A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. August 8, 2014. / We study the nonlinear models arising in heat transfer in extended surfaces
(fins) and in solid slab (hot body). Here thermal conductivity, internal generation
and heat transfer coefficient are temperature dependent. As such the
models are rendered nonlinear. We employ Lie point symmetry techniques to
analyse these models. Firstly we employ Lie point symmetry methods and
determine the exact solutions for heat transfer in fins of spherical geometry.
These solutions are compared with the solutions of heat transfer in fins of rectangular
and radial geometries. Secondly, we consider models describing heat
transfer in a hot body, for example, a plane wall. We then employ the preliminary
group classification methods to determine the cases of the arbitrary
function for which the principal Lie algebra is extended by one. Furthermore
we the exact solutions.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/16865 |
| Date | 04 February 2015 |
| Contributors | Moleofane, Kamogelo Jacobeth |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf, application/pdf |
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