AMR thermodynamics: Semi-analytic modeling

• Semi-analytic equations for cooling power and magnetic work of an AMR.
• Effective magnetocaloric properties governing performance are identified.
• Comparison to experimental data using gadolinium.

Temperature span, cooling power, work, and efficiency are key performance metrics describing active magnetic regenerators used as refrigerators. Numerical methods to calculate these parameters efficiently and accurately are needed. This paper proposes a set of semi-analytic relationships to determine cooling power and magnetic work as a function of temperature span, regenerator characteristics, operating conditions, and magnetic field waveform. Appropriate effective values for magnetocaloric effect and specific heat are defined. Semi-analytic predictions for cooling power and work are validated against experimental data for room-temperature tests as well as a more complex numerical model describing magnetic work. The semi-analytic approach is found to predict performance well over the range of operating conditions considered.