Analysis of heat transfer in a hot body with non-constant internal heat generation and thermal conductivity

Lourenco, Marcio Alexandre
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Heat transfer in a wall with temperature dependent thermal conductivity and internal heat generation is considered. We rst focus on the steady state models followed by the transient heat transfer models. It turns out that the models considered are non-linear. We deliberately omit the group-classi cation of the arbitrary functions appearing in the models, but rather select forms of physical importance. In one case, thermal conductivity and internal heat generation are both given by the exponential function and in the other case they are given by the power law. We employ the classical Lie point symmetry analysis to determine the exact solutions, while also determining the optimal system for each case. The exact solutions for the transient models are di cult to construct. However, we rst use the obtained exact solution for the steady state case as a benchmark for the 1D Di erential Transform Method (DTM). Since con dence in DTM is established, we construct steady state approximate series solutions. We apply the 2D DTM to the transient problem. Lastly we determine the conservation laws using the direct method and the associated Lie point symmetries for the transient problem
A dissertation submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of requirements for the degree of Master of Science. May 27, 2016.