Classical symmetry reductions of steady nonlinear one-dimensional heat transfer models

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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.
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.