Heat and mass transfer in annular liquid jets: I. Formulation

Heat and mass transfer phenomena in annular liquid jets are analyzed at high Reynolds numbers by means of a model derived from the governing equations that takes into account the e€ects of surface tension and boundary conditions at the gas± liquid interfaces and the large di€erences between the thermal and mass di€usivities, densities, dynamic viscosities, and thermal conductivities between gases and liquids. The model clearly illustrates the sti€ness in both space and time associated with the concentration, linear momentum and energy boundary layers, and the initial cooling of the gases enclosed by the jet when, starting from a steady state where gases are injected into the volume enclosed by the jet at a rate equal to the heat and mass absorption rates by the liquid, gas injection is stopped. It is shown that, owing to the non-linear integrodi€erential coupling between the ̄uid dynamics and heat and mass transfer processes, the pressure of the gases enclosed by the jet may vary in either a monotonic or an oscillatory manner depending on the large number of non-dimensional parameters that govern the heat and mass transfer phenomena. For the underpressurized jets considered here, it is shown that thermal equilibrium is achieved at a much faster rate than that associated with mass transfer, double di€usive phenomena in the liquid may occur, and the mass and volume of the gases enclosed by the jet may increase or decrease as functions of time until a steady equilibrium condition is reached. Ó 2000 Elsevier Science Inc. All rights reserved.