- -

Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study

RiuNet: Institutional repository of the Polithecnic University of Valencia

Share/Send to

Cited by

Statistics

Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study

Show simple item record

Files in this item

dc.contributor.author López Molina, Juan Antonio es_ES
dc.contributor.author Rivera Ortun, María José es_ES
dc.contributor.author Berjano, Enrique es_ES
dc.date.accessioned 2017-05-04T12:33:08Z
dc.date.available 2017-05-04T12:33:08Z
dc.date.issued 2014-10-08
dc.identifier.issn 1471-2946
dc.identifier.uri http://hdl.handle.net/10251/80585
dc.description.abstract [EN] Parabolic heat equation based on Fourier's theory (FHE), and hyperbolic heat equation (HHE), has been used to mathematically model the temperature distributions of biological tissue during thermal ablation. However, both equations have certain theoretical limitations. The FHE assumes an infinite thermal energy propagation speed, whereas the HHE might possibly be in breach of the second law of thermodynamics. The relativistic heat equation (RHE) is a hyperbolic-like equation, whose theoretical model is based on the theory of relativity and which was designed to overcome these theoretical impediments. In this study, the three heat equations for modelling of thermal ablation of biological tissues (FHE, HHE and RHE) were solved analytically and the temperature distributions compared. We found that RHE temperature values were always lower than those of the FHE, while the HHE values were higher than the FHE, except for the early stages of heating and at points away from the electrode. Although both HHE and RHE are mathematically hyperbolic, peaks were only found in the HHE temperature profiles. The three solutions converged for infinite time or infinite distance from the electrode. The percentage differences between the FHE and the other equations were larger for higher values of thermal relaxation time in HHE. es_ES
dc.description.sponsorship This work received financial support from the Spanish Government (Ministerio de Ciencia e Innovacion, Ref. TEC2011-27133-C02-01). en_EN
dc.language Inglés es_ES
dc.publisher Royal Society, The es_ES
dc.relation Ministerio de Ciencia e Innovación, Spain [TEC2011-27133-C02-01] es_ES
dc.relation.ispartof Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences es_ES
dc.rights Reserva de todos los derechos es_ES
dc.subject Analytical model es_ES
dc.subject Fourier heat equation es_ES
dc.subject Hyperbolic heat equation es_ES
dc.subject Radiofrequency ablation es_ES
dc.subject Relativistic heat conduction es_ES
dc.subject Thermal ablation es_ES
dc.subject.classification MATEMATICA APLICADA es_ES
dc.subject.classification TECNOLOGIA ELECTRONICA es_ES
dc.title Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study es_ES
dc.type Artículo es_ES
dc.identifier.doi 10.1098/rspa.2014.0547
dc.rights.accessRights Abierto es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería del Diseño - Escola Tècnica Superior d'Enginyeria del Disseny es_ES
dc.contributor.affiliation Universitat Politècnica de València. Escuela Técnica Superior de Ingeniería Agronómica y del Medio Natural - Escola Tècnica Superior d'Enginyeria Agronòmica i del Medi Natural es_ES
dc.description.bibliographicCitation López Molina, JA.; Rivera Ortun, MJ.; Berjano, E. (2014). Fourier, hyperbolic and relativistic heat transfer equations: a comparative analytical study. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 470:1-16. doi:10.1098/rspa.2014.0547 es_ES
dc.description.accrualMethod Senia es_ES
dc.relation.publisherversion http://doi.org/10.1098/rspa.2014.0547 es_ES
dc.description.upvformatpinicio 1 es_ES
dc.description.upvformatpfin 16 es_ES
dc.type.version info:eu-repo/semantics/publishedVersion es_ES
dc.description.volume 470 es_ES
dc.relation.senia 276476 es_ES
dc.identifier.eissn 1471-2946


This item appears in the following Collection(s)

Show simple item record