The paper proposes a two-dimensional mathematical model of the combustion synthesis of chemical compounds and alloys in the conditions of thermal explosion during the induction heating of the powder compact in a steel cylindrical mold. A set of chemical reactions is described by a reaction network with effective kinetic parameters. The kinetic aspect concerns the possible strong retardation of the reaction network with the accumulation of the synthesis product. The proposed model allows investigating macroscopic physical processes during the synthesis of the intermetallic compound in changing the heating rate and reactor dimensions. A comparative analysis is given to the constant thermal conductivity and thermal conductivity affected by temperature. Consideration of the temperature dependence of thermal conductivity in the proposed model, can lead to a quantitative change in the delay time of combustion and a qualitative change in the temperature distribution in the cylindrical mold volume.

本文提出了在钢制圆柱模具中感应加热粉末压块过程中，在热爆炸条件下化合物和合金燃烧合成的二维数学模型。一组化学反应由具有有效动力学参数的反应网络描述。动力学方面涉及随着合成产物的积累，反应网络可能的强烈延迟。所提出的模型允许研究金属间化合物合成过程中改变加热速率和反应器尺寸的宏观物理过程。对恒定热导率和受温度影响的热导率进行了对比分析。在所提出的模型中考虑热导率的温度依赖性，