Numerical approach determining the optimal distance separating two heat sources heated by joule effect in a square cavity

This study presents a comprehensive two-dimensional numerical analysis of natural laminar convection within a square cavity containing two circular heat sources, which simulate electric cables generating heat due to Joule heating. This scenario is particularly relevant in aeronautics, where excessive heating of electrical installations can lead to significant material and human safety risks. The primary objective of this research is to identify the optimal spacing between the two heat sources to mitigate the risk of overheating and ensure the safe operation of the electrical installation. To achieve this, various configurations were analyzed by adjusting the distance between the heat sources while also varying the Rayleigh number across a range from 103 to 106. The governing equations for the fluid flow and heat transfer were solved using a FORTRAN-based numerical code employing the finite volume method. The results indicate that the heat transfer characteristics within the cavity are significantly influenced by both the distance between the heat sources and the Rayleigh number. The analysis revealed that the average Nusselt number (Nuavg) peaked at a value of 14.69 when the distance between the heat sources was set at 0.7 units and the Rayleigh number was at 106. This finding suggests that maintaining this specific spacing between the electrical cables can optimize heat dissipation and enhance the safety of the installation. In conclusion, the study recommends adopting a spacing of 0.7 units between the electrical cables to ensure optimal thermal performance and minimize the risk of overheating, thereby safeguarding both the materials and personnel involved in aeronautical operations.