  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 Gruneisen 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 used 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.
