Thesis Ph.D. ((Applied Mathematics)) -- University of Limpopo, 2022 / The world is under threat from the devastating effects of the continued depletion of the Ozone layer. Increased global warming is causing catastrophic ecological damage and imbalance due to accelerated melting of glaciers, rampant runaway veld res, widespread floods and other extreme events. The delegates to the Cop26 Climate Change Summit were reminded that the continued burning of fossil fuels is releasing carbon into the atmosphere at an unprecedented pace and scale and that the world is already in trouble. Complete substitution of fossil fuels with clean energy sources is the only solution through which the world can be saved from the deleterious effects of global warming. However, total dependence on renewable energy sources can only be possible through novel technology that enables efficient energy utilization and conservation. For instance, the evolution of advanced techniques in manufacturing processes has led to the reduction in the size of various industrial and engineering designs that consume reduced amounts of energy. Efficient energy utilization in thermo-fluid flow systems can be achieved through entropy generation minimization. Entropy is a thermodynamic quantity that represents the unavailability of a system's thermal energy for conversion into mechanical work. In this study, thermodynamic analysis of reactive variable properties third-grade fluid flow in channels with varied geometries and subjected to different physical effects was investigated with the second law of thermodynamics as the area of focus. Entropy generation and inherent irreversibility analysis were the main focus of the study where the sensitivities of these quantities to the embedded parameters were numerically and graphically described and analysed. The semi-analytic Adomian decomposition method, the semi-implicit fi nite difference scheme and the spectral quasilinearisation method were employed to solve the nonlinear differential equations modelling the flow systems. The results reveal that the effects of the parameters on flow velocity, fluid temperature, entropy generation and inherent irreversibility cannot be neglected. In particular, conditions for entropy generation minimization were successfully established and documented. / University of Limpopo

Thesis (MEng)--University of Stellenbosch, 2000. / ENGLISH ABSTRACT: This study investigates the implementation of the finite volume numerical method applicable to non-orthogonal control volumes and the application of the method to calculate the thermo-flow field within the collector area of a solar chimney power generating plant. The discretisation of the governing equations for the transient, Newtonian, incompressible and turbulent fluid flow, including heat transfer, is presented for a non-orthogonal coordinate frame. The standard k - E turbulence model, modified to include rough surfaces, is included and evaluated in the method. An implicit solution procedure (SIP-semi implicit procedure) as an alternative to a direct solution procedure for the calculation of the flow field on nonstaggered grids is investigated, presented and evaluated in this study. The Rhie and Chow interpolation practice was employed with the pressurecorrection equation to eliminate the presence of pressure oscillations on nonstaggered grids. The computer code for the solution of the three-dimensional thermo-flow fields is developed in FORTRAN 77. The code is evaluated against simple test cases for which analytical and experimental results exist. It is also applied to the analysis of the thermo-flow field of the air flow through a radial solar collector. KEYWORDS: NUMERICAL METHOD, FINITE VOLUME, NON-ORTHOGONAL, k+-e TURBULENCE MODEL, SIP / AFRIKAANSE OPSOMMING: Die studie ondersoek die implementering van 'n eindige volume numeriese metode van toepassing op nie-ortogonale kontrole volumes asook die toepassing van die metode om die termo-vloei veld binne die kollekteerder area van 'n sonskoorsteen krag aanleg te bereken. Die diskretisering van die behoudsvergelykings vir die tyd-afhanlike, Newtonse, onsamedrukbare en turbulente vloei, insluitende hitteoordrag, word beskryf vir 'n nie-ortogonale koordinaatstelsel. Die standaard k - E turbulensiemodel, aangepas om growwe oppervlakrandvoorwaardes te hanteer, is ingesluit en geevalueer in die studie. 'n Implisiete oplossings metode (SIP-semi implisiete prosedure) as alternatief vir 'n direkte oplossingsmetode is ondersoek en geimplimenteer vir die berekening van die vloeiveld met nie-verspringde roosters. 'n Rhie en Chow interpolasie metode is gebruik tesame met die drukkorreksie-vergelