Semi-analytical and numerical models for magnetic field induced magneto-elastocaloric cooling in the multiferroic composite system

Abstract

Based on the experimental investigations on the ultra-low magnetic field induced magneto-elastocaloric cooling performance of a multiferroic composite system (consisting of magnetostrictive alloy and shape memory alloy elements), semi-analytical and numerical models are developed to describe the thermo-magneto-mechanically coupled responses of such composite system. Firstly, magneto-mechanically coupled and thermo-mechanically coupled constitutive models are employed to describe the deformations of magnetostrictive alloy (MEA) and shape memory alloy (SMA), respectively. Combining the equations of force balance, deformation compatibility, thermodynamic equilibrium, and the constitutive equations for the constituent elements of the composite system, a semi-analytical model is proposed based on the lumped analysis of heat transfer, and a semi-analytical relation is established between the applied magnetic field and the maximum cooling temperature. Then, a numerical model is constructed to predict the whole deformation, magnetization and heat transfer processes of the multiferroic composite system, which is solved by finite volume method and a newly proposed iterative algorithm. Finally, the capabilities of these two models are verified by comparing the simulated results with the experimental data, and the proposed models are further used to investigate the influence of the geometric dimensions of MEA/SMA elements and the pre-load on the refrigeration capacity of the composite system.