NanoHeat · Mathematical modelling of nanoscale heat flow and phase change

Mathematical modelling of nanoscale heat flow and phase change

Nanotechnology is a rapidly growing interdisciplinary area, with breakthroughs having important implications in fields such as medicine, manufacturing, electronics, and energy storage. However, one of the key issues that arise when designing nanodevices, which typically have sizes that are on the order of hundreds of nanometers, is thermal management. The inability of nanoscale components to efficiently conduct heat can lead to performance degradation and ultimately device failure. Therefore, it is crucial to understand how thermal energy is transported across nanometer length scales. Mathematical modelling of nanoscale heat transfer can provide novel insights into this process while avoiding the high costs associated with carrying out experiments. However, advances in nanotechnology have shown that traditional models of heat transfer are unable to predict the experimentally measured thermal responses of nanodevices. Thus, new mathematical models are required to describe nanoscale heat transfer. Several experiments have shown that spherical nanoparticles melt at temperatures that are substantially lower than the usual (bulk) melting temperature of the same material. In the case of gold nanoparticles, recent reports indicate that room-temperature melting is possible. The low melting temperature of nanodevices, when combined with inefficient heat dissipation, increases the potential for catastrophic device failure. This implies there is also a need to develop models that can predict the melting temperatures of nanoscale objects and understand how nanoscale heat transport is coupled to the onset and dynamics of phase change. The objectives of this project were to: 1. Identify extensions of Fourier's law that may be applied to nanoscale heat transfer 2. Solve extended mathematical models of heat transfer in practical scenarios 3. Through comparison with experimental data, determine the most suitable continuum model for nanoscale heat transfer 4. Develop new models of phase change on the nanoscale that (a) capture the size-dependence of material properties such as melting temperature and (b) are based on non-Fourier laws of heat transfer. 5. Solve extended mathematical models of nanoscale phase change in practical scenarios The project members were successful at carrying out these five objectives. Continuum models of heat transfer based on the Guyer-Krumhansl (GK) equation were found to accurately predict the thermal response of nanowires. Simple expressions for the effective thermal conductivity (ETC) of nanocomponents were derived from these models. The ETC is one of the most important parameters in nanoscale heat transfer because it directly describes how well a material or component can conduct heat. New equations were derived to predict the melting temperature of nanoparticles and shown to be in excellent agreement with experimental data obtained from tin nanoparticles. New mathematical models for nanoscale phase change revealed that non-classical heat-conduction mechanisms can play a very important role in melting and should therefore be considered in future studies.

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