Coupled Electro-Thermal Modeling of the Temperature Field in an Aluminum Reduction Cell Using the Finite Difference Method

The energy-intensive nature of primary aluminum production necessitates advanced computational tools for process optimization. This study presents a coupled electro-thermal model of an aluminum reduction cell, developed within the framework of smart manufacturing. Using the finite difference method (FDM) implemented in MATLAB R2025b, the model resolves the three-dimensional configuration of a cell with eight prebaked anodes across four distinct physical domains (electrolyte, anodes, cathode, and gas phase). The computational grid comprises approximately 45,000 nodes with refined vertical resolution (Δz = 0.025 m) in the interelectrode gap. The electrostatic solution converges within 150–200 iterations using successive over-relaxation (SOR, ω = 1.5), with a total runtime under 15 min for 30,000 s of simulated physical time on a standard desktop workstation. Simulation results reveal characteristic temperature profiles with maxima reaching 1150 °C and a thermal uniformity index of approximately 130 °C across the central cross-section. The predicted specific energy consumption of 14.0 MWh/t Al aligns with industrial benchmarks. This computationally accessible virtual testbed enables rapid assessment of design modifications and process parameters, supporting the goals of energy efficiency and enhanced operational stability in primary aluminum production.