Model of thermal radiation using heat absorption by CO2 in submicron pores with application to magnesium-zinc ferrite fine disperse particles synthesis via combustion

Abstract

Microscopic and macroscopic heat fluxes have been calculated on the basis of the self-consistent analysis of micro and macro scales taking into account absorption of thermal radiation by the CO2 molecules in micro pores. The macroscopic fluxes have been considered with the help of A. Shack modification to the Stefan-Boltzmann law at the given degree of blackness of a surface of a solid phase. These fluxes are received by averaging of the microscopic fluxes taking into account the influence of Knudsen's layer and absorption of heat during combustion of carbon. In the case of a submicron scale the models of slipping of a gas phase and jump of temperature of gas inside Knudsen's layers in the vicinity of pore borders are used. The intensities of macroscopic fluxes are presented through the parameters of similarity and depend on the emissivity of pore surfaces, on the coefficients of molecule reflection and thermal accommodation. The governing system of equations on a macroscopic scale includes heat exchange between the gaseous and solid phases. The macro fluxes are calculated by means of averaging of micro fluxes taking into account the effect of Knudsen's layer and the heat absorption during the carbon combustion. The synthesis of magnesium-zinc ferrite submicron particles is modelled numerically. The results of thermal front numerical simulation allow us to evaluate the impact of CO2 absorption, emissivity along with the slippage on the heat and mass transfer. It was found that an increase in the intensity of radiation corresponds to the decrease in the rate of submicron particles growth.