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A parametric and comparative study of a permanent magnet structure

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Abstract

Permanent magnets remain the primary source of magnetic field in magnetic refrigerators and thermomagnetic motors, generally being evaluated by the \({\Lambda }_{{\text{cool}}}\) parameter, which is applicable to a magnetic field source used in a magnetic refrigeration system. The main objective of this work is to perform a parametric and comparative analysis of a C-shaped and double C-shaped permanent magnet based on a common parameter to any arrangement of magnets, namely the figure of merit \({M}^{*}\). The analysis was conducted through computational modeling and simulation with COMSOL Multiphysics® software. Different soft magnetic materials were used in the simulations and the best-performing material was used in the magnetic circuit of the C-shaped permanent magnet to evaluate the magnetic force acting on a set of gadolinium plates. It was observed that the soft magnetic material has a significant impact on \({M}^{*}\). No significant impact on \({M}^{*}\) was observed regarding to the number of gaps as long as more magnetized blocks are employed in the arrangement. Consequently, a greater gap accompanied by a lower magnetic flux density has the potential to result in an increased magnetostatic force density.

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Data and code availability

The datasets generated during the current study and others information are available from the corresponding author on reasonable request.

References

  1. V.K. Pecharsky, K.A. Gschneidner, Giant magnetocaloric effect in Gd5Si2Ge2. Phys. Rev. Lett. 78, 4494–4497 (1997). https://doi.org/10.1103/PhysRevLett.78.4494

    Article  CAS  ADS  Google Scholar 

  2. S.J. Lee, J.M. Kenkel, V.K. Pecharsky, D.C. Jiles, Permanent magnet array for the magnetic refrigerator. J. Appl. Phys. 91, 8894–8896 (2002). https://doi.org/10.1063/1.1451906

    Article  CAS  ADS  Google Scholar 

  3. B.F. Yu, Q. Gao, B. Zhang et al., Review on research of room temperature magnetic refrigeration. Int. J. Refrig.Refrig. 26, 622–636 (2003). https://doi.org/10.1016/S0140-7007(03)00048-3

    Article  Google Scholar 

  4. C.S. Alves, F.C. Colman, G.L. Foleiss et al., Numerical simulation and design of a thermomagnetic motor. Appl. Therm. Eng. 61, 616–622 (2013). https://doi.org/10.1016/j.applthermaleng.2013.07.053

    Article  CAS  Google Scholar 

  5. J.R. Gómez, R.F. Garcia, A.D.M. Catoira, M.R. Gómez, Magnetocaloric effect: a review of the thermodynamic cycles in magnetic refrigeration. Renew. Sustain. Energy Rev. 17, 74–82 (2013). https://doi.org/10.1016/j.rser.2012.09.027

    Article  Google Scholar 

  6. C.V.X. Bessa, L.D.R. Ferreira, O. Horikawa, S. Gama, On the relevance of temperature, applied magnetic field and demagnetizing factor on the performance of thermomagnetic motors. Appl. Therm. Eng. 145, 245–250 (2018). https://doi.org/10.1016/j.applthermaleng.2018.09.061

    Article  Google Scholar 

  7. U. Tomc, S. Nosan, K. Klinar, A. Kitanovski, Towards powerful magnetocaloric devices with static electro-permanent magnets. J. Adv. Res. (2022). https://doi.org/10.1016/j.jare.2022.05.001

    Article  PubMed  PubMed Central  Google Scholar 

  8. K. Halbach, Design of permanent multipole magnets with oriented rare earth colbalt material. Nucl. Instrum. Methods. Instrum. Methods 169, 1–10 (1980). https://doi.org/10.1016/0029-554X(80)90094-4

    Article  CAS  ADS  Google Scholar 

  9. R. Bjørk, C.R.H. Bahl, A. Smith, N. Pryds, Comparison of adjustable permanent magnetic field sources. J. Magn. Magn. Mater. 322, 3664–3671 (2010). https://doi.org/10.1016/j.jmmm.2010.07.022

