An improved analytical model for combustion synthesis has been developed. The features of the model include consideration of the thermophysical and chemical properties of both the reactants and products, as well as considerations of porosity for both reactants and products. An analysis of the variation of the dimensionless velocity with the variation of dimensionless thermal conductivity, density, and heat capacity is carried out. The equations for the combustion temperature and combustion velocity with the inclusion of nonreacting diluents and different thermophysical and chemical properties of the reactants and products is also developed. An equation for the velocity as a function of the nonmelting reactant radius and the different thermophysical and chemical properties of the reactants and products is derived using a diffusion kinetic equation. Master plots for general solid-solid reaction systems, which relate dimensionless velocity, thermal conductivity, density, and heat capacity, are presented. Application of this model to the combustion synthesis of TIC has been carried out to study the variation of combustion front motion with the radius of carbon particles. A comparison of velocities for NiAl predicted by the model as a function of the reactant porosity is presented and compared with the experimentally determined value. The comparison is noted to be close except when the thin zone approximation is no longer valid.
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