Mass transfer enhancement by chemical reaction in turbulent tube flow

Section 21.4 of Transport Phenomena (BSL2 after its three authors: Bird, Stewart, and Lightfoot; second ed.; full reference given in [1]) addresses the problem of mass transfer enhancement by a homogeneous and irreversible first-order chemical reaction in turbulent tube flow. The authors discuss several solution approaches of historical interest, and provide a complete transport model for solute A based on the laws of conservation of mass and momentum, from which the local Sherwood number, Sh, can be obtained as a function of the dimensionless axial distance into the mass transfer zone and the Damköhler number, Da. The latter accounts for the effect of reaction kinetics on solute transport. However, BSL2 is very sketchy in the solution details of their model, and does not validate the key results relative to other studies. Thus, the usefulness of the authors’ modelling approach cannot be properly assessed. In this work, a fully documented numerical solution of the original transport problem is given, along with comprehensive results such as velocity and concentration profiles, as well as Sh values outside the range of axial positions given in BSL2. Mass transfer enhancement factors (ratio of Sh with chemical reaction/Sh without reaction) are also calculated and compared with the literature. Our results show that accurate estimates of enhancement factors in turbulent tube flow with chemical reaction can be obtained using the straightforward BSL2 modelling approach, which may be readily adapted to examine other situations relevant to chemical engineering.