    Article  CAS  ADS  Google Scholar 

  10. A. Tura, A. Rowe, Permanent magnet magnetic refrigerator design and experimental characterization. Int. J. Refrig. 34, 628–639 (2011). https://doi.org/10.1016/j.ijrefrig.2010.12.009

    Article  CAS  Google Scholar 

  11. P.V. Trevizoli, J.A. Lozano, G.F. Peixer, J.R. Barbosa, Design of nested Halbach cylinder arrays for magnetic refrigeration applications. J. Magn. Magn. Mater. 395, 109–122 (2015). https://doi.org/10.1016/j.jmmm.2015.07.023

    Article  CAS  ADS  Google Scholar 

  12. R. Bjørk, A. Smith, C.R.H. Bahl, Analysis of the magnetic field, force, and torque for two-dimensional Halbach cylinders. J. Magn. Magn. Mater. 322, 133–141 (2010). https://doi.org/10.1016/j.jmmm.2009.08.044

    Article  CAS  ADS  Google Scholar 

  13. Dura Magnetics. In: The benefits and drawbacks to using halbach array designs and configurations. https://www.duramag.com. Accessed 30 Jan 2023

  14. C. Vasile, C. Muller, Innovative design of a magnetocaloric system. Int. J. Refrig. 29, 1318–1326 (2006). https://doi.org/10.1016/j.ijrefrig.2006.07.016

    Article  CAS  Google Scholar 

  15. G.H. Kaneko, W.A.S. Conceição, F.C. Colman et al., Design and experimental evaluation of a linear thermomagnetic motor using gadolinium: preliminary results. Appl. Therm. Eng. 186, 116472 (2021). https://doi.org/10.1016/j.applthermaleng.2020.116472

    Article  CAS  Google Scholar 

  16. R. Bjørk, C.R.H. Bahl, A. Smith, N. Pryds, Optimization and improvement of Halbach cylinder design. J. Appl. Phys. 104, 013910 (2008). https://doi.org/10.1063/1.2952537

    Article  CAS  ADS  Google Scholar 

  17. R. Bjørk, C.R.H. Bahl, A. Smith, N. Pryds, Review and comparison of magnet designs for magnetic refrigeration. Int. J. Refrig.Refrig. 33, 437–448 (2010). https://doi.org/10.1016/j.ijrefrig.2009.12.012

    Article  CAS  Google Scholar 

  18. J.H. Jensen, M.G. Abele, Maximally efficient permanent magnet structures. J. Appl. Phys. 79, 1157–1163 (1996). https://doi.org/10.1063/1.360914

    Article  CAS  ADS  Google Scholar 

  19. S. Ahmim, M. Almanza, V. Loyau et al., Self-oscillation and heat management in a LaFeSi based thermomagnetic generator. J. Magn. Magn. Mater. 540, 168428 (2021). https://doi.org/10.1016/j.jmmm.2021.168428

    Article  CAS  Google Scholar 

  20. E.H.G. Evaristo, F.C. Colman, C.S. Alves, P.V. Trevizoli, Mathematical modelling and simulation results of a linear thermomagnetic motor with gravity return. J. Magn. Magn. Mater. 544, 168668 (2022). https://doi.org/10.1016/j.jmmm.2021.168668

    Article  CAS  Google Scholar 

  21. H. Ren, X. Zhuang, N.T. Trung, T. Rabczuk, A nonlocal operator method for finite deformation higher-order gradient elasticity. Comput. Methods Appl. Mech. Eng.. Methods Appl. Mech. Eng. (2021). https://doi.org/10.1016/j.cma.2021.113963

    Article  Google Scholar 

  22. T. Rabczuk, H. Ren, X. Zhuang, A nonlocal operator method for partial differential equations with application to electromagnetic waveguide problem. Comput. Mater. Continua 59, 31–55 (2019). https://doi.org/10.32604/cmc.2019.04567

