A three-dimensional thermo-magnetically coupled model for magnetocaloric materials undergoing a first-order phase transition

Solid-state refrigeration based on the magnetocaloric effect offers an energy-efficient and environment-friendly alternative to conventional vapor-compression cooling. Developing a robust theoretical model is crucial for evaluating device performance and guiding design improvements. In this paper, a three-dimensional thermo-magnetically coupled model is constructed within the framework of irreversible thermodynamics. To accurately describe the magnetic field- and temperature-dependent specific heat capacity, a Cauchy-Lorentz function is introduced. Based on the Helmholtz free energy and the first and second laws of thermodynamics, the equations governing entropy, magnetization, and the spatiotemporal temperature evolution are derived and implemented into a finite-element framework to resolve the non-uniform physical fields in non-ellipsoidal specimens. The predicted adiabatic temperature change agrees well with the experimental data of LaFe 11.5 Mn 0.24 Si 1.26 alloy under magnetic fields of 0.8–1.5 T and ambient temperatures of 304–318 K. Furthermore, among six investigated specimen geometries the spherical one yields the highest temperature change, with the smallest reduction ratio (∼20.7%) relative to that in the adiabatic case without the demagnetization effect (4.4 K), whereas the needle-shaped specimen loses nearly 100%. The proposed model serves as a valuable theoretical tool for designing and optimizing magnetocaloric refrigeration devices made from La-Fe-Si-based alloys.