Thermal conductivity of the side ledge in aluminium electrolysis cells: compounds as a function of temperature and grain size

Abstract

In aluminium electrolysis cells, a ledge of frozen electrolyte is formed, attached to the sides of the cell. The control of the side ledge thickness is essential in ensuring a reasonable lifetime for the cells. Numerical modelling of the side ledge thickness requires an accurate knowledge of the thermal transport properties as a function of temperature. Unfortunately, there is a considerable lack of experimental data for the large majority of the phases constituting the side ledge. The aim of this work is to provide, for each phase possibly present in the side ledge, a formulation of the thermal conductivity as a function of both temperature and size. To achieve this, we consider reliable physical models linking the density of the lattice vibration energy and the phonon mean free path to key parameters: the high temperature limit of the Debye temperature and the Güneisen constant. These model parameters can be obtained by simultaneous fitting of (i) the heat capacity, (ii) the thermal expansion tensor coefficient and (iii) the adiabatic elastic constants, on relevant physical models. Where data is missing, first principles (ab initio) calculations are utilised to determine directly the model parameters. For compounds for which data is available, the model's predictions are found to be in very good agreement with the reported experimental data.

Experimental Determination of the Thermal Diffusivity of α-Cryolite up to 810 K and Comparison with First Principles Predictions

“…We predict that addition of 0.9 wt % of γ-Al 2 O 3 in cryolite increases the thermal diffusivity from 0.65% (at 300 K) to 1.1% (at 836 K). Given the discussion above, the thermal diffusivity of the porous synthetic cryolite sample can be assumed to be identical to that of the dense cryolite In the regular regime, both the radiation-corrected thermal diffusivity and the conductive (true) thermal diffusivity deduced from the apparent thermal diffusivity (raw experimental data) are in excellent agreement with our previous DFT predictions 4 at temperatures up to 810 K, that is, very close to the α → β phase transition temperature of cryolite. Note that the excellent agreement found between DFT and the present MHM experiment results in some error cancelation in the prediction of thermal conductivity, heat capacity, and thermal expansion.…”

“…In summary, in the present study, we have recorded a series of MHM measurements to determine the apparent thermal diffusivity of a porous α-Na 3 AlF 6 + 0.9 wt % γ-Al 2 O 3 mixture from 473 to 810 K. The thermal diffusivity of this mixture is found to be almost identical to that of pure and dense α-Na 3 AlF 6 . In addition to providing a new set of experimental data for the temperature-dependent thermal diffusivity of cryolite, which is not available in the literature, the excellent agreement found between the experiments and the calculations confirmed the reliability and the high accuracy of our DFTbased method 4 in predicting the thermal transport properties of various phases potentially present in the side ledge of an aluminum electrolysis cell. This study is a good example proving that using first principle calculations to compensate for a lack of data, when carried out combining numerical calculations with physical principles, can lead to very good predictions, even for systems with complex phases.…”

“…A theoretical expression for the thermal conductivity (K), heat capacity, and density as a function of temperature of the cryolite (α and β) and γ-alumina has been formulated in our recent work. 4 The approach used to describe the lattice thermal conductivity is based on the Callaway−Slack 12,13 expression…”

“…The parameters describing the thermal conductivity, the heat capacity, and the density as a function of temperature are reported in Table 1, obtained from the study by Gheribi and Chartrand. 4 The heat capacity at constant pressure includes only the vibrational contribution; that is, the defect contribution is neglected. The theoretical expression of C P as a function of temperature is given by 15 C P = C V D (1 + γαT), where C V D is the Debye heat capacity at constant volume.…”

“…This suggests the good reliability of the theoretical temperature-dependent thermal conductivity predictions of the phases potentially present in the side ledge, obtained in our previous work. 4,6 However, given that cryolite is the main constituent of the side ledge, it would also be interesting to obtain experimental information on its thermal transport properties. From a theoretical point of view, such information would be crucial when confirming the reliability of our approach in predicting the lattice thermal conductivity of complex compounds.…”