    Article  Google Scholar 

  23. G.H. Kaneko, P.V. Trevizoli, A.C Souza, et al., Design and assembling of a magnetic circuit for a thermomagnetic motor apparatus. In: Brazilian Congress of Thermal Sciences and Engineering. Associação Brasileira de Engenharia e Ciências Mecânicas (2018). https://doi.org/10.1007/s40430-019-1898-1

  24. BAKKER MAGNETICS. https://bakkermagnetics.com/. Accessed 9 Nov 2022

  25. T. Tadic, B.G. Fallone, Design and optimization of superconducting MRI magnet systems with magnetic materials. IEEE Trans. Appl. Supercond. 22, 4400107 (2012). https://doi.org/10.1109/TASC.2012.2183871

    Article  CAS  Google Scholar 

  26. R. Lopez, J.R. Anglada, Development of a compact and fast trimmable FeCo magnet for medical gantries. Phys. Rev. Accel. Beams 23, 072401 (2020). https://doi.org/10.1103/PHYSREVACCELBEAMS.23.072401

    Article  CAS  ADS  Google Scholar 

  27. Mumetal—Magnetic Shield Corp. http://www.mu-metal.com. Accessed 14 Mar 2023

  28. Magnetic Shields—Electromagnetic Engineering. https://magneticshields.co.uk. Accessed 14 May 2022

  29. Z. Sun, A. Schnabel, M. Burghoff, L. Li, Calculation of an optimized design of magnetic shields with integrated demagnetization coils. AIP Adv. 6, 075220 (2016). https://doi.org/10.1063/1.4960329

    Article  CAS  ADS  Google Scholar 

  30. Hull R, Chennupati Jagadish U, Yoshiyuki Kawazoe A, et al (2017) Springer Series in Material Science—High Performance Soft Magnetic Materials

  31. Matlab ®. https://www.mathworks.com

  32. COMSOL Multiphysics ®. https://www.comsol.com

  33. Griffiths DJ, Introduction to Electrodynamics, 4th ed, Cambridge: Cambridge University Press (2017). ISBN 978-1108420419

  34. S.Y. Dan’kov, A.M. Tishin, V.K. Pecharsky, K.A. Gschneidner, Magnetic phase transitions and the magnetothermal properties of gadolinium. Phys. Rev. B 57, 3478–3490 (1998). https://doi.org/10.1103/PhysRevB.57.3478

    Article  ADS  Google Scholar 

  35. M.U. Mehmood, K.Y. Zeeshan et al., Design and operation of a thermomagnetic engine for the exploitation of low-grade thermal energy. Int. J. Energy Res. 45, 15298–15311 (2021). https://doi.org/10.1002/er.6804

    Article  Google Scholar 

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Acknowledgements

The authors acknowledge financial support from Universidade Federal de Pernambuco, Universidade Federal Rural de Pernambuco, Instituto Federal de Educação e Tecnologia de Pernambuco, Fundação de Amparo a Ciência e Pesquisa de Pernambuco (APQ-1361-3.05/12), and Conselho Nacional de Desenvolvimento Científico e Tecnológico (MCTI/CNPQ/Universal 14/2014—460973/2014-2).

Funding

Fundação de Amparo à Pesquisa do Estado de Pernambuco, APQ-1361-3.05/12, Alvaro Antonio Villa Ochoa, Conselho Nacional de Desenvolvimento Científico e Tecnológico, MCTI/CNPQ/Universal 14/2014-460973/2014-2, Alvaro Antonio Villa Ochoa.

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de Souza, A.C., Imamura, W., Kaneko, G.H. et al. A parametric and comparative study of a permanent magnet structure. Appl. Phys. A 130, 200 (2024). https://doi.org/10.1007/s00339-024-07361-6

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