tailieunhanh - Heat and Mass Transfer Modeling and Simulation Part 10

Tham khảo tài liệu 'heat and mass transfer modeling and simulation part 10', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Modeling and Simulation of Chemical System Vaporization at High Temperature Application to the Vitrification of Fly Ashes and Radioactive Wastes by Thermal Plasma 171 4. Transfer equation Determination of the stoichiometric coefficient To simplify the writing and calculation of the mass transfer equation at the interface a dimensionless quantity Xj called stoichiometric coefficient of a metal J has been introduced and corresponding to X j nOj nMj 13 where no-j is the mole number of oxygen in the liquid phase related to metal J whereas the term nM represents the total mole number of metal J in the liquid phase which contains m species. For example if N is the total mole number of metals in the mixing melted material for an unspecified metal J the expressions of Xj is as follows X j - m 2 Wi i 1 jj N Eauuu ij ij j 1 14 m 2 j i 1 aij and aik are respectively the stoichiometric coefficients of the element J and oxygen in species i . ni represents the number of moles of species i . uij is the valence of metal J in oxide i . Example In an initial mixture of Al-Si-Fe-O-Cl for example the species which can exist in the liquid phase at 1700 K are as follows SiO2 Fe2SiO4 Fe3O4 FeO Al2O3 AlCl3 FeCl2. The iron stoichiometric coefficients XFe in the system is given by the following expression X 4. 4 nFe2SiO4 x 8 4 nFe3O4 nFeO 2 nFe2SiO4 3 nFe3O4 nFeO 15 Transfer equation From equation 13 the oxygen mole number in the liquid phase related to metal J can be deduced . nO- j X j - 16 If equation 16 is differentiated relatively to time and each term is divided by the surface of the interface value A it comes 1 dnO- j 1 dnM 1 dX j X nM A dt A j dt A M dt 17 172 Heat and Mass Transfer - Modeling and Simulation The interfacial density of molar flux of a species i is . 1 dll ỈÍ - - A t 18 Introducing equation 18 in equation 17 leads to Mv x. ĨL. ln dx cim la Mj -X j. JMj A dt 19 Ỉa M represent the surfacic molar flux densities of oxygen related to metal J .