Non-classical thermal transport and phase change at the nanoscale
For 200 years, Fourier’s law has been used to describe heat transfer with excellent results. However, as technology advances, more and more situations arise where heat conduction is not well described by the classical equations. Examples are applications with extremely short time scales such as ultr...
| Autor: | |
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| Tipo de recurso: | tesis doctoral |
| Estado: | Versión publicada |
| Fecha de publicación: | 2019 |
| País: | España |
| Institución: | CBUC, CESCA |
| Repositorio: | TDR. Tesis Doctorales en Red |
| OAI Identifier: | oai:www.tdx.cat:10803/667237 |
| Acceso en línea: | http://hdl.handle.net/10803/667237 https://dx.doi.org/10.5821/dissertation-2117-166463 |
| Access Level: | acceso abierto |
| Palabra clave: | Àrees temàtiques de la UPC::Matemàtiques i estadística 512 536 |
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Non-classical thermal transport and phase change at the nanoscale |
| title |
Non-classical thermal transport and phase change at the nanoscale |
| spellingShingle |
Non-classical thermal transport and phase change at the nanoscale Calvo Schwarzwälder, Marc Àrees temàtiques de la UPC::Matemàtiques i estadística 512 536 |
| title_short |
Non-classical thermal transport and phase change at the nanoscale |
| title_full |
Non-classical thermal transport and phase change at the nanoscale |
| title_fullStr |
Non-classical thermal transport and phase change at the nanoscale |
| title_full_unstemmed |
Non-classical thermal transport and phase change at the nanoscale |
| title_sort |
Non-classical thermal transport and phase change at the nanoscale |
| dc.creator.none.fl_str_mv |
Calvo Schwarzwälder, Marc |
| author |
Calvo Schwarzwälder, Marc |
| author_facet |
Calvo Schwarzwälder, Marc |
| author_role |
author |
| dc.contributor.none.fl_str_mv |
Myers, Tim Álvarez Calafell, Francesc Xavier Universitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística |
| dc.subject.none.fl_str_mv |
Àrees temàtiques de la UPC::Matemàtiques i estadística 512 536 |
| topic |
Àrees temàtiques de la UPC::Matemàtiques i estadística 512 536 |
| description |
For 200 years, Fourier’s law has been used to describe heat transfer with excellent results. However, as technology advances, more and more situations arise where heat conduction is not well described by the classical equations. Examples are applications with extremely short time scales such as ultra fast laser heating, or very small length scales such as the heat conduction through nanowires or nanostructures in general. In this thesis we investigate alternative models which aim to correctly describe the non-classical effects that appear in extreme situations and which Fourier’s law fails to describe. A popular approach is the Guyer-Krumhansl equation and the framework of phonon hydrodynamics. This formalism is particularly appealing from a mathematical point of view since it is analogous to the Navier-Stokes equations of fluid mechanics, and from a physical point of view, since it is able to describe the physics in a simple and elegant way. In the first part of the thesis we use phonon hydrodynamics to predict the size-dependent thermal conductivity observed experimentally in nanostructures such as nanowires or thin films. In particular, we show that the Guyer-Krumhansl equation is suitable to capture the dependence of the thermal conductivity on the size of the physical system under consider- ation. During the modelling process we use the analogy with fluids to incorporate a slip boundary condition with a slip coefficient that depends on the ratio of the phonon mean free path to the characteristic size of the system. With only one fitting parameter we are able to accurately reproduce experimental observations corresponding to nanowires and nanorods of different sizes. The second part of the thesis consists of studying the effect of the non-classical fea- tures on melting and solidification processes. We consider different extensions and in- corporate them into the mathematical description of a solidification process in a simple, one-dimensional geometry. In chapter 5 we employ an effective Fourier law which replaces the original thermal conductivity by a size-dependent expression that accounts for non-local effects. In chapter 6 we use the Maxwell-Cattaneo and the Guyer-Krumhansl equations to formulate the Maxwell-Cattaneo-Stefan and the Guyer-Krumhansl-Stefan problems respec- tively. After performing a detailed asymptotic analysis we are able to reduce both models to a system of two ordinary differential equations and obtain excellent agreement with the cor- responding numerical solutions. In situations near Fourier resonance, which is a particular case where non-classical effects in the Guyer-Krumhansl model cancel each other out, the solidification kinetics are very similar to those described by the classical model. However, in this case we see that non-classical effects are still observable in the evolution of the heat flux through the solid, which suggests that this is a quantity which is more convenient to determine the presence of these effects in phase change processes. |
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2019 |
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2019 2019 2019 |
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info:eu-repo/semantics/doctoralThesis info:eu-repo/semantics/publishedVersion |
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doctoralThesis |
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publishedVersion |
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http://hdl.handle.net/10803/667237 https://dx.doi.org/10.5821/dissertation-2117-166463 |
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http://hdl.handle.net/10803/667237 https://dx.doi.org/10.5821/dissertation-2117-166463 |
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Inglés |
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Inglés |
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http://creativecommons.org/licenses/by-nc/4.0/ info:eu-repo/semantics/openAccess |
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http://creativecommons.org/licenses/by-nc/4.0/ |
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openAccess |
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212 p. application/pdf application/pdf |
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Universitat Politècnica de Catalunya |
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Universitat Politècnica de Catalunya |
