# A mathematical model of the reduction of carbon/alumina powder mixture in a flowing nitrogen stream

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## Abstract

The correlation between the geometrical factor *g* and half thickness of the sample was determined as *g*=1/(1+64.7*L*), and the correlation between the Sherwood number and Reynolds number was found to be *N*_{sh}=0.46*N* _{Re} ^{0.42} . The reaction occurring between nitrogen, aluminium oxide and carbon was predicted fairly well by this model.

## Keywords

Polymer Aluminium Reynolds Number Theoretical Prediction Control Region## Nomenclature

- \(C_{Al_2 O_3 } ,C_C ,C_{A1N} \)
Concentrations of solids Al

_{2}O_{3}, carbon and AlN, respectively, (kgmolm^{−3})- \(\begin{gathered} D_{e_{Al_2 O_3 CO} } , D_{e_{Al_2 O_3 CO_2 } } , \hfill \\ D_{e_{Al_2 O_3 N_2 } } ,D_{e_{COCO_2 } } , \hfill \\ D_{e_{CO_2 N_2 } } \hfill \\ \end{gathered} \)
Effective normal diffusivities (m

^{2}s^{−1})*g*Geometric factor (m

^{−1})*k*_{a}, k_{b}, k_{c}Reaction rate constants (m

^{3}s^{−1}kg^{−1}mol^{−1})*K*_{E}Equilibrium constant

*L*Half thickness of solid matrix (m)

- \(\begin{gathered} N_{Al_2 O} ,N_{CO} ,N_{CO_2 } , \hfill \\ N_{N_2 } , \hfill \\ \end{gathered} \)
Fluxes of gases Al

_{2}O, CO, CO_{2}and N_{2}, respectively (kgmols^{−1}m^{−2})*N*_{Re}Reynolds number

*N*_{sh}Sherwood number

*N*_{sc}Schmidt number

- \(\begin{gathered} P_{Al_2 O} ,P_{CO} ,P_{CO_2 } , \hfill \\ P_{N_2 } , \hfill \\ \end{gathered} \)
Partial pressures of Al

_{2}O_{3}, CO, CO_{2}and N_{2}, respectively (atm)*P*_{t}Total pressure (atm)

*R*Gas constant (kJ kg

^{−1}mol^{−1}K^{−1})*t*Reaction time (s)

*T*Absolute temperature (K)

- \(X_{Al_2 O_3 } ,X_C ,Y_{AlN} \)
Conversions of solids Al

_{2}O_{3}, carbon and yield of solid AlN, respectively*z*Coordinate (m)

- ε
Porosity

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## References

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