-8502(99)00575-3

Convective diffusion in Poiseuille flow is investigated for a non-uniform distribution of the diffusing constituent at the tube inlet. The analytical solution is provided together with an efficient method to evaluate it numerically, including an appropriate recurrence-calculation scheme that facilitates the numerical effort. The solution is illustrated by considering relevant examples from the literature. In particular, homogeneous nucleation in a laminar flow diffusion chamber is analyzed, and the results show that the usual experimental inlet non-uniformities have a significant influence on the calculation of the saturation ratio and the nucleation rate. Notation C concentration D diffusivity f normalized inlet profile F eigenfunction I n constants in infinite series, cf. equation (6) J nucleation rate Le Lewis number, ( Le=α/D) M molecular weight P vapor partial pressure Pe heat transfer Peclet number, Pe=2R t U m /α Pe m mass transfer Peclet number, Pe m =2R t U m /D r,R dimensionless, dimensional radial coordinate R n constants in infinite series, cf. equation (5) R t tube radius R universal gas constant S saturation ratio, S=P/P sat T temperature ΔT centerline-to-wall gas temperature difference, cf. equation (21) U velocity x,X dimensionless, dimensional axial coordinate Greek letters α thermal diffusivity θ dimensionless concentration (or temperature) λ eigenvalue, thermal conductivity Λ n constants in infinite series, cf. equation (5) Subscripts 0 inlet section av average d deposition m mean over the tube cross section max maximum n order ( n=1, 2,… ) sat saturation w wall