Abstract
A numerical study of self-propagating combustion synthesis is carried out to determine the effect of the heat of reaction(Q), the activation energy (E), the frequency factor (K0), thermal conductivity(K*), and initial temperature(T 0 on the combustion velocity and combustion temperature in the presence of cooling at one end. The numerical procedure allows for the formation and solidification of nonstoichiometric combustion products. This includes the phase change of the product through its solidification and eutectic range. Calculations are carried out for the Ti-C system with an objective of predicting solutions which are comparable to previously reported, experimentally determined values. Calculations are also compared with the thin zone analytical solution to the combustion problem. The use of lowK 0 values to bring the solutions close to the experimentally determined numbers is discussed. Solutions are presented to elucidate the effect of relevant parameters on the thickness of the combustion and preheat zones. Conditions where extinction is expected to occur are identified. The effect of the thermal conductivity on the velocity may be to increase or decrease the velocity, depending on the value ofK 0. At lowK 0 values, an increase in the thermal conductivity may lead to a decrease in the combustion velocity. The effect of the initial temperature on the combustion velocity and temperature is to increase both; however, the increase in the combustion temperature may not be proportional to the increase in the initial temperature. The activation energyE has a pronounced effect on reducing the combustion velocity while not influencing the combustion temperature. The time rate of the solidification process which determines the final microstructure is discussed.
Published Version
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