Constructal entransy dissipation minimization of an electromagnet

How to determine the optimal distribution of high conductivity material through the given volume such that the heat generated at every point was transferred most effectively to its boundary has become the focus of attention in the current constructal theory literature. In general, the minimization of maximum temperature difference in the volume is taken as the optimization objective. A physical quantity, entransy, has been identified as a basis for optimizing heat transfer processes in terms of the analogy between heat and electrical conduction recently. Heat transfer analyses show that the entransy of an object describes its heat transfer ability, as the electrical energy in a capacitor describes its charge transfer ability. Entransy dissipation occurs during heat transfer processes, as a measure of the heat transfer irreversibility with the dissipation related thermal resistance. Based on entransy dissipation, the mean temperature difference of solenoid (electromagnet) with high thermal conductivity material inserted is deduced, which can be taken as the fundamental for heat transfer optimization using the extremum principle of entransy dissipation. Then, the electromagnet working at steady state (constant magnetic field, constant heat generating rate per unit volume) is optimized for entransy dissipation minimization (i.e., mean temperature difference minimization) with and without volume constraint. The variation of minimum mean temperature difference with volume and magnetic field and the corresponding optimal constructs are obtained. The effect of high thermal conductivity material on the magnetic field is analyzed. The optimization results show that for fixed G parameter and phi, the minimum mean temperature difference decreases as the number of cooling disks n increases but the decreasing magnitude of minimum mean temperature difference is relatively decreased. As n increases, the radius of the solenoid decreases, the length of the solenoid increases, and the volume decreases. The solenoid optimized based on minimization of entransy dissipation with fixed magnetic induction is considerably larger than the winding optimized solely from the electromagnetic point of view. The mean temperature difference decrease as the volume increases. (C) 2009 American Institute of Physics. [DOI: 10.1063/1.3124451]