Turbulent mass transfer with a first-order chemical reaction on a wall at pr ⪢ 1

Abstract

Mass transfer between a turbulent fluid flow and a flat smooth wall with a first-order chemical reaction on it has been investigated. An extreme case of an infinitely high reaction rate (constant concentration of passive admixture on the wall) has been analysed. Three possible cases are considered consecutively. For very short plates which cannot be described by the boundary-layer approximation, a computer solution has been obtained by the finite difference method. This solution completely allows for both the edge (longitudinal molecular diffusion of a passive admixture) and surface (finite rate of a chemical reaction) effects which are rather essential for small-length plates. For those plates which can be interpreted by the boundary-layer approximation with the neglect of the effect of turbulent mass transfer, the analytical solution to the problem has been derived. The numerical data are compared with those obtained by the method of the equally accessible surface and in the boundary-layer approximation. As a result, the lower region limit of the plate sizes can be established where the edge effects may be neglected. These results may be directly applied to the theory of electrodiffusional and thermal (with coatings) small-size film sensors, designed for measuring local characteristics of friction, and heat and mass transfer to a smooth solid wall in a fluid flow. Considering long plates for which turbulent mass transfer is of importance, a simple approximate solution of the problem is obtained. The numerical parameters involved in this solution are thus chosen to fit the asymptotic results obtained close to the leading edge of the plate and far from it. These results make it possible to determine the mass-transfer entry region in the arbitrary cross section channel and to suggest simple formulae for calculating the local and channel length-averaged mass transfer intensity in the entry region. These formulae are checked by the reported experimental data.