A simplified model for bi-component droplet heating and evaporation is developed and applied for the analysis of the observed average droplet temperatures in a monodisperse spray. The model takes into account all key processes, which take place during this heating and evaporation, including the distribution of temperature and diffusion of liquid species inside the droplet and the effects of the non-unity activity coefficient (ideal and non-ideal models). The effects of recirculation in the moving droplets on heat and mass diffusion within them are taken into account using the effective thermal conductivity and the effective diffusivity models. The previously obtained analytical solution of the transient heat conduction equation inside droplets is incorporated in the numerical code alongside the original analytical solution of the species diffusion equation inside droplets. The predicted time evolution of the average temperatures is shown to be reasonably close to the measured one, especially in the case of pure acetone and acetone-rich mixture droplets. It is shown that the temperatures predicted by the simplified model and the earlier reported vortex model are reasonably close. Also, the temperatures predicted by the ideal and non-ideal models differ by not more than several degrees. This can justify the application of the simplified model with the activity coefficient equal to 1 for the interpretation of the time evolution of temperatures measured with errors more than several degrees.\ud \u

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a b s t r a c tThe earlier reported simplified model for multi-component droplet heating and evaporation is generalised to take into account the coupling between droplets and the ambient gas. The effects of interaction between droplets are also considered. The size of the gas volume, where the interaction between droplets and gas needs to be taken into account, is estimated based on the characteristic thermal and mass diffusion scales. The model is applied to the analysis of the experimentally observed heating and evaporation of monodispersed n-decane/3-pentanone mixture droplets at atmospheric pressure. It is pointed out that the effect of coupling leads to noticeably better agreement between the predictions of the model and the experimentally observed average droplet temperatures. In most cases, the observed droplet temperatures lie between the average and central temperatures, predicted by the coupled solution. For the cases reported in this study, the observed time evolution of droplet radii cannot be used for the validation of the model. It is pointed out that the number of terms in the series in the expressions for droplet temperature and species mass fraction can be reduced to just three, with possible errors less than about 0.5%. In this case, the model can be recommended for the implementation into computational fluid dynamics (CFD) codes and used for various engineering applications, including those in internal combustion engines.Crown

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