Analytical solution for diffusion and circulation in a vaporizing droplet

The problem of convective diffusion in a liquid droplet with internal circulation is studied.Both the vaporizing and the non-vaporizing cases are considered. An approach which simplifies the governing equations is taken and series solution for both the temperature boundary condition and temperature gradient boundary condition cases are obtained. The results are in reasonably close agreement with the finite-difference solution of the more exact analysis. In the non-vaporizing droplet case, the coupled gas-phase and liquid-phase problem is examined. Solution for the droplet surface temperature in the form of a linear Volterra Integral Equation, utilizing the series solution, is obtained. The results are very promising for future simplifications in spray combustion analyses.