{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,9]],"date-time":"2026-05-09T17:12:33Z","timestamp":1778346753645,"version":"3.51.4"},"reference-count":35,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T00:00:00Z","timestamp":1556582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>In this work we analyse the temperature distribution in a conductor disk in transitory regime. The disk is in motion in a stationary magnetic field generated by a permanent magnet and so, the electric currents induced inside it generate heat. The system acts as a magnetic brake and is analysed using infrared sensor techniques. In addition, for the simulation and analysis of the magnetic brake, a new thermal convective matrix for the 3D Cell Method (CM) is proposed. The results of the simulation have been verified by comparing the numerical results with those obtained by the Finite Element Method (FEM) and with experimental data obtained by infrared technology. The difference between the experimental results obtained by infrared sensors and those obtained in the simulations is less than 0.0459%.<\/jats:p>","DOI":"10.3390\/s19092028","type":"journal-article","created":{"date-parts":[[2019,4,30]],"date-time":"2019-04-30T08:51:44Z","timestamp":1556614304000},"page":"2028","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Thermal Analysis of a Magnetic Brake Using Infrared Techniques and 3D Cell Method with a New Convective Constitutive Matrix"],"prefix":"10.3390","volume":"19","author":[{"given":"Jos\u00e9 Miguel","family":"Monz\u00f3n-Verona","sequence":"first","affiliation":[{"name":"Electrical Engineering Department, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"},{"name":"Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Pablo Ignacio","family":"Gonz\u00e1lez-Dom\u00ednguez","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"},{"name":"Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Santiago","family":"Garc\u00eda-Alonso","sequence":"additional","affiliation":[{"name":"Department of Electronic Engineering and Automatics (DIEA), University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Francisco Jorge","family":"Santana-Mart\u00edn","sequence":"additional","affiliation":[{"name":"Electrical Engineering Department, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"},{"name":"Institute for Applied Microelectronics, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Juan Francisco","family":"C\u00e1rdenes-Mart\u00edn","sequence":"additional","affiliation":[{"name":"Mechanical Engineering Department, University of Las Palmas de Gran Canaria, 35017 Las Palmas de Gran Canaria, Spain"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2019,4,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"5203205","DOI":"10.1109\/TASC.2018.2795010","article-title":"Semi-three-dimensional analytical torque calculation and experimental testing of an eddy current brake with permanent magnets","volume":"28","author":"Shin","year":"2018","journal-title":"IEEE Trans. Appl. Superconduct."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"9688","DOI":"10.3390\/en8099688","article-title":"Investigation of electromagnetic, thermal and mechanical characteristics of a five-phase dual-rotor permanent-magnet synchronous motor","volume":"8","author":"Zhao","year":"2015","journal-title":"Energies"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"290","DOI":"10.4028\/www.scientific.net\/AMM.392.290","article-title":"Electromagnetic-thermal modeling of electromagnetic brake using finite-element analysis","volume":"392","author":"Zhang","year":"2013","journal-title":"Appl. Mech. Mater."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"319","DOI":"10.1109\/TMAG.2005.860782","article-title":"Parametric analysis of eddy-current brake performance by 3-d finite-element analysis","volume":"42","author":"Gay","year":"2006","journal-title":"IEEE Trans. Magn."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"3004","DOI":"10.1109\/TMAG.2003.816723","article-title":"Comparison of three types of permanent magnet linear eddy-current brakes according to magnetization pattern","volume":"39","author":"Jang","year":"2003","journal-title":"IEEE Trans. Magn."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"205","DOI":"10.3233\/JAE-2012-1585","article-title":"3-d nonlinear transient analysis and design of eddy current brake for high-speed trains","volume":"40","author":"Zhang","year":"2012","journal-title":"Int. J. Appl. Electromagn. Mech."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2528\/PIER00080101","article-title":"Finite formulation of the electromagnetic field","volume":"32","author":"Tonti","year":"2001","journal-title":"Prog. Electromagn. Res."},{"key":"ref_8","first-page":"237","article-title":"A Direct Discrete Formulation of Field Laws: The Cell Method","volume":"2","author":"Tonti","year":"2001","journal-title":"CMES Comput. Model. Eng. Sci."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"9102","DOI":"10.3390\/s101009102","article-title":"Electro-Quasistatic Analysis of an Electrostatic Induction Micromotor Using the Cell Method","volume":"10","year":"2010","journal-title":"Sensors"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"1260","DOI":"10.1016\/j.jcp.2013.08.016","article-title":"Why starting from differential equations for computational physics?","volume":"257","author":"Tonti","year":"2014","journal-title":"J. Comput. Phys."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Tonti, E. (2013). The Mathematical Structure of Classical and Relativistic Physics, Birkh\u00e4user.","DOI":"10.1007\/978-1-4614-7422-7"},{"key":"ref_12","doi-asserted-by":"crossref","unstructured":"Usamentiaga, R., and Fernando Garc\u00eda, D. (2017). Infrared Thermography Sensor for Temperature and Speed Measurement of Moving Material. Sensors, 17.","DOI":"10.3390\/s17051157"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Monz\u00f3n-Verona, J.M., Gonz\u00e1lez-Dom\u00ednguez, P.I., and Garc\u00eda-Alonso, S. (2018). New constitutive matrix in the 3D cell method to obtain a Lorentz electric field in a magnetic brake. Sensors, 18.","DOI":"10.3390\/s18103185"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"1259","DOI":"10.1109\/TMAG.2005.844841","article-title":"Discrete constitutive equations in A-\u03c7 geometric eddy-current formulation","volume":"41","author":"Specogna","year":"2005","journal-title":"IEEE Trans. Magn."