A dissertation submitted to the Faculty of Science,
University of the Witwatersrand, in fulfillment of the
requirements for the degree of Master of Science.
March 28, 2013 / The search for solutions to the important differential equations arising in extended
surface heat transfer continues unabated. Extended surfaces, in the
form of longitudinal fins are considered. First we consider the steady state
problem and then the transient heat transfer models. Here, thermal conductivity
and heat transfer coefficient are assumed to be functions of temperature.
Thermal conductivity is considered to be given by the power law in one case
and by the linear function of temperature in the other; whereas heat transfer
coefficient is only given by the power law. Explicit analytical expressions for
the temperature profile, fin efficiency and heat flux for steady state problems
are derived using the one-dimensional Differential Transform Method (1D DTM).
The obtained results from 1D DTM are compared with the exact solutions
to verify the accuracy of the proposed method. The results reveal that the 1D
DTM can achieve suitable results in predicting the solutions of these problems.
The effects of some physical parameters such as the thermo-geometric
fin parameter and thermal conductivity gradient, on temperature distribution
are illustrated and explained. Also, we apply the two-dimensional Differential
Transform Method (2D DTM) to models describing transient heat transfer in
longitudinal fins. Furthermore, conservation laws for transient heat conduction
equations are derived using the direct method and the multiplier method, and
finally we find Lie point symmetries associated with the conserved vectors.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:wits/oai:wiredspace.wits.ac.za:10539/12915 |
| Date | 29 July 2013 |
| Creators | Ndlovu, Partner Luyanda |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
| Format | application/pdf |
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