{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,25]],"date-time":"2026-03-25T23:14:06Z","timestamp":1774480446485,"version":"3.50.1"},"reference-count":30,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T00:00:00Z","timestamp":1580428800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"CONACYT (M\u00e9xico), Tempus Public Foundation (Hungary) and Energy Engineering Department of Budapest University of Technology and Economics (Hungary).","award":["Without number"],"award-info":[{"award-number":["Without number"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>There has been much interest in semiconductor superlattices because of their low thermal conductivities. This makes them especially suitable for applications in a variety of devices for the thermoelectric generation of energy, heat control at the nanometric length scale, etc. Recent experiments have confirmed that the effective thermal conductivity of superlattices at room temperature have a minimum for very short periods (in the order of nanometers) as some kinetic calculations had anticipated previously. This work will show advances on a thermodynamic theory of heat transport in nanometric 1D multilayer systems by considering the separation of ballistic and diffusive heat fluxes, which are both described by Guyer-Krumhansl constitutive equations. The dispersion relations, as derived from the ballistic and diffusive heat transport equations, are used to derive an effective heat conductivity of the superlattice and to explain the minimum of the effective thermal conductivity.<\/jats:p>","DOI":"10.3390\/e22020167","type":"journal-article","created":{"date-parts":[[2020,1,31]],"date-time":"2020-01-31T11:55:56Z","timestamp":1580471756000},"page":"167","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":15,"title":["Ballistic-Diffusive Model for Heat Transport in Superlattices and the Minimum Effective Heat Conductivity"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9787-0592","authenticated-orcid":false,"given":"Federico","family":"V\u00e1zquez","sequence":"first","affiliation":[{"name":"Department of Physics, UAEM, Science Research Center, Av. Universidad 1001, 62209 Cuernavaca, Mexico"}],"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, BME, Faculty of Mechanical Engineering, M\u0171egyetem rkp. 2, 1111 Budapest, Hungary"},{"name":"Department of Theoretical Physics, Wigner Research Centre for Physics, Konkoly-Thege M. \u00fat 29-33, 1121 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, BME, Faculty of Mechanical Engineering, M\u0171egyetem rkp. 2, 1111 Budapest, Hungary"},{"name":"Department of Theoretical Physics, Wigner Research Centre for Physics, Konkoly-Thege M. \u00fat 29-33, 1121 Budapest, Hungary"},{"name":"Montavid Thermodynamic Research Group, 1112 Budapest, Hungary"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2020,1,31]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"127","DOI":"10.1080\/15567265.2015.1031857","article-title":"Evaluating Broader Impacts of Nanoscale Thermal Transport Research","volume":"19","author":"Shi","year":"2015","journal-title":"Nanoscale Microscale Thermophys. 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