Visco-elastic liquid with relaxation : symmetries, conservation laws and solutions
- Authors: Kartal, Ozgül
- Date: 2012-02-06
- Subjects: Symmetric spaces , Partial differential equations , Lie groups , Non-Newtonian fluids
- Type: Thesis
- Identifier: uj:2008 , http://hdl.handle.net/10210/4361
- Description: M.Sc. , In this dissertation, a symmetry analysis of a third order non-linear partial differential equation which describes the filtration of a non-Newtonian liquid in porous media is performed. A review of the derivation of the partial differential equation is given which is based on the Darcy Law. The partial differential equation contains a parameter n and a function f. We derive the Lie Point Symmetries of the partial differential equation for all cases of n and f. These symmetries are used to find the invariant solutions of the partial differential equation. We find that there is only one conservation law for the partial differential equation with f and n arbitrary and we prove that there is no potential symmetry corresponding to this conservation law for any case of n and f.
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- Authors: Kartal, Ozgül
- Date: 2012-02-06
- Subjects: Symmetric spaces , Partial differential equations , Lie groups , Non-Newtonian fluids
- Type: Thesis
- Identifier: uj:2008 , http://hdl.handle.net/10210/4361
- Description: M.Sc. , In this dissertation, a symmetry analysis of a third order non-linear partial differential equation which describes the filtration of a non-Newtonian liquid in porous media is performed. A review of the derivation of the partial differential equation is given which is based on the Darcy Law. The partial differential equation contains a parameter n and a function f. We derive the Lie Point Symmetries of the partial differential equation for all cases of n and f. These symmetries are used to find the invariant solutions of the partial differential equation. We find that there is only one conservation law for the partial differential equation with f and n arbitrary and we prove that there is no potential symmetry corresponding to this conservation law for any case of n and f.
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Hyperdeterminant and an integrable partial differential equation
- Authors: Steeb, Willi-Hans
- Date: 2011-08-22
- Subjects: Hyperdeterminant , Legendre transformation , Partial differential equations
- Type: Article
- Identifier: uj:5971 , http://hdl.handle.net/10210/8416
- Description: Discuss an integrable partial differential equation arising from the hyperdeterminant.
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- Authors: Steeb, Willi-Hans
- Date: 2011-08-22
- Subjects: Hyperdeterminant , Legendre transformation , Partial differential equations
- Type: Article
- Identifier: uj:5971 , http://hdl.handle.net/10210/8416
- Description: Discuss an integrable partial differential equation arising from the hyperdeterminant.
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A symmetry analysis of a second order nonlinear diffusion equation
- Authors: Joubert, Ernst Johannes
- Date: 2014-04-03
- Subjects: Nonlinear differential equations , Partial differential equations , Symmetry
- Type: Thesis
- Identifier: uj:10522 , http://hdl.handle.net/10210/10023
- Description: M.Sc. (Mathematics) , Please refer to full text to view abstract
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- Authors: Joubert, Ernst Johannes
- Date: 2014-04-03
- Subjects: Nonlinear differential equations , Partial differential equations , Symmetry
- Type: Thesis
- Identifier: uj:10522 , http://hdl.handle.net/10210/10023
- Description: M.Sc. (Mathematics) , Please refer to full text to view abstract
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Heat and mass transfer in unsteady rotating fluid flow with binary chemical reaction and activation energy
- Awad, Faiz G., Motsa, Sandile, Khumalo, Melusi
- Authors: Awad, Faiz G. , Motsa, Sandile , Khumalo, Melusi
- Date: 2014
- Subjects: Spectral relaxation method , Arrhenius activation energy , Partial differential equations
- Type: Article
- Identifier: uj:5437 , http://hdl.handle.net/10210/12594
- Description: In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.
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- Authors: Awad, Faiz G. , Motsa, Sandile , Khumalo, Melusi
- Date: 2014
- Subjects: Spectral relaxation method , Arrhenius activation energy , Partial differential equations
- Type: Article
- Identifier: uj:5437 , http://hdl.handle.net/10210/12594
- Description: In this study, the Spectral Relaxation Method (SRM) is used to solve the coupled highly nonlinear system of partial differential equations due to an unsteady flow over a stretching surface in an incompressible rotating viscous fluid in presence of binary chemical reaction and Arrhenius activation energy. The velocity, temperature and concentration distributions as well as the skin-friction, heat and mass transfer coefficients have been obtained and discussed for various physical parametric values. The numerical results obtained by (SRM) are then presented graphically and discussed to highlight the physical implications of the simulations.
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Spectral relaxation method and spectral quasilinearization method for solving unsteady boundary layer flow problems
- Motsa, Sandile Sydney, Dlamini, Phumlani Goodwill, Khumalo, Melusi
- Authors: Motsa, Sandile Sydney , Dlamini, Phumlani Goodwill , Khumalo, Melusi
- Date: 2014
- Subjects: Nonlinear partial differential equations , Spectral quasilinearization method , Partial differential equations , Spectral relaxation method
- Type: Article
- Identifier: uj:5431 , http://hdl.handle.net/10210/12050
- Description: Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.
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- Authors: Motsa, Sandile Sydney , Dlamini, Phumlani Goodwill , Khumalo, Melusi
- Date: 2014
- Subjects: Nonlinear partial differential equations , Spectral quasilinearization method , Partial differential equations , Spectral relaxation method
- Type: Article
- Identifier: uj:5431 , http://hdl.handle.net/10210/12050
- Description: Nonlinear partial differential equations (PDEs) modelling unsteady boundary-layer flows are solved by the spectral relaxation method (SRM) and the spectral quasilinearization method (SQLM). The SRM and SQLM are Chebyshev pseudospectral based methods that have been successfully used to solve nonlinear boundary layer flow problems described by systems of ordinary differential equations. In this paper application of these methods is extended, for the first time, to systems of nonlinear PDEs that model unsteady boundary layer flow. The new extension is tested on two problems: boundary layer flow caused by an impulsively stretching plate and a coupled four-equation system that models the problem of unsteady MHD flow and mass transfer in a porous space. Numerous simulation experiments are conducted to determine the accuracy and compare the computational performance of the proposed methods against the popular Keller-box finite difference scheme which is widely accepted as being one of the ideal tools for solving nonlinear PDEs that model boundary layer flow problems. The results indicate that the methods are more efficient in terms of computational accuracy and speed compared with the Keller-box.
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