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Journal of Materials Science

, Volume 30, Issue 20, pp 5043–5048 | Cite as

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

  • H. K. Chen
  • C. I. Lin
Article
  • 38 Downloads

Abstract

A physico-chemical model has been formulated to provide a description of the reduction of carbon/alumina powder mixture in a flowing nitrogen stream. Simultaneous differential equations were derived on the basis of this model. These equations were solved by numerical methods. The chemical reaction rate expression, which was determined in the chemical reaction control region, was used after the model had been employed for interpreting the experimental data. The expressions for effective gas diffusivities, which have been left as a fitting parameter for calculation of theoretical predictions, were determined as
$$\begin{gathered} D_{e_{Al_2 OCO} } = 4.29 x 10^{ - 5} exp ( - 25971 J mol^{ - 1} /RT) m^2 s^{ - 1} \hfill \\ D_{e_{Al_2 OCO} } = 2.49 x 10^{ - 5} exp ( - 31512 J mol^{ - 1} /RT) m^2 s^{ - 1} \hfill \\ D_{e_{Al_2 ON_2 } } = 3.13 x 10^{ - 5} exp ( - 29718 J mol^{ - 1} /RT) m^2 s^{ - 1} \hfill \\ \end{gathered} $$

The correlation between the geometrical factor g and half thickness of the sample was determined as g=1/(1+64.7L), and the correlation between the Sherwood number and Reynolds number was found to be Nsh=0.46N 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 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

\(C_{Al_2 O_3 } ,C_C ,C_{A1N} \)

Concentrations of solids Al2O3, 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 (m2s−1)

g

Geometric factor (m−1)

ka, kb, kc

Reaction rate constants (m3s−1kg−1mol−1)

KE

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 Al2O, CO, CO2 and N2, respectively (kgmols−1 m−2)

NRe

Reynolds number

Nsh

Sherwood number

Nsc

Schmidt number

\(\begin{gathered} P_{Al_2 O} ,P_{CO} ,P_{CO_2 } , \hfill \\ P_{N_2 } , \hfill \\ \end{gathered} \)

Partial pressures of Al2O3, CO, CO2 and N2, respectively (atm)

Pt

Total pressure (atm)

R

Gas constant (kJ kg−1mol−1K−1)

t

Reaction time (s)

T

Absolute temperature (K)

\(X_{Al_2 O_3 } ,X_C ,Y_{AlN} \)

Conversions of solids Al2O3, carbon and yield of solid AlN, respectively

z

Coordinate (m)

ε

Porosity

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Copyright information

© Chapman & Hall 1995

Authors and Affiliations

  • H. K. Chen
    • 1
  • C. I. Lin
    • 1
  1. 1.Department of Chemical EngineeringNational Taiwan Institute of TechnologyTaipeiTaiwan

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