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TDX (Tesis Doctorals en Xarxa) reponame:TDR. Tesis Doctorales en Red instname:CBUC, CESCA |
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CBUC, CESCA |
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TDR. Tesis Doctorales en Red |
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TDR. Tesis Doctorales en Red |
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1869417835503026176 |
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Non-classical thermal transport and phase change at the nanoscaleCalvo Schwarzwälder, MarcÀrees temàtiques de la UPC::Matemàtiques i estadística512536For 200 years, Fourier’s law has been used to describe heat transfer with excellent results. However, as technology advances, more and more situations arise where heat conduction is not well described by the classical equations. Examples are applications with extremely short time scales such as ultra fast laser heating, or very small length scales such as the heat conduction through nanowires or nanostructures in general. In this thesis we investigate alternative models which aim to correctly describe the non-classical effects that appear in extreme situations and which Fourier’s law fails to describe. A popular approach is the Guyer-Krumhansl equation and the framework of phonon hydrodynamics. This formalism is particularly appealing from a mathematical point of view since it is analogous to the Navier-Stokes equations of fluid mechanics, and from a physical point of view, since it is able to describe the physics in a simple and elegant way. In the first part of the thesis we use phonon hydrodynamics to predict the size-dependent thermal conductivity observed experimentally in nanostructures such as nanowires or thin films. In particular, we show that the Guyer-Krumhansl equation is suitable to capture the dependence of the thermal conductivity on the size of the physical system under consider- ation. During the modelling process we use the analogy with fluids to incorporate a slip boundary condition with a slip coefficient that depends on the ratio of the phonon mean free path to the characteristic size of the system. With only one fitting parameter we are able to accurately reproduce experimental observations corresponding to nanowires and nanorods of different sizes. The second part of the thesis consists of studying the effect of the non-classical fea- tures on melting and solidification processes. We consider different extensions and in- corporate them into the mathematical description of a solidification process in a simple, one-dimensional geometry. In chapter 5 we employ an effective Fourier law which replaces the original thermal conductivity by a size-dependent expression that accounts for non-local effects. In chapter 6 we use the Maxwell-Cattaneo and the Guyer-Krumhansl equations to formulate the Maxwell-Cattaneo-Stefan and the Guyer-Krumhansl-Stefan problems respec- tively. After performing a detailed asymptotic analysis we are able to reduce both models to a system of two ordinary differential equations and obtain excellent agreement with the cor- responding numerical solutions. In situations near Fourier resonance, which is a particular case where non-classical effects in the Guyer-Krumhansl model cancel each other out, the solidification kinetics are very similar to those described by the classical model. However, in this case we see that non-classical effects are still observable in the evolution of the heat flux through the solid, which suggests that this is a quantity which is more convenient to determine the presence of these effects in phase change processes.La llei de Fourier ha estat una peça clau per a descriure la conducció de calor des de que fou proposada fa gairabé 200 anys. No obstant, a mesura que avança la tecnologia ens hi trobem més sovint amb situacions on les equacions clàssiques perden la seva validesa. En aquesta tesi investiguem alguns models alternatius que tenen com a objectiu descriure la conducció de calor en situacions on la llei de Fourier no és aplicable. Un model que s'ha aconseguit establir com un extensió vàlida de la llei de Fourier és l'equació de Guyer i Krumhansl i el marc de la hidrodinàmica de fonons derivat d'aquesta. Es tracta d'un model particularment interessant, ja que les equacions són anàlogues a les equacions per a fluids dins de la hidrodinàmica clàssica. A la primera part de la tesi considerem aquesta equació per a descriure la conducció de calor estàtica per nanofibres de seccions transversals circulars i rectangulars. En particular, calculem una conductivitat tèrmica efectiva i trobem que és possible reproduïr els resultats experimentals amb un sol paràmetre d'adjust. En el cas de nanofibres cilíndriques, no és necessari cap paràmetre d'adjust si es consideren unes certes condicions de vora per al flux. Una conseqüència d'haver de considerar extensions per a la llei de Fourier és que s'ha d'estudiar l'efecte que tenen aquests canvis en la descripció de processos de canvi de fase. En la segona part de la tesi investiguem els efectes que tenen diversos models sobre la solidificació d'un líquid unidimensional. Al capítol 5 estudiem el cas en el que considerem la conductivitat tèrmica com a una funció de la mida del sòlid i que incorpora característiques que són importants quan el tamany del sòlid és comparable a les longituds característiques dels fonons, mentres que al capítol 6 considerem l'equació de Guyer i Krumhansl dels capítols anteriors. En ambdós casos, un anàlisi asimptòtic ens permet reduïr la complexitat del problema i proposar models reduïts formats per un parell de'equacions diferencials ordinàries.DOCTORAT EN MATEMÀTICA APLICADA (Pla 2012)Universitat Politècnica de CatalunyaMyers, TimÁlvarez Calafell, Francesc XavierUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística201920192019info:eu-repo/semantics/doctoralThesisinfo:eu-repo/semantics/publishedVersion212 p.application/pdfapplication/pdfhttp://hdl.handle.net/10803/667237https://dx.doi.org/10.5821/dissertation-2117-166463TDX (Tesis Doctorals en Xarxa)reponame:TDR. Tesis Doctorales en Redinstname:CBUC, CESCAInglésL'accés als continguts d'aquesta tesi queda condicionat a l'acceptació de les condicions d'ús establertes per la següent llicència Creative Commons: http://creativecommons.org/licenses/by-nc/4.0/http://creativecommons.org/licenses/by-nc/4.0/info:eu-repo/semantics/openAccessoai:www.tdx.cat:10803/6672372026-06-14T12:46:07Z |
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15,301629 |