Heat and mass transfer in annular liquid jets: III. Combustion within the volume enclosed by the jet

The nonlinear dynamics of and heat and mass transfer processes in annular liquid jets are analyzed by means of a nonlinear system of integrodi€erential equations which account for the liquid motion and the gases enclosed by the jet. Both linear and sinusoidal heat and mass addition sources are considered to take place homogeneously within the volume enclosed by the jet's inner interface in an attempt to simulate the combustion of hazardous wastes or materials within this volume. It is shown that the liquid's temperature at the jet's inner interface increases rapidly with linear heat addition, but drops also quickly to its initial value once heat addition is ended, whereas the pressure coecient and the volume enclosed by the jet increase until they reach a maximum value and then decrease in an oscillatory manner towards their steady values. For the case of sinusoidal heat addition, it is shown that the pressure coecient and interfacial concentration, temperature and heat and mass ̄uxes oscillate in a sinusoidal manner with the same frequency as that of the sinusoidal heat source. It is also shown that mass transfer phenomena are much slower than heat transfer ones. For the case of linear mass addition, it is shown that the temperature of the gases enclosed by the jet ®rst decreases because of dilution and then it increases until it reaches a constant value that corresponds to the same temperature for the gases and the ̄owing liquid. The pressure of the gases enclosed by the jet ®rst increases because of mass addition and then slowly decreases because of mass absorption by the jet. Ó 2000 Elsevier Science Inc. All rights reserved.