Thermodynamic optimization of a linear thermomagnetic motor

Thermomagnetic motors can be applied to recover low-grade thermal energy waste and convert it into mechanical energy, therefore, used as an energy harvester. The present work proposes a mathematical model to simulate the heat transfer and the thermodynamic cycle of a linear thermomagnetic motor coupled to a spring mechanism. The simulation results are the input information in a subroutine to optimize the motor design based on two objective functions: to minimize the total entropy generated and to minimize the back work ratio, defined as the ratio between the pumping power and the total produced power. The mathematical model solves coupled the energy equations for the fluid and solid phases, and the entropy generation model includes four contributions: interstitial heat transfer (finite temperature difference), axial conduction in the fluid and solid phases, and viscous dissipation. Gadolinium is used as soft magnetic material due to the availability of properties data. Four design and operating conditions constraints are taken into account: heat exchanger length, spring constant, mass flow rate, and warm stream temperature (heat source), and their optimized values are, respectively, 52 mm, 1560 N/m, 80 kg/h at any warm stream temperature ranging from 310-330 K. At these combinations, the optimum thermomagnetic motor is able to produce a net power of 5.00 +/- 0.15 W with a minimum back-work ratio of about 12%. The proposed methodology can be used to optimize the design of novel thermomagnetic motors or to optimize geometric parameters and operating conditions of state-of-the-art concepts.