Thermal and diffusive relaxation of an evaporating drop with internal heat liberation

Abstract

The problem of nonsteady-state evaporation or growth of a radiating drop with uniformly distributed internal heat sources is considered. The Reynolds R=ua/v ≪1 and Peclet PD= ua/D ≪1 numbers are assumed to be small (a is the radius of the drop, u the velocity of its relative motion, andv, D, χ the coefficients of viscosity, diffusion and thermal diffusivity of the vapor-gas medium). This enables the convective transfer of vapor and heat to be neglected, and the concentration and temperature fields to be regarded as spherically symmetric [1]. In view of the fact that the density of saturated vapor is less than the density of liquid the convective flow caused by the change in radius of the drop is not taken into account [2]. It has already been shown [3,4], that for χ≪χr (χ, χr are the coefficients of molecular and radiative thermal conductivity) there exists a bounded region ryo (1/α) √χ/χr (α is the absorption coefficient for radiation in the gas), in which the effect of radiation on the temperature relaxation of the vapor-gas medium is negligible. If the conditiona ≪ (1/α) √χ/χr is satisfied, then the temperature at the outer boundary of this region will be practically the same as the temperature at infinity T=T∞. This means that terms in the energy equation connected with energy transferred by radiation can be neglected. It is assumed that the free path of molecules in the gas is less than the radius of the drop, and so concentration and temperature discontinuities close to the surface of the drop can be neglected [2].