Constructal thermal optimization of an electromagnet

This paper addresses the fundamental problem of optimizing the geometry of an electromagnet by maximizing at the same time its magnetic performance and thermal performance. The solenoid has a cylindrical shape and a uniform current density. Cooling discs made of high thermal conductivity material are inserted in the coil to collect the heat generated by Joule heating. The collected heat is evacuated to the ambient. For a given magnetic performance and volume, the maximum temperature inside the electromagnet is minimized by selecting the shape of the coil (length and outer radius), the number of cooling discs, and the amount of high thermal conductivity material. The two objectives pursued in this geometric optimization (magnetic and thermal) show that the constructal design method can be extended to the generation of architecture for multi-objective systems.