Analytical Model of Microexplosion of a Hydrocarbon–Water Composite Droplet

An analytical solution of the problem of heating a composite spherical droplet consisting of a liquid hydrocarbon and a microdroplet of water in a hot gas flow is presented. A microdroplet of water is located in the center of a droplet of hydrocarbon. At the hydrocarbon–water interface, the conjugation conditions are specified; at the outer boundary of the hydrocarbon droplet — a condition of convective heat exchange. The unsteady temperature of a drop is represented by an analytical formula, which is an expansion of the solution in terms of eigenfunctions of the Sturm–Liouville problem. The eigenvalues are found numerically from the characteristic equation. A condition for the orthogonality of eigenfunctios in a composite droplet with discontinuous thermophysical properties is derived. The results of calculations using the obtained analytical formula are in satisfactory agreement with the experimental data. Erroneous methods are discussed in previously presented publications by other authors.