This research studies two nonlinear differential equations arising in fluid mechanics.
Firstly, the Zakharov-Kuznetsov's equation in (3+1) dimensions with an arbitrary
power law nonlinearity is considered. The method of Lie symmetry analysis is used
to carry out the integration of Zakharov-Kuznetsov's equation. Also, the extended
tanh-function method and t he G'/G method are used to integrate the Zakharov-Kuznetsov's equation. The non-topological soliton solution is obtained by the aid of
solitary wave ansatz method. Numerical simulation is given to support the analytical
development.
Secondly. the nonlinear flow problem of an incompressible viscous fluid is considered.
The fluid is taken in a channel having two weakly permeable moving porous walls.
An incompressible fluid fills the porous space inside the channel. The fluid is magnetohydrodynamic
in the presence of a time-dependent magnetic field. Lie group
method is applied along with perturbation method in the derivation of analytic solution.
The effects of the magnetic field, porous medium, permeation Reynolds number
and wall dilation rate on the axial velocity arc shown and discussed. / Thesis (M.Sc.(Applied Mathematics) North-West University, Mafikeng Campus, 2010
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:nwu/oai:dspace.nwu.ac.za:10394/15796 |
| Date | January 2010 |
| Creators | Matebese, Belinda Thembisa |
| Source Sets | South African National ETD Portal |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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