Jassim Katwan, Osama M.
Discrete modelling of heat transfer.
MSc(R) thesis, University of Glasgow.
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The research involves the development of a discrete lattice approach for modelling heat
transfer, which can be an attractive alternative to other numerical approaches, such as
the nite element method. In this work, the spatial arrangement of the lattice elements
is determined by the Delaunay triangulation and the Voronoi tessellation. The objective
of the present work is to investigate in more detail this type of lattice model for heat
In the lattice models studied here the domain to be analysed is discretised by a network
of discrete lattice elements. The spatial arrangement of these elements is determined by
connecting nodes placed within the domain. There are two methods to determine the
connections between the nodes in the domain. In the rst one, the connections are dened
as the edges of the Delaunay triangulation. In the second method, the nodes are dened
by the edges of Voronoi cells, based on a Voronoi tessellation of the domain. These
connections dene the arrangement of the pipe elements, which are used to perform the
heat transfer analysis. The cross-sections of the pipe elements for the two approaches
are chosen in several dierent ways to be consistent with the discretisation approach.
It was shown that with this approach, analytical solutions could be represented accu-
rately. Several stationary and non-stationary heat transfer problems were analysed. The
performance of the two approaches was evaluated by comparing the numerical results
with analytical solutions. Both temperature and ux distributions were studied.
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