MULTICOMPONENT TRANSIENT DROPLET VAPORIZATION WITH INTERNAL CIRCULATION: INTEGRAL EQUATION FORMULATION AND APPROXIMATE SOLUTION

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Abstract
The problem of transient droplet vaporization in a hot convective environment is examined. A model that accounts for liquid-phase internal circulation, transient droplet heating and species diffusion, and axisymmetric gas-phase convection is used. The coupled vaporization problem is formulated as a Volterra-type integral equation with the liquid-phase temperature and species concentration at the droplet surface being unknown functions of time. The integral equation formulation is subsequently transformed into a system of first-order ordinary differential equations, which are solved by the Runge-Kutta scheme. Since only the liquid-phase temperature and species concentration at the droplet surface are needed for determining the vaporization rate and the heat flux, the integral equation formulation has the advantage of eliminating the spatial dependence from the problem, thereby reducing the amount of compulation time.

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