3. Electronic Theses and Dissertations (ETDs) - All submissions
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Item Thermal analysis of continuously moving solid and porous fins using approximate analytical methods(2019) Ndlovu, Partner LuyandaIn various industrial and engineering applications, fins (extended surfaces) are frequently adopted to enhance the rate of heat dissipation between a system and its surroundings. The heat transfer mechanism of a fin is to conduct heat from a heat source to the fin surface via conduction, and then dissipate heat to the surrounding fluid via convection, radiation, or simultaneous convection-radiation. In order to improve the rate of heat transfer through finned surfaces, it is necessary to understand a fin’s dynamic response to change in temperature. The study of heat transfer though fins continues to be of scientific interest and recently, the study of moving fins has attracted a lot of research interests. The study of heat transfer through fins is modeled by differential equations. In search for solutions to differential equations arising in physics and engineering, analytical methods are very useful as it is difficult if not impossible to find the exact solutions. In recent years, the availability of faster processing equipment further means that we are able to compute analytical solutions to highly nonlinear equations that are more accurate in representing the physical phenomena. The modeling of heat transfer through fins reduces the experimental costs and gives insight into various parameters influencing the heat transfer process. In this thesis, the Variational Iteration Method (VIM) and the Differential Transform Method (DTM) are used to solve the nonlinear boundary value problems describing heat transfer in solid and porous fins undergoing convective-radiative heat dissipation. Validation of analytical solutions is also obtained by comparison with numerical solutions. The aim is to derive mathematical models describing heat transfer though fins, analyze the impact of the embedding thermo-physical parameters, compare the accuracy and computational efficiency of these two modern day analytical methods. The study of porous fins is performed using Darcy’s model to formulate the governing heat transfer equations. As far as we know, the transient study of heat transfer through moving fins has not been performed anywhere in literature. Related work on finned heat transfer is modeled using steady state models with the assumption that the transient response dies out quickly. Since a broad range of governing parameters are investigated, the results could be useful in a number of industrial and engineering applications.Item Supersymmetric quantum mechanics and path integrals(2017) Ayad Mohamed Ali, AhmedSupersymmetry plays a main role in all current thinking about superstring theory. Indeed, many remarkable properties of string theory have been explained using supersymmetry as a tool. In this dissertation, we review the basics formulation of supersymmetric quantum mechanics starting with introducing the concepts of supercharges and superalgebra. We show that, if there is a supersymmetric state, it is the zero-energy ground state. If such a state exists, the supersymmetry is unbroken otherwise it is broken. So far, there has been no unbroken supersymmetry observed in nature, and if nature is described by supersymmetry, it must be broken. In fact, supersymmetry may be broken spontaneously at any order of perturbation theory, or dynamically due to non-perturbative e ects. The goal of this dissertation is to study the methods of supersymmetry breaking. For this purpose, a special attention is given to discuss the normalization of the ground state of the supersymmetric harmonic oscillator. Then we explain that perturbation theory gives us incorrect results for both the ground state wave function as well as the energy spectrum and it fails to give an explanation to the supersymmetry breaking. Later in the dissertation, a review of the uses of instantons in quantum mechanics is given. In particular, instantons are used to compute the tunneling e ects within the path integral approach to quantum mechanics. As a result, we give evidence that the instantons, which are a non-perturbative e ect in quantum mechanics and can not be seen in perturbation theory, leads to calculate the corrections to the ground state energy and provides a possible explanation for the supersymmetry breaking.Item The propagation of a linear hydraulic fracture with tortuosity and fluid leak-off at the fluid-rock interface(2018) Mabasa, RishileIn this work, the propagation of a pre-existing hydraulic fracture in permeable rock is investigated. Apartiallyopentortuousfracturewithleak-offisreplacedbyatwo-dimensional symmetric model fracture with a modified Reynolds’ flow law to account for the effect of asperities on the fluid flow. The model is closed by considering a linear crack law, which considers the presence of touching asperities, and a Perkins-Kern and Nordgren (PKN) approximation, which relates the half-width of the model fracture to the normal stress at the fracture walls. The result is a nonlinear diffusion equation that accounts for leak-off atthefluid-rockinterfaceasaresultoftherock’spermeability. The leak-off velocity is not specified a priori and its functional form is determined by calculating Lie point symmetries of the governing non-linear diffusion equation for a model fracture which leads to a group invariant solution of the half-width of the fracture and the leak-off velocity