Concurrent Solenoid Design Optimization From Thermal and Electromagnetic Standpoints

This paper extends the previous effort by Gosselin and Bejan to optimize an electromagnet according to the constructal design approach. This paper pursues two objectives in the solenoid design: a constant Fabry factor of 0.16 and a minimum hot-spot temperature in the coil. In order to minimize the hot-spot temperature, cooling discs made of high thermal conductivity materials are inserted to transport heat to disc surfaces fixed at constant temperature (heat sink). Subsequently, two cooling disc configurations are investigated in this paper: discs with heat sinks on the outer surface and on both the inner and outer surfaces. A mathematical model for each configuration is presented and numerically verified using a commercial FEA software. These models are then used to examine the hot-spot temperature variation with respect to the number of cooling discs. In addition, optimal solenoid radius and length, as well as cooling disc volume, are determined for a range of fixed solenoid volumes; thereby, the ideal solenoid volume resulting in the minimum hot-spot temperature is found. In summary, the qualitative trend of the tradeoff between heat transfer and electromagnetic performances are analyzed, and the optimal design is deduced for the maximum performance from a combined standpoint.