{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T02:52:54Z","timestamp":1778035974759,"version":"3.51.4"},"reference-count":48,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2018,10,30]],"date-time":"2018-10-30T00:00:00Z","timestamp":1540857600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003549","name":"Orsz\u00e1gos Tudom\u00e1nyos Kutat\u00e1si Alapprogramok","doi-asserted-by":"publisher","award":["K116197"],"award-info":[{"award-number":["K116197"]}],"id":[{"id":"10.13039\/501100003549","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003549","name":"Orsz\u00e1gos Tudom\u00e1nyos Kutat\u00e1si Alapprogramok","doi-asserted-by":"publisher","award":["K123815"],"award-info":[{"award-number":["K123815"]}],"id":[{"id":"10.13039\/501100003549","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003549","name":"Orsz\u00e1gos Tudom\u00e1nyos Kutat\u00e1si Alapprogramok","doi-asserted-by":"publisher","award":["K124366"],"award-info":[{"award-number":["K124366"]}],"id":[{"id":"10.13039\/501100003549","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100003549","name":"Orsz\u00e1gos Tudom\u00e1nyos Kutat\u00e1si Alapprogramok","doi-asserted-by":"publisher","award":["K116375"],"award-info":[{"award-number":["K116375"]}],"id":[{"id":"10.13039\/501100003549","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The non-Fourier heat conduction phenomenon on room temperature is analyzed from various aspects. The first one shows its experimental side, in what form it occurs, and how we treated it. It is demonstrated that the Guyer-Krumhansl equation can be the next appropriate extension of Fourier\u2019s law for room-temperature phenomena in modeling of heterogeneous materials. The second approach provides an interpretation of generalized heat conduction equations using a simple thermo-mechanical background. Here, Fourier heat conduction is coupled to elasticity via thermal expansion, resulting in a particular generalized heat equation for the temperature field. Both aforementioned approaches show the size dependency of non-Fourier heat conduction. Finally, a third approach is presented, called pseudo-temperature modeling. It is shown that non-Fourier temperature history can be produced by mixing different solutions of Fourier\u2019s law. That kind of explanation indicates the interpretation of underlying heat conduction mechanics behind non-Fourier phenomena.<\/jats:p>","DOI":"10.3390\/e20110832","type":"journal-article","created":{"date-parts":[[2018,10,31]],"date-time":"2018-10-31T03:50:56Z","timestamp":1540957856000},"page":"832","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Emergence of Non-Fourier Hierarchies"],"prefix":"10.3390","volume":"20","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-2708-7065","authenticated-orcid":false,"given":"Tam\u00e1s","family":"F\u00fcl\u00f6p","sequence":"first","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, 1112 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5822-6035","authenticated-orcid":false,"given":"R\u00f3bert","family":"Kov\u00e1cs","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, 1112 Budapest, Hungary"},{"name":"Department of Theoretical Physics, Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, 1525 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c1d\u00e1m","family":"Lovas","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"\u00c1gnes","family":"Rieth","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Tam\u00e1s","family":"Fodor","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2492-0392","authenticated-orcid":false,"given":"M\u00e1ty\u00e1s","family":"Sz\u00fccs","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, 1112 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9396-4073","authenticated-orcid":false,"given":"P\u00e9ter","family":"V\u00e1n","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, 1112 Budapest, Hungary"},{"name":"Department of Theoretical Physics, Institute for Particle and Nuclear Physics, Wigner Research Centre for Physics, 1525 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6359-768X","authenticated-orcid":false,"given":"Gyula","family":"Gr\u00f3f","sequence":"additional","affiliation":[{"name":"Department of Energy Engineering, Faculty of Mechanical Engineering, BME, 1521 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2018,10,30]]},"reference":[{"key":"ref_1","unstructured":"Fourier, J. 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