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"702","DOI":"10.1109\/TMAG.2007.916016","article-title":"A coupled thermoelectromagnetic formulation based on the cell method","volume":"44","author":"Alotto","year":"2008","journal-title":"IEEE Trans. Magn."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1515\/phys-2018-0005","article-title":"Thermal constitutive matrix applied to asynchronous electrical machine using the cell method","volume":"16","year":"2018","journal-title":"Open Phys."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"1059","DOI":"10.1002\/num.20210","article-title":"Exact integration formulas for the finite volume element method on simplicial meshes","volume":"23","author":"Voitovich","year":"2007","journal-title":"Numer. Methods Partial Differ. Equ."},{"key":"ref_18","unstructured":"Wichmann, E.H. (1979). F\u00edsica Cu\u00e1ntica, Editorial Revert\u00e9. Chapter 1."},{"key":"ref_19","unstructured":"Eisberg, R., and Resnick, R. (1978). F\u00edsica Cu\u00e1ntica, \u00c1tomos, Mol\u00e9culas, S\u00f3lidos, N\u00facleos y Part\u00edculas, Editorial Limusa. Chapter 1."},{"key":"ref_20","unstructured":"(2019, February 13). Melexis Inspired Engineering. Available online: https:\/\/www.melexis.com\/en\/product\/MLX90614\/Digital-Plug-Play-Infrared-Thermometer-TO-Can."},{"key":"ref_21","unstructured":"(2019, February 13). Merlin Lazer. Available online: http:\/\/www.merlinlazer.com\/T425-Thermal-Imaging-Camera."},{"key":"ref_22","first-page":"1010603","article-title":"GetDP: A general finite-element solver for the de Rham complex","volume":"Volume 7","author":"Geuzaine","year":"2008","journal-title":"PAMM Volume 7 Issue 1. Special Issue: Sixth International Congress on Industrial Applied Mathematics (ICIAM07) and GAMM Annual Meeting, Z\u00fcrich 2007"},{"key":"ref_23","unstructured":"(2019, March 19). Portable, Extensible Toolkit for Scientific Computation, Available online: http:\/\/www.mcs.anl.gov\/petsc."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"1309","DOI":"10.1002\/nme.2579","article-title":"Gmsh: A three-dimensional finite element mesh generator with built-in preand post-processing facilities","volume":"79","author":"Geuzaine","year":"2009","journal-title":"Int. J. Numer. Methods Eng"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1176","DOI":"10.1109\/TIA.2011.2156371","article-title":"Measurement and CFD Prediction of Heat Transfer in Air-Cooled Disc-Type Electrical Machines","volume":"47","author":"Howey","year":"2011","journal-title":"IEEE Trans. Ind. Appl."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ijthermalsci.2012.11.009","article-title":"Review of fluid flow and convective heat transfer within rotating disk cavities with impinging jet","volume":"67","author":"Harmand","year":"2013","journal-title":"Int. J. Therm. Sci."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"120","DOI":"10.2514\/8.2175","article-title":"Heat transfer by laminar flow from a rotating plate","volume":"19","author":"Millsaps","year":"1952","journal-title":"J. Aeronaut. Sci."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"232","DOI":"10.1017\/S0305004100013323","article-title":"On the resistance to the rotation of a disc immersed in a fluid","volume":"31","author":"Goldstein","year":"1935","journal-title":"Math. Proc. Camb. Philos. Soc."},{"key":"ref_29","first-page":"672","article-title":"Heat transfer from a non-isothermal disk rotating in still air","volume":"81","author":"Hartnett","year":"1959","journal-title":"J. Heat Transf."},{"key":"ref_30","unstructured":"Yunus, A., Cimbala, J.M., and Sknarina, S.F. (2006). Mec\u00e1nica de Fluidos: Fundamentos y Aplicaciones, McGraw-Hill. Annex 1: Tables of air properties at 1 atm of presure; Table A-9, 1\u00aa edici\u00f3n."},{"key":"ref_31","unstructured":"(2019, February 13). Maxim Integrated. Available online: https:\/\/www.maximintegrated.com\/en\/products\/sensors\/DS18B20.html."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1038\/nmeth.2019","article-title":"Fiji: An open-source platform for biological-image analysisl","volume":"9","author":"Schindelin","year":"2012","journal-title":"Nat. Methods"},{"key":"ref_33","first-page":"317","article-title":"Errores frecuentes en la interpretaci\u00f3n del coeficiente de determinaci\u00f3n lineal","volume":"XXXVIII","year":"2005","journal-title":"Anuario Jur\u00eddico y Econ\u00f3mico Escurialense"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"679","DOI":"10.1016\/j.ijforecast.2006.03.001","article-title":"Another look at measures of forecast accuracy","volume":"22","author":"Hyndman","year":"2006","journal-title":"Int. J. Forecast."},{"key":"ref_35","unstructured":"Sanabria, J., Garc\u00eda, J., and Lhomme, J.P. (2006). Calibraci\u00f3n y Validaci\u00f3n de Modelos de Pron\u00f3stico de Heladas en el Valle del Mantaro, ECIPERU."}],"container-title":["Sensors"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/9\/2028\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T12:48:12Z","timestamp":1760186892000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1424-8220\/19\/9\/2028"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,4,30]]},"references-count":35,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2019,5]]}},"alternative-id":["s19092028"],"URL":"https:\/\/doi.org\/10.3390\/s19092028","relation":{},"ISSN":["1424-8220"],"issn-type":[{"value":"1424-8220","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,4,30]]}}}