# Heat-transfer model for the acheson process

- Received:

DOI: 10.1007/s11661-001-0220-9

- Cite this article as:
- Gupta, G.S., Vasanth Kumar, P., Rudolph, V.R. et al. Metall and Mat Trans A (2001) 32: 1301. doi:10.1007/s11661-001-0220-9

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## Abstract

The Acheson process is used to manufacture silicon carbide (SiC) in a resistor furnace using petroleum coke and silica as raw materials. The process is highly inefficient, as only 10 to 15 pct of the charge gets converted into silicon carbide. No published attempt has been made to optimize this century-old process by applying mathematical modeling. Therefore, a simultaneous heat- and mass-transfer model has been developed for the resistance-heating furnace, considering silicon carbide formation as a typical carbothermal reaction. Coupled transient partial differential equations have been worked out. These equations have been solved numerically, using the implicit finite-difference method in their nondimensional form, to obtain the profiles of solid temperature and volume fraction reacted in the furnace. The trend of the computed results appears to be realistic; comparison of the results with published experimental work validates the applicability of the model’s predictions. The effects of various parameters on the process have been studied. These include void fraction, power inputs, initial concentration of silicon carbide present in the charge, *etc*.

### Nomenclature

*Q*_{R}heat generation term

*r*coordinate in the radial direction

*t*time

*C*_{p}specific heat

*x*fraction of silica reacted

- \(\dot R\)
the rate of reaction for SiC formation

*K*a constant

*M*molecular weight

- R
universal gas constant

*T*absolute temperature

- Δ
*S* diffusion distance

*A*area of diffusion

*L*length of the furnace

*p*partial pressure

*D*diffusion coefficient

*Q*heat loss at the furnace wall

*h*convective heat-transfer coefficient between air and the steel shell

*r*_{1}and*r*_{2}radius of the graphite core and furnace inwall, respectively

*r*_{3}furnace radius, including refractories

*r*_{4}furnace radius, including steel shell

- Δ
*H*_{R} heat of reaction for Reaction [1]

*R*_{e}resistance

*I*current

### Subscripts

*e*effective

*s*solid

- 0 and
*i* initial

- SiC
silicon carbide

*ss*steel shell

- ref
refractory

- CO
carbon monoxide

*t*_{T}*nondimensional time for the heat-balance equation

*t*_{C}*nondimensional time for the mass-balance equation

### Superscript

- *
nondimensional quantities

### Greek Symbols

*κ*thermal conductivity

*ρ*density

*ɛ*void fraction