Thesis (M.Sc. (Applied Mathematics)) --University of Limpopo, 2007 / 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.

This study investigates Compressed Air Energy Storage (CAES) application in the electrical power and transportation industries. Information concerning current CAES projects is presented. A thorough thermodynamic analysis of the CAES process is completed; including theoretical efficiency determination for several variants of the compression and expansion processes. Industry claimed efficiencies ranging from 26% to 82% are presented and explained. Isothermal and Isentropic efficiency baselines are developed. Energy density of compressed air on both a mass and volume basis is compared to other energy storage methods. Best expected efficiency of a hypothetical CAES system is determined to be 34% using currently achievable efficiencies and 63% considering 100% efficient compression and expansion. A .5 kW CAES system, built from commercial off the shelf components (COTS) to demonstrate the CAES concept, is documented and discussed. This system includes a LabView data acquisition system which was used to record all test results. LabView was also used to develop a complete test bed program that determined real time thermodynamic state properties, component efficiencies, mass flow rates, power outputs and several other performance characteristics of the demonstration system. The LabView program allowed real time efficiency and power optimization of the demonstration system. Results of demonstration system testing are thoroughly discussed. Total system efficiency was very poor; 3.6% electrical conversion efficiency, .040 refrigeration coefficient of performance (COP) and a 5.0% overall efficiency which considers both cooling and electrical storage properties. Several paths for possible future projects involving the demonstration system and CAES are presented.

Earthquakes are amongst the most destructive of natural phenomena and have been the subject of significant research effort over many decades, to predict the onset of seismic events. Electromagnetic emissions detected prior to earthquakes provide a potential data source for seismic predictions and research suggests that specific pre-seismic electromagnetic activity can be directly related to specific earthquakes although it is still an open issue as to the precise links between these electromagnetic emissions and subsequent earthquakes. In this research, findings of the long memory or the self-organization of several pre-earthquake MHz electromagnetic time-series provide significant outcomes regarding the earthquake prediction. It is also recognised that enhanced radon gas emission has an equally long history as being associated with seismic activity. In general, several anomalous soil radon emissions have been observed prior to earthquakes and this has been recorded all over the world. The abnormal soil radon exhalation from the interior of the earth has been associated with earthquakes and is considered as an important field of research. The research reported in this thesis compared and contrasted the merits of combining electromagnetic emission data and radon exhalation data as precursors of earthquakes with the aim of enhancing earthquake prediction methodology. The findings from the long-memory analysis of radon disturbances in the soil indicated a very significant issue: the radon disturbances in the soil prior to earthquakes exhibit similar behaviour as the MHz RF disturbances of general failure. So, the radon precursors and the MHz electromagnetic correspond to the same pre-earthquake phase. Geological explanations were proposed in view of the asperity model. Persistent and anti-persistent MHz anomalies were due to the micro-cracking of the heterogeneous medium of the earth's crust which may have led the system's evolution towards the global failure. Fractal methods have been used on historical data, to investigate MHz electromagnetic time-series spectra on emissions preceding major earthquakes over the period 2007 to 2014 and the characteristics of enhanced radon emissions have been studied over the period 2008 to 2015 for seismic events occurring in the Aegean Region. It has been found that both the electromagnetic emissions and the radon exhalation data exhibit similar fractal behaviour and are associated with impending seismic activity. Hence both phenomena are relevant to earthquake predictions and should both be employed in any systematic approach to this problem as the varying geological and geographic conditions under which earthquakes can occur, might preclude one or other data from being measurable. According to the several techniques applied in this thesis, all should be employed in sequential steps, albeit the power-law spectral fractal analysis is the most significant to trace long-memory patterns of 1/f processes as those of the processes of earthquakes.

With the algorithm’s suitability for exploiting current petascale and next-generation exascale supercomputers, stable and structure-preserving properties are necessary to develop predictive computational tools. In this dissertation, summation-by-parts (SBP) operators and a new relaxation Runge–Kutta (RRK) scheme are used to construct mimetic and structure-preserving full discretization for non-reactive compressible computational fluid dynamics (CFD) and reaction-diffusion models. In the first chapter, we provide the necessary background and a literature survey that forms the basis of this dissertation. Next, we provide a short overview of entropy stability for general conservation laws. The second chapter covers the analysis of the Eulerian model for compressible and heat-conducting flows. We provide the necessary background of the new system of parabolic partial differential equation (PDE). Then, we present the entropy stability analysis of the model at the continuous level. Subsequently, using the SBP, we construct an entropy-stable discretization of any order for unstructured grids with tensor-product elements. The third chapter discusses the implementation of RRK methods. We start by reviewing the RRK scheme constructed to guarantee conservation or stability with respect to any inner-product norm. Then, we present the extension and generalization of RRK schemes to general convex functionals and their application to compressible fluid flow problems. The final chapter demonstrates the far-reaching capabilities of the SBP operators and RRK schemes presenting the development of a novel fully discrete Lyapunov stable discretization for reaction models with spatial diffusion. Finally, we conclude this dissertation with an overview of our achievements and future research directions.

