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[References: 18 tit.]

A mathematical model of high-temperature oxidation of a nanosize aluminum particle has been presented. The model takes account of the diffusion of the oxidant and the aluminum vapor through a spherical layer of alumina around the aluminum melt, and also of the dependence of the rate of the reaction between the oxygen and the aluminum on temperature. Calculations of the time of burning of a nanosize aluminum particle of diameter 80 mm as a function of the temperature and pressure of the surrounding gas and of the oxygen concentration turned out to be in agreement with the results of experimental measurements presented in scientifi c literature. The exponents in the dependence of the burning time of a nanosize aluminum particle on the particle diameter and the temperature and pressure of the ambient medium have been determined; it has been shown that the exponents are dependent on temperature, pressure, and particle diameter.