Dissipation and heat-transfer management in high-voltage heating elements

• Micro-scale model of high-voltage electrical heating elements for thermal-energy-storage systems and broader Joule heating applications. • Direct computation, dimensional and geometric simlitude harnessed to develop a low-dimensional macro-scale model of electrical heating elements with helical heating wires. • Three or more orders of magnitude increase in computational economy over existing literature. • Computational interpretation of experiments with temperature-dependent material properties. • Natural convection heat transfer coefficient for air under non-Oberbeck-Boussinesq conditions. The global transition toward renewable energies has brought special interest in electrified industrial heating systems, including thermal energy storage systems. While extensive research has been undertaken to design electrical heaters—focusing on macro-scale analyses, no research has addressed in a computationally efficient manner the micro-scale design of electrical heating elements to maximize power, and to avoid dielectric breakdown and heating-wire melting. This research addresses the micro-scale Joule heating and heat-transfer problem, furnishing a design rationale to inform macro-scale design of electrical heating elements under any voltage and external heat-transfer resistance. The model is used to interpret a recent literature report of an electrical heating element in air. From measured surface temperatures and the power dissipation, we ascertain the natural convection heat transfer coefficient and the internal temperature distribution, unveiling how close the heating wire comes to melting. The natural convection heat transfer coefficient for ambient air under non-Oberbeck-Boussinesq conditions is found to be significantly enhanced. By drawing on dimensional and geometric simlitude, the model may be translated to other thermal-fluid systems to optimize in-the-field performance.