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This paper aims to introduce an alternative for modeling levitation forces between NdFeB magnets and bulks of high-temperature superconductors (HTS). The presented approach should be evaluated through two different formulations and compared with experimental results.

The T-A and H-ϕ formulations are among the most efficient approaches for modeling superconducting materials. COMSOL Multiphysics was used to apply them to magnetic levitation models and predict the forces involved.The permanent magnet movement is modeled by combining moving meshes and magnetic field identity pairs in both 2D and 3D studies.

It is shown that it is possible to use the homogenization technique for the T-A formulation in 3D models combined with mixed formulation boundaries and moving meshes to simulate the whole device’s geometry.

The case studies are limited to the formulations’ implementation and a brief assessment regarding degrees of freedom. The intent is to make the simulation straightforward rather than establish a benchmark.

The H-ϕ formulation considers the HTS bulk domain as isotropic, whereas the T-A formulation homogenization approach treats it as anisotropic. The originality of the paper lies in contrasting these different modeling approaches while incorporating the external magnetic field movement by means of the Lagrangian–Eulerian method.

The purpose of the present work is to study the impacts of rapid cooling and Tb rare-earth additions on the structural, thermal and mechanical behavior of Bi–0.5Ag lead-free solder for high-temperature applications.

Effect of rapid solidification processing on structural, thermal and mechanical properties of Bi-Ag lead-free solder reinforced Tb rare-earth element.

The obtained results indicated that the microstructure consists of rhombohedral Bi-rich phase and Ag99.5Bi0.5 intermetallic compound (IMC). The addition of Tb could effectively reduce the onset and melting point. The elastic modulus of Tb-containing solders was enhanced to about 90% at 0.5 Tb. The higher elastic modulus may be attributed to solid solution strengthening effect, solubility extension, microstructure refinement and precipitation hardening of uniform distribution Ag99.5Bi0.5 IMC particles which can reasonably modify the microstructure, as well as inhibit the segregation and hinder the motion of dislocations.

It is recommended that the lead-free Bi-0.5Ag-0.5Tb solder be a candidate instead of common solder alloy (Sn-37Pb) for high temperature and high performance applications.