RECURSIVE FORMULAE FOR DROPLETS TRANSIENT HEATING AND EVAPORATION MODELS VIA A COMBINED METHOD OF INTEGRAL TRANSFORMS

The transient heating of a spherical droplet at rest in a hot gas environment, is analysed when the temperature distribution is initially assumed to be non uniform inside the droplet. A combined method of integral transforms, namely the classical Fourier cosine transform together with the unilateral Laplace transform, is used in solving the resulting initial-boundary value problem, stated in the dimensionless form. Explicit solutions of the problem are first obtained in the Laplace domain, and then analytical approximations in short time limits (timessteps) are derived for the droplet internal and surface temperature fields. The analytical approximation for the droplet internal temperature during the time step is proven to be highly accurate, while the innovative recursive formula obtained for the droplet surface temperature may lead to computationally efficient droplets and sprays vaporization models.