Liquid-fuel burning with nonunitary Lewis number

An analysis is presented for liquid-fuel vaporization and burning with nonunitary Lewis number (i.e., nonsimilar heat and mass diffusion) in a general geometrical situation, e.g., a dense spray. Variable transport properties are considered and only Stefan flow is allowed. The analysis builds on the approach of Imaoka and Sirignano for unitary Lewis number. Fickian diffusion with differing diffusivities for each species is considered. It is shown that the problem can conveniently be separated, using a mass-flux potential function, into a one-dimensional problem for the quasi-steady, gas-phase scalar properties and a three-dimensional problem for the mass-flux potential, which satisfies Laplace's equation. This allows some previous calculations of the potential function for unitary Lewis number to be used for the potential-function solution. The scalar properties are shown to be functions of the mass-flux potential only. It is demonstrated that a mass-flux-weighted sensible specific enthalpy is more natural and convenient than the traditional mass-weighted value. This modification results in a new definition of the Lewis number. A generalization of the classical Spalding heat transfer number is presented. The theory predicts scalar gas-phase profiles, flame position, and vaporization rates. Quantitative results are presented for special cases where the Lewis number is piecewise constant. The thin-flame temperature and the effective latent heat of vaporization can be determined as functions of the liquid-surface temperature via solution of nonlinear algebraic equations; these values do not depend on the specific configuration and therefore have some universality.