Mathematical model of the forced cooling of anodes used in the aluminium industry : a thesis presented in partial fulfilment of the requirements for the degree of Master of Science in Mathematics at Massey University
The aluminium industry consumes large amounts of electrodes, especially anodes, to operate the smelters. These anodes must be baked at high temperatures in order to give them certain mechanical and electrical properties, after which they are cooled. Baking is done in large furnaces made up of pits inside which the anodes are placed in layers and surrounded by packing coke. The furnaces are of two types - open and closed. In a closed furnace, the pits are lined with refractory bricks inside which flues run vertically and large covers are used to close over parts of the furnace.
This thesis presents a mathematical model of part of a forced cooling section of a closed furnace, where air is being sucked or blown through the flues by fans, so that the anodes cool more rapidly. Both one- and two-dimensional models are developed in order to calculate the transient temperature distribution in the anodes, packing coke and side flue wall. For the two-dimensional model, the transient temperature and pressure distributions of the air in the side wall flues and fire shafts are also calculated. After exploring an analytical method for the one-dimensional case, numerical techniques are used thereafter.
Given initial block and air temperatures, the two-dimensional model allows calculation of the appropriate temperature and pressure distributions for various mass flows of air in the side wall flues and fire shafts. The results show that for a sufficiently high mass flow, the anodes can be cooled enough so that they can be safely removed from the pits after three fire cycles (the length of time the anodes are exposed to forced cooling).