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Title: Homogenisation of the electrothermal behaviour of granular material
Author: Rooney, Caoimhe
ISNI:       0000 0004 8508 3748
Awarding Body: University of Oxford
Current Institution: University of Oxford
Date of Award: 2019
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Granular material is a critical component of many industrial applications and is particularly important for metallurgical processes. In particular, granular carbon experiences electrical heating in a metallurgical furnace known as a calciner. As the temperature of the carbon increases, its chemical and physical properties transform, namely to resemble those of graphite. However, the high temperatures within the calciner make ex- perimental measurements very difficult to obtain. Consequently, a funda- mental understanding of the inner mechanisms of the process has proved to be most challenging. Mathematical models can be used to assimilate the behaviour of the fur- nace by studying the tight coupling between electric and thermal conduc- tion. However, for the multitude of particles present within the calciner, direct or discrete models that consider every particle individually are com- putationally intractable. It has been shown that the electrothermal be- haviour on the scale of a particle is crucial to explain the behaviour on the scale of the furnace, yet the former scale is several orders of magnitude smaller than the latter. In this thesis, we propose mathematical models to approximate the physi- cal phenomena that govern the operation of the calciner furnace, validate their accuracy and demonstrate their numerical feasibility. The models that we study are founded upon the homogenisation technique known as the method of multiple scales. This is a systematic, effective-medium ap- proach that exploits the vast discrepancy between the scale of the furnace and the scale of the particles to extract homogeneous effective parameters from the heterogeneous media. In particular, we discuss how to extend the standard multiple scales technique to include a nonlinear, nonlocal, integral boundary condition for radiative transfer. Furthermore and signif- icantly, we demonstrate the influence of contact resistance by considering jumps in the electric potential at contact interfaces and conducting an asymptotic analysis to study the effect of microscopic contacts.
Supervisor: Howison, Sam ; Please, Colin Sponsor: Engineering and Physical Sciences Research Council ; ElMet
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: Mathematics ; Applied Mathematics