1. There is a crisis in economics. The discipline evolved in nineteenth century Europe and is difficult to adapt to modern conditions, even in the West, and particularly in alien cultures. Application of conventional economic analysis to economic activity in a culture as alien as traditional China highlights the biases in assumptions of the paradigm. 2. The concepts, models and vocabulary evolved over one hundred years ago predate important developments in the natural sciences. It is now necessary for economists to concede no goods can ever be 'produced', and they are not 'consumed' either. In clear terms matter is transformed, but is not created or destroyed (First Law of Thermodynamics). 3. When people transform matter, in lay language we say energy is 'used'. In a simple cottage industry, 'raw material' is transformed into a commodity in front of our eyes by the use of human energy and the release of energy from a 'fuel'. In modem complex economic activity, it is difficult or impossible to keep track of the processes from raw matter to transformed 'product' although the principle is the same. 4. The Second Law of Thermodynamics states that in any transformation, energy is not created or destroyed, but becomes 'less available'. In short, entropy increases. This appears to work well for pure physics and chemistry, but its application to analysis of economic activity has only been notional. 5. There is a reason why economists borrowing terms from hard science experience difficulty. It is because physicists and chemists have addressed specific laboratory and engineering problems, but not the broader economic issues. The hypothesis gradually evolved in this research program that not only economic concepts and terms needed reworking, but those in physics as well. The definitions of energy as 'ability to do works and of entropy as 'unavailable energy' jar the logic of our commonsense. 6. The notion of 'available energy' was traced back to the phenomenon in physical chemistry known as exothermicity, or the release of energy during a chemical reaction. It was reasoned that while scientists had focussed on this phenomenon and measured it carefully they saw no need to ask where the energy came from, or to measure its transformation. From the perspective of analysing economic activity, the question was important. 7. It was hypothesised that the energy released from a fuel as electromagnetic radiation (mainly heat) was the residual of the set of coulombic forces within atoms that maintain the structure of shells of electrons around the protons. This idea in turn came from the presumption that molecular bonding is a residual of vectors of the set of coulombic forces within atoms, and the likelihood that in an exothermic reaction, after the reactants are said (by scientists) to 'seek equilibrium', product molecules have a portion of the coulombic forces 'left over' and not required to maintain their structures. An estimate was made of the coulombic forces extant in various fuels, and compared with the known data for their release of energy. 8. The idea was developed in detail. The concept we call in economics, 'production', and should call 'transformation' can only occur when forces locked within atoms are released as electromagnetic forces. (Gravitational forces exist because matter has been put 'there' by electromagnetic radiation). When 100 grams of dry grass fuel is burnt, about 2 megajoules of electromagnetic radiation are released. It was estimated that the coulombic forces between each electron and proton in that amount dry grass total 150 gigajoules (or giganewtons, since the reference is to forces). 9. Within the boundary of a simple economic activity, the ratio of aggregated coulombic forces locked up within atoms to the electromagnetic forces radiated out was estimated at the beginning of the activity, and then after a duration. The ratio of forces always tends towards 'evening out'. This measurement captures the entropy phenomenon which has been said by Georgescu-Roegen to be the basis of all economic activity. 10. At the roots of the economic paradigm founded by Adam Smith is the premise that the material world, as a set of substances, is a stage on which economic actors 'add value', bid prices up and down, and by their rational perception manage their livelihoods and surroundings well. From the findings of this research program it is contended that the surroundings of economic actors can be classed into two categories: locked up (coulombic) electromagnetic forces, and radiated electromagnetic forces. The former has a tendency to convert to the latter. All action, including all economic activity, and all life can be traced to a point in space and time where this conversion is (naturally) occurring. The phenomenon is analogous to a slope where water cascades, and gravitational potential energy converts to other (either useless or useful) forms of energy. To appreciate the nature of this phenomena, and to attempt to fathom its dimensions, sets our perceptions of ourselves as economic actors in a quite different and very humbling context.