Theses and Dissertations (Applied Mathematics)
http://hdl.handle.net/10386/65
2016-05-01T09:04:13ZEntropy analysis in a channel flow with temperature dependent viscosity
http://hdl.handle.net/10386/956
Entropy analysis in a channel flow with temperature dependent viscosity
Ndaba, Cynthia Reitumetse
The thermodynamic irreversibility in any fluid flow process can be quantified through entropy analysis. The first law of thermodynamics is simply an expression of the conservation of energy principle. The second law of thermodynamics states that all real processes are irreversible. Entropy generation is a measure of the account of irreversibility associated with the real processes. As entropy generation takes place, the quality of energy (i.e. exergy) decreases. In order to preserve the quality of energy in a fluid flow process or at least to reduce the entropy generation, it is important to study the distribution of the entropy generation within the fluid volume. In this dissertation, the inherent irreversibility in the flow of a variable viscosity fluid in both a closed channel and an open channel is investigated. The channel is assumed to be narrow, so that the lubrication approximation may be applied and the fluid viscosity is assumed to vary linearly with temperature. Both the lower and the upper surfaces of the channel are maintained at different temperature. The simplified form of governing equations is obtained and solved analytically using a perturbation technique. Expressions for fluid velocity and temperature are derived which essentially expedite to obtain expressions for volumetric entropy generation numbers, irreversibility distribution ratio and the Bejan number in the flow field.
In chapter 1, a historic background of the study is highlighted. Both closed and open channels problem are investigated in chapters 2 and 3. In chapter 4, generally discussion on the overall results obtained from the investigation is displayed together with possible areas of future research work.
Thesis (M.Sc. (Applied Mathematics)) --University of Limpopo, 2007
2007-01-01T00:00:00ZVariable viscosity arterial blood flow: its nature and stability
http://hdl.handle.net/10386/613
Variable viscosity arterial blood flow: its nature and stability
Mfumadi, Komane Boldwin
Understanding the effects of blood viscosity variation plays a very crucial role in hemodynamics, thrombosis and inflammation and could provide useful information for diagnostics and therapy of (cardio) vascular diseases. Blood viscosity, which arises from frictional interactions between all major blood constituents, i.e. plasma, plasma proteins and red blood cells, constitutes blood inherent resistance to flow in the blood vessel. Generally, blood viscosity in large arteries is lower near the vessel wall due to the presence of plasma layer in this peripheral region than the viscosity in the central core region which depends on the hematocrit.
In this dissertation, the flow of blood in a large artery is investigated theoretically using the fluid dynamics equations of continuity and momentum. Treating artery as a rigid channel with uniform width and blood as a variable viscosity incompressible Newtonian fluid, the basic flow structure and its stability to small disturbances are examined. A fourth-order eigenvalue problem which reduces to the well known Orrâ€“Sommerfeld equation in some limiting cases is obtained and solved numerically by a spectral collocation technique with expansions in Chebyshev polynomials implemented in MATLAB. Graphical results for the basic flow axial velocity, disturbance growth rate and marginal stability curve are presented and discussed. It is worth pointing out that, a decrease in plasma viscosity near the arterial wall has a stabilizing effect on the flow.
Thesis (M.Sc. (Applied Mathematics)) -- University of Limpopo, 2008
2008-01-01T00:00:00ZModelling the transmission dynamics of infectious diseases with vaccination and temporary immunity
http://hdl.handle.net/10386/347
Modelling the transmission dynamics of infectious diseases with vaccination and temporary immunity
Kgasago, Tshepo Matenatena Blessings
In this dissertation, two non-linear mathematical models are proposed and analyzed to investigate the spread of infectious diseases in a variable size population through horizontal transmission in the presence of preventive or therapeutic vaccines which are capable of inducing temporary immunity and wane in time. In modeling the transmission dynamics, the population is divided into three subclasses namely; Susceptibles, Infectives and Vaccinated groups. It is assumed that both Vaccinated and Susceptible individuals are recruited into the community and can only become infected via contacts with the infectives group but the rate at which the vaccinated group may contract the diseases is extremely very low depending on the efficacy of the vaccine. All infectives are assumed to move at a constant rate to both Vaccinated and Susceptible groups.
These models are analyzed by using the stability theory of differential equations and numerical simulation. The models exhibit two equilibria namely; the disease-free and the endemic equilibria. It is shown that if the vaccination reproduction number R0 < 1, the disease-free equilibrium is always globally asymptotically stable and in such a case the endemic equilibrium does not exist and the disease can be totally eliminated in the community. However, if R0 > 1, a unique endemic equilibrium exists that is locally asymptotically stable and consequently the equilibrium values of infective, vaccinated and susceptible population can be maintained at desired levels. Numerical simulations implemented on MAPLE using both Adomian decomposition technique and Runge-Kutta integration schemes, support our analytical conclusions and illustrate possible behaviour scenarios of the models.
Thesis (M.Sc.) (Applied Mathematics) --University of Limpopo, 2008.
2008-01-01T00:00:00Z