# A Modeling Approach for Time-Dependent Geometry Applied to Transient Heat Transfer of Aluminum Electrolysis Cells

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## Abstract

The thermal balance of aluminum electrolysis cells (AEC) have to be rigorously controlled in order to improve the efficiency and sustainability of this industrial process. A new modeling strategy is developed to consider the displacements of solid bodies and moving boundaries in finite element models. The transient thermal-electric modeling of the AEC demonstrates the effect of an increase in operating voltage on both the anode cover and the side ledge. With higher heat generation, the anode cover deteriorates and the side ledge thickness decreases. Since the anode cover is characterized by irreversible transformations, the top heat dissipation remains higher even when the operating voltage comes back to its typical value. For the first time, the transient temperature and electric fields throughout the anode life are simulated and validated by industrial measurements. The modeling predictions have been validated from instrumented anodes and manual measurements, all performed on operating AEC.

## Nomenclature

## Symbol

*A*Area (m

^{2})*c*_{p}Specific heat capacity (J/kg K)

*E*Electric field (V/m)

*F*View factor

*H*Height (cm or m)

*h*Convection heat transfer coefficient (W/m

^{2}K)*J*Current density (A/m

^{2})*k*Thermal conductivity (W/m K)

*L*Length (cm or m)

*q*Heat transfer rate (W)

*q″*Heat flux (W/m

^{2})- \( \dot{q} \)
Rate of energy generation per unit volume (W/m

^{3})*t*Time (s, h or day)

*T*Temperature (K or °C)

*V*Electric potential or voltage (V)

## Greek

*δ*_{ij}Kronecker delta

- \( \nabla \)
Gradient vector field

*ε*Emissivity

*ρ*Density (kg/m

^{3})*σ*Electrical conductivity (S/m); Stefan–Boltzmann constant (W/m

^{2}K^{4})

## Abbreviation

- ACD
Anode–cathode distance

- ACM
Anode cover material

- AEC
Aluminum electrolysis cell

- BMI
Bath–metal interface

- CAD
Computer-aided design

- CC
Center channel

- CFD
Computational fluid dynamics

- CR
Cryolite ratio

- HFS
Heat flux sensor

- MARE
Mean absolute relative error

- OA
On the anode

- SC
Side channel

## Style

**bold**A vector

- [brackets]
A matrix or a concentration of a chemical species

## Notes

### Acknowledgments

This study was supported by Rio Tinto Aluminium, the “Conseil de Recherches en Sciences Naturelles et en Génie du Canada” (CRSNG) and the “Fonds de Recherche du Québec - Nature et Technologies” (FRQNT). The authors wish to thank the staff at Rio Tinto Grande-Baie smelter and Arvida Research & Development Center (ARDC), especially Mr. Jean-François Bilodeau and Mr. Sébastien Guérard from ARDC, for the support provided during the realization of this work.

### Conflict of interest

The authors declare that they have no competing interests.

## Supplementary material

Supplementary material 2 (MP4 39624 kb)

Supplementary material 3 (MP4 46052 kb)

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