Unsteady heating and radiation effects of small particles in a thermal plasma

Abstract

Based on exact solutions for the heat flux to a particle exposed to a thermal plasma given in a previous paper, initial unsteady heating (including heating of the solid phase, melting of the solid phase, heating of the liquid phase, and evaporation) and radiation effects are considered. Closed-form solutions can be obtained for particles with infinite thermal conductivities. The results show that the time periods required for the various steps are all proportional to the square of the particle radius, suggesting that reduced time periods which are independent of the particle radius are appropriate bases for comparison. Results are presented for three materials (alumina, tungsten, and graphite) and three types of plasmas (argon, argon-hydrogen mixture, and nitrogen). It is shown that evaporation (or sublimation) is by the slowest step among all processes in a plasma reactor if complete evaporation (or sublimation) of the particles is desired. Studies of the temperature history of particles with finite thermal conductivities show that temperature gradients within the particles depend on the ratio of the particles' thermal resistance to that of the plasma. In spite of the difference in initial heating, the analytical expressions based on infinite thermal conductivities predict the correct total time spent for both heating and evaporation even for low-conductivity materials such as alumina. The effect of radiation losses from a particle during heating becomes important for large particles, for high-boiling-point materials, and for low enthalpy differences between the plasma and the particle surface.