# Thermal Metamaterials

Lead Research Organisation:
University of Manchester

Department Name: Mathematics

### Abstract

The ability to predict the temperature distribution in a material or component given some heat source at a given location is critical in a number of engineering and technological applications. In particular it is critical to be able to manipulate the heat flux in a desired manner so that heat can be directed to specific regions of space. Typically this is difficult because the process depends on the geometry of the component and the medium from which it is made. Modifying the manner by which heat is distributed or modifying the heat flux can lead to significant savings in terms of energy usage, which is becoming an important concern in modern devices.

Metamaterials are new materials that have properties not normally exhibited by standard engineering media. In particular they have been used previously to redirect sound or electromagnetic waves in an ingenious fashion, leading to e.g. quiet zones or surfaces that completely absorb sound or microwaves at a given frequency. The key notion for the design of metamaterials is to employ a specific microstructure that manipulates the macroscopic field in question (e.g. sound waves, with the wavelength of the sound wave being much longer than the microstructure of the medium). So far metamaterials have been employed mainly in the acoustics and electromagnetic communities. However similar ideas have recently started to be employed in order to attempt to manipulate temperature fields and thus the notion of a thermal metamaterial can now be investigated.

This project will explore the potential of thermal metamaterials and their ability to redirect and manipulate temperature fields in a range of engineering materials. The student will employ mathematical analysis, homogenization theory and micromechanics, coupled with experiments performed by industrial collaborators to develop new microstructural material designs in order to manipulate and redirect heat in new ways. A specific objective of the project is to understand what the distribution of microstructure should be (theoretically) for a given thermal source and component geometry in order to ensure uniform temperature distributions over surfaces (hence ensuring effective heat dissipation). This will then be followed up by understanding if this is indeed practical (what materials are available, what their properties are and the cost of the material). If the design is not practical the question then becomes what is the closest or optimal solution, in terms of microstructure distribution and available materials? The mathematical tools devised can also lead to optimization of material properties in other application areas (acoustics, electromagnetics, etc.).

The project aims are scientifically interesting and also have the potential to lead to significant technological advances in thermal engineering, underpinned by formal applied mathematics, coupled with experiments performed by industrial collaborators.

The project resides firmly in the following EPSRC research areas: Continuum Mechanics, Energy Efficiency, Engineering Design, Manufacturing technologies, Materials Engineering - Composites, Materials Engineering - metals and alloys.

Metamaterials are new materials that have properties not normally exhibited by standard engineering media. In particular they have been used previously to redirect sound or electromagnetic waves in an ingenious fashion, leading to e.g. quiet zones or surfaces that completely absorb sound or microwaves at a given frequency. The key notion for the design of metamaterials is to employ a specific microstructure that manipulates the macroscopic field in question (e.g. sound waves, with the wavelength of the sound wave being much longer than the microstructure of the medium). So far metamaterials have been employed mainly in the acoustics and electromagnetic communities. However similar ideas have recently started to be employed in order to attempt to manipulate temperature fields and thus the notion of a thermal metamaterial can now be investigated.

This project will explore the potential of thermal metamaterials and their ability to redirect and manipulate temperature fields in a range of engineering materials. The student will employ mathematical analysis, homogenization theory and micromechanics, coupled with experiments performed by industrial collaborators to develop new microstructural material designs in order to manipulate and redirect heat in new ways. A specific objective of the project is to understand what the distribution of microstructure should be (theoretically) for a given thermal source and component geometry in order to ensure uniform temperature distributions over surfaces (hence ensuring effective heat dissipation). This will then be followed up by understanding if this is indeed practical (what materials are available, what their properties are and the cost of the material). If the design is not practical the question then becomes what is the closest or optimal solution, in terms of microstructure distribution and available materials? The mathematical tools devised can also lead to optimization of material properties in other application areas (acoustics, electromagnetics, etc.).

The project aims are scientifically interesting and also have the potential to lead to significant technological advances in thermal engineering, underpinned by formal applied mathematics, coupled with experiments performed by industrial collaborators.

The project resides firmly in the following EPSRC research areas: Continuum Mechanics, Energy Efficiency, Engineering Design, Manufacturing technologies, Materials Engineering - Composites, Materials Engineering - metals and alloys.

### Studentship Projects

Project Reference | Relationship | Related To | Start | End | Student Name |
---|---|---|---|---|---|

EP/R513131/1 | 01/10/2018 | 30/09/2023 | |||

2194334 | Studentship | EP/R513131/1 | 01/04/2019 | 30/09/2022 | Eleanor Russell |