Includes bibliographical references. / This thesis is concerned with the numerical modelling of the transient nonlinear heat conduction problem in solid continua. The hyperbolic governing equation is specialised to a parabolic equation which is sufficient for most engineering applications. The theoretical development includes the effects of conduction, specific heat, internal heat generation and the boundary conditions of convection, radiation, specified temperatures and flux, as well as point sources in the domain. The finite element spatial semidiscretisation of the equations is formally derived from the weak form of the governing equations. Temporal discretisation is obtained through an implicit/explicit difference scheme. The material properties are allowed to be temperature dependent, and consequently a modified Newton-Raphson iterative scheme is employed to solve the equations. The fully discretised equations are solved by implementing the algorithm in an existing finite element stress analysis code. Modelling is possible using four or eight-noded isoparametric elements, and solution control is possible through choice of time step size and choice of time integration method. Five examples are employed to demonstrate the ability of the program. The results compare well with published analytical solutions.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:uct/oai:localhost:11427/17618 |
| Date | January 1986 |
| Creators | Korvink, Jan Gerrit |
| Contributors | Martin, JB |
| Publisher | University of Cape Town, Faculty of Engineering and the Built Environment, Department of Mechanical Engineering |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Master Thesis, Masters, MSc (Eng) |
| Format | application/pdf |
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