Title:

A mathematical study of the effect of a moving boundary and a thermal boundary layer on droplet heating and evaporation

Two new solutions to the heat conduction equation, describing transient heating of an evaporating droplet, are suggested. Both solutions take into account the effect of the reduction of the droplet radius due to evaporation, assuming that this radius is a linear function of time. It has been pointed out that the new approach predicts lower droplet surface temperatures and slower evaporation rates compared with the traditional approach. New solutions to the heat conduction equation, describing transient heating of an evaporating droplet, are suggested, assuming that the time evolution of droplet radius Rd(t) is known. The results of calculations are compared with the results obtained using the previously suggested approach, when the droplet radius was assumed to be a linear function of time during individual time steps, for typical Diesel enginelike conditions. Both solutions predict the same results which indicates that both models are likely to be correct. Two new solutions to the equation, describing the diffusion of species during multicomponent droplet evaporation, are suggested. The first solution is the explicit analytical solution to this equation while the second one reduces the solution of the differential species diffusion equation to the solution of the Volterra integral equation of the second kind. Both solutions take into account the effect of the reduction of the droplet radius due to evaporation, assuming that this radius is a linear function of time. The analytical solution has been incorporated into a zero dimensional CFD code and applied to the analysis of bicomponent (50% ethanol 50% acetone mixture) droplet evaporation at atmospheric pressure. The transient heat conduction equation, describing heating of a body immersed into gas with inhomogeneous temperature distribution, is solved analytically, assu ming that, at a certain distance from the body, gas temperature remains constant. The solution is applied to modelling of body heating in conditions close to those observed in Diesel engines. In the long time limit, the distribution of temperature in the body and gas practically does not depend on the initial distribution of gas temperature.
