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 nonclassical effects that appear in extreme situations and which Fourier’s law fails to describe. A popular approach is the GuyerKrumhansl equation and the framework of phonon hydrodynamics. This formalism is particularly appealing from a mathematical point of view since it is analogous to the NavierStokes 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 sizedependent thermal conductivity observed experimentally in nanostructures such as nanowires or thin films. In particular, we show that the GuyerKrumhansl 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 nonclassical 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, onedimensional geometry. In chapter 5 we employ an effective Fourier law which replaces the original thermal conductivity by a sizedependent expression that accounts for nonlocal effects. In chapter 6 we use the MaxwellCattaneo and the GuyerKrumhansl equations to formulate the MaxwellCattaneoStefan and the GuyerKrumhanslStefan 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 nonclassical effects in the GuyerKrumhansl 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 nonclassical 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.
Date of Award  12 Oct 2019 

Original language  English 

Awarding Institution   Universitat Politècnica de Catalunya (UPC)


Supervisor  Francesc Xavier Alvarez Calafell (Codirector) & Tim Myers (Director) 

Nonclassical thermal transport and phase change at the nanoscale
Calvo Schwarzwälder, M. (Author). 12 Oct 2019
Student thesis: Doctoral thesis
Author: Calvo Schwarzwälder, M.,
12 Oct 2019 Supervisor: Alvarez Calafell, F. X. (Codirector) & Myers, T. (External person) (Director)
Student thesis: Doctoral thesis
Student thesis: Doctoral thesis