Topology optimization for heat flow manipulation

Topology optimization for heat flow manipulation

Neofytou, A.

Böttger, A.J. (mentor)

Mechanical, Maritime and Materials Engineering

Materials Science and Engineering

2016-08-30

The aim of this thesis is to explore the use of topology optimization in designing materials for heat flow manipulation. Specifically shielding, concentrating or even inverting the heat current was examined. The possibility to scale the problem from macro- to nano-dimensions by using topology optimization for nanoscale heat conduction was also investigated. An optimization tool for heat flux shielding, focusing and reversal is presented. Different objective functions were defined in order to shield, focus or reverse heat flow within an area surrounded by a composite material with anisotropic thermal conductivity. The composite material under consideration consisted of thermally conductive elliptical inclusions embedded in a poor conductive matrix. The effective thermal conductivity was defined based on the equivalent inclusion theory. The dependence of the anisotropic thermal conductivity on the angle that the inclusions make with the imposed gradient was then approximated via a coordinate transformation. The material distribution method for topology optimization was then used to find the optimum angle distribution of the inclusion angle for heat shielding, focusing and reversal. The use of topology optimization for heat conduction in nanostructures was also investigated. At such small length scales the classical Fourier model for heat conduction is no longer applicable. As the dimensions of a structure become comparable to the mean free path of heat carriers (electrons or phonons), heat transfer changes from diffusive to semi-ballistic. Length scale effects such as scattering of the heat carriers with other phonons, material interfaces and boundaries become important. To take into account all this length effects, a more accurate model is given by the kinetic theory. Specifically the Boltzmann Transport Equation (BTE) for phonon transport was used to model the transfer of heat. To solve the BTE, a deterministic discrete ordinates method (DOM) was used in combination with the finite element method. Using COMSOL Multiphysics, the Boltzmann transport equation was successfully coupled with the MMA optimization algorithm and a Helmholtz PDE based filter. The method was implemented for the optimization of a simple system in order to illustrate its applicability.

http://resolver.tudelft.nl/uuid:a78669fd-e6b3-4f9b-8690-3423f11d3354

Student theses

master thesis

(c) 2016 Neofytou, A.