respectively. We consider different forms of the Lie point symmetry of the governing equations by taking some of the constants in the generator to be zero. This leads to three cases of the group invariant solution, namely the general case, thetravelingwavesolutionandtheexponentialsolution. TwoexactanalyticalsolutionsareobtainedasaresultofassociationofaLiepointsymmetry with a conserved vector. However, the constant volume working condition is not furtherinvestigatedastherequirementsforittoholdarenotsufficientforthemodelconsidered. Other operating conditions at the fracture entry are also obtained by analysing the different properties of the partially open fracture. Numerical solutions of the halfwidthandtheleak-offdeptharecomputed. Thepropagationofalinearhydraulicfracture withtortuosityforthreecasesoftheLiepointsymmetryarefullyanalysedbynumerically solvingforthehalf-widthandthelengthofthefracture. Thederivationandanalysisofthewidthaveragedfluidvelocityleadstothederivation of an approximate analytical solution for the half-width of the model fracture which will then be compared to the numerical solution obtained. The approximate solution could prove useful when analytical solutions are unattainable or when numerical solutions are difficult to compute. The effects of leak-off and no leak-off in tortuous hydraulic fracture are compared to gain insight on the effect porosity has on the characteristics of the model fracture with tortuosityItem The determination of form drag coefficient for rigid, emergent objects in open channel flow(2017) Jackson, Kyle SheldonThe development of methods which are better able to predict the effect of large scale emergent roughness elements on the flow characteristics requires a better understanding of the drag coefficient under conditions likely to occur in the field. A laboratory investigation was carried out with newly developed equipment to quantify the drag force on various shaped cylinders, as well as the drag on an individual cylinder surrounded by an array of cylinders. The relationship between the drag coefficient and cylinder Reynolds number for a single circular cylinder was found to be of similar form but larger in magnitude than the established relationship for an infinitely long cylinder; the relationship departs from the infinite cylinder relationship for low cylinder Reynolds numbers. Contrary to previous research, the results for the multiple cylinder investigation did not reveal a clear relationship between the cylinder density and drag coefficient. Equations were developed and verified with existing laboratory data. These should be improved and extended by further research for field use.Item High temperature packed bed thermal storage for solar gas turbines(2016) Klein, PeterSolar powered gas micro-turbines present opportunities for off-grid power generation. Due to the intermittent nature of the solar energy supply, existing Solar Gas Turbine (SGT) plants employ hybridisation with fossil fuels to generate dispatchable power. In this work sensible heat and latent heat storage solutions are investigated as a means of increasing the solar share of a SGT cycle, thus reducing the consumption of diesel fuel. The sensible heat storage concept was based on a pressurised packed bed of spherical ceramic particles, using air as the heat transfer fluid. An axisymmetric, two-phase heat transfer model of the system was developed, based on the continuous solid phase approach. The model was successfully validated against experimental data from a packed bed of alumino-silicate particles over the temperature ranges of gas turbine cycles (350-900 °C and 600-900 °C). The validated numerical model was utilised to conduct a parametric design study of a six hour (1.55 MWhth) storage system for a gas micro-turbine. The results show that a high storage efficiency and high utilisation factor can be achieved when combining sensible heat storage in alumina with fossil fuel hybridisation, with somewhat lower values without hybridisation. An analysis of different inventory geometries showed that a packed bed of spherical particles is best suited to pressurised sensible heat storage. The latent heat storage concept was based on a pressurised packed bed of Encapsulated Phase Change Material (EPCM) particles. Sodium sulphate was identified as a suitable phase change material for the gas turbine cycle. The sensible heat storage model was extended to account for intra-particle temperature gradients and phase change within the particles. The intra-particle phase change model was validated against published experimental data for a single EPCM sphere heated and cooled by convection. The full EPCM storage model was further successfully validated against experimental data from a packed bed of macro- encapsulated sodium sulphate particles with alumina shells, up to a temperature of 950 °C. A comparison of the two storage concepts for a 7 m3 bed shows that a packed bed of en- capsulated sodium sulphate particles would have a 36% lower energy storage capacity than a bed of solid alumina particles. This is due to the limited melt fraction in the EPCM bed when a temperature limit is placed on the base. Increasing the packed bed volume to 10.5 m3 would provide a comparable thermal performance to the 7 m3 solid alumina bed, at a 12% lower storage mass. A hybrid three-layer packed bed is proposed to increase the volumetric energy storage density. Modelling shows that this concept could provide a small increase of 5.3% in the amount of energy discharged above 850 °C, compared to the solid alumina particles only.