Numerical investigation of heat transfer in one-dimensional longitudinal fins - Rusagara, Innocent (My University, 2015)
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.
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.
Keywords: Heat transmission.; Numerical analysis.