General pure convection residence time distribution theory of fully developed laminar flows in straight planar and axisymmetric channels

摘要

In literature, the diffusion-free residence time distribution (RTD) of laminar flows - the so-called convection model - has been determined for various velocity profiles mostly on a case-by-case basis. In his analytical paper, we derive general mathematical relations which allow computing the diffusionfree differential and cumulative RTD in straight planar, circular and concentric annular channels for arbitrary monotonic and piece-wise monotonic one-dimensional velocity profiles. The theory is used to determine the RTD of plane Couette-Poiseuille flow with non-monotonic velocity profile, and the optimal value of the volumetric flow rate where the RTD becomes most narrow It is shown that any velocity profile that depends in a sub layer linearly on the distance from a stationary or moving no slip wall has a differential RTD which follows a -3 power law as the residence time approaches its maximum. The variance of the RTD is directly associated with the asymptotic behavioral the RTD and can be finite or infinite. (C) 2014 Elsevier Ltd. All rights reserved,