Influence of channel cross-sectional shape on diffusion-free residence time distribution in fully developed laminar Newtonian flow

Abstract

In this paper, we utilize a recently proposed analytical/semi-analytical method to study the effect of the channel cross-sectional shape on the diffusion-free residence time distribution (RTD) in fully developed laminar flow of a Newtonian fluid. The diffusion-free RTD is obtained for elliptical channels of arbitrary aspect ratio, for a family of moon-shaped channels, and for an equilateral triangular channel. The non-dimensional RTDs for these channel cross-sections are compared and the influence of the channel shape is found to be rather small. The RTDs can well be approximated by a simple convection model which involves the non-dimensional first appearance time, which represents the ratio between the mean and maximum velocity of the laminar flow, as only parameter. A comparison with recently published results for rectangular channels of arbitrary aspect ratio shows that the one-parameter convection model is unsuited for rectangular channels and a second parameter is required. A first attempt toward the development of such a two-parameter convection model is undertaken, which would then allow predicting the diffusion-free RTD of fully developed laminar flow in straight channels of arbitrary cross-sectional shape.