Analytical modelling of drop heating and evaporation in drop clouds: Effect of temperature dependent gas properties and cloud shape

The conservation equations describing the heat and mass transfer from an arbitrary number of interacting drops floating in a gaseous environment are analytically solved under steady-state conditions using a point source model, accounting analytically for the temperature dependence of the thermo-physical properties in the gaseous mixture. The model accuracy is assessed by comparison with exact analytical solutions available for pairs of interacting drops, accurate numerical predictions for drop arrays and experimental measurements for drop streams. A statistical description of drop clouds is used to propose a correlation for evaluating the screening effect in clouds of arbitrary shape and drop numerosity. The model is used to study the influence of cloud compactness and shape on global and local drop evaporation characteristics and the effect of operating conditions and temperature dependence of thermo-physical properties on total mass and heat rates for different chemical species is discussed.