Analytical and numerical modeling of the composite “hydrocarbon – water” drop heating

Analytical and numerical solutions for the heating of a composite “hydrocarbon–water” drop with a water micro-droplet located in the center of a spherical drop of hydrocarbon are compared. The conjugation conditions are fulfilled at the interface: continuity of temperature and heat flux. At the outer boundary of the droplet, a condition of heat exchange with a hot gas streamlining the droplet is set. The analytical formula is based on the decomposition of the solution in a series of eigenfunctions of the Sturm–Liouville problem. An original conservative difference scheme for the numerical integration of the equations of thermal conductivity inside a composite droplet is constructed to take into account the abrupt change in thermophysical properties at the interface of hydrocarbon–water media. The calculation results obtained using the analytical formula and the numerical integration method are consistent with each other. The numerical scheme includes radiative heat transfer and the effect of evaporation on the heat transfer coefficient. A comparison of the simulation results with experimental data is presented.