A distributed mathematical model of ignition of a magnesium particle with allowance for the heterogeneous chemical reaction and the region of the thermal influence of the particle on the gas is developed. A solution of the problem in a steady formulation is found, which allows expanding the classification of the thermal history of the particle-gas system. A numerical model for solving the considered class of boundaryvalue problems of magnesium-particle ignition is proposed, and the mathematical model is verified in terms of the ignition delay as a function of the Nusselt number. A limiting size of the gas layer near the particle, which determines the ignition mode, is identified. Stability of some heating regimes to finite and infinitesimal disturbances is demonstrated. It is shown that the ignition process can be controlled by a highfrequency thermal action on unstable states of the particle-gas system.The problem of physicomathematical modeling of ignition and combustion of metal samples is of considerable interest for various branches of industry [1]. The main objects described in [1] are the pointwise and partly distributed models of ignition of small metal particles with low-temperature oxidation proceeding on the particle surface. The heat dissipated into the gas phase was ignored. This means that the thickness of the socalled "surrounding" film is negligibly small. It seems of interest to study the effect of this factor on the thermal history of the reacting particle. We consider a metal particle of radius r p surrounded by a gas layer of thickness L − r p . We assume an exothermic chemical reaction of oxidation to proceed on the sample surface. Then the mathematical model that describes the temperature fields in the sample T 2 and in the ambient gas T 1 has the formwhere ν is the factor of symmetry equal to 0, 1, and 2 for the planar, cylindrical, and spherical cases, respectively, ρ i , λ i , and c i are the density, thermal conductivity, and specific heat of the phases; the subscript i = 1 and 2 refers to parameters of the gas and the particle, respectively.Equations (1) and (2) should satisfy the following boundary and initial conditions:Here q 0 is the heat release per unit mass of the oxide, ρ 3 is the oxide density, h is the oxide-film thickness, dh/(dt) is the rate of variation of the oxide-film thickness, K is the preexponent in the oxidation law, E is the activation energy of low-temperature oxidation, R is the universal gas constant, α = Nu/2 is the heat-transfer coefficient, Nu is the Nusselt number, and

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A semi-empirical model of molecular dynamics is proposed within the molecular dynamics approach. The model is verified against the experimental dependence of the melting temperature of aluminum nanoparticles on their size. The specific heat of the particle and the phase transition heat are determined as functions of the initial size and temperature of the particle. It is demonstrated that these dependences tend to the limiting dependences, which describe the particle size in the volume phase, as the particle size increases. A comparison of the aluminum nanoparticle melting characteristics calculated by the model of molecular dynamics and by the phenomenological model reveals reasonable agreement in terms of the melting time.

A distributed two-dimensional mathematical model of ignition and combustion of magnesium particles with allowance for the heterogeneous chemical reaction and for the region of the thermal influence of the particle on the gas is developed. Problems of particle ignition under the action of uniform and nonuniform thermal fields in a rectangular microchannel are solved.

Molecular dynamics modeling of melting of aluminum nanoparticles with the use of the DL POLY simulation package and two types of parametrization of the embedded atom potential is performed. Predicted melting temperatures are compared with available experimental and numerical data. A significant scatter of data (melting temperatures as functions of the nanoparticle size) is noted. The previously proposed semi-empirical model of molecular dynamics for the description of the thermal history of the aluminum nanoparticle is justified. The specific heats obtained in this study ensure a qualitatively correct description of their dependence on temperature and on the crystal rib size.