A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2014. / In this thesis we will establish effective numerical schemes appropriate for the solution
of a non-linear partial differential equation modelling heat transfer in one dimensional
longitudinal fins. We will consider the problem as it stands without any physical simplification.
The main methodology is based on balancing the non-linear source term
as well as the application of numerical relaxation techniques. In either approach we
will incorporate the no-flux condition for singular fins. By doing so, we obtain appropriate
numerical schemes which improve results found in literature. To generalize,
we will provide a relaxed numerical scheme that is applicable for both integer and
fractional order non-linear heat transfer equations for one dimensional longitudinal
fins.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/17669 |
| Date | 07 May 2015 |
| Creators | Rusagara, Innocent |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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