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This paper presents a semi-analytical model of the spherically symmetric droplet transient heating and evaporation in a subcritical environment. In the numerical procedure of the model, the droplet radius is assumed to be fixed during a short time step, but varies from each time step to the next. This variation is obtained through an approximate analytical solution of the heat diffusion equation inside the stagnant droplet, by considering the volume-average or core temperature at the beginning of each time step. Depending on the temperature evolution of the gas phase assumed in quasi-steady state at the immediate vicinity of the droplet, explicit solutions are obtained in the Laplace domain for the droplet internal and surface temperatures. Next, analytical approximations in short time limits, corresponding to the asymptotic expansions of the Laplace domain solutions are derived. In particular, the reduction in droplet radius during the evaporation process is approximated by an analytical expression that is in close agreement with the numerical results. All equations are then applied in their dimensionless form to model the transient heating and evaporation of pure fuel droplets of various sizes. The new model provides a consistent description of both the initial heating phase and the entire evaporation phase of the droplet. Furthermore, the results demonstrate significantly greater computational efficiency than evaporation models using successive time steps, particularly when the series solution of the heat diffusion equation is employed within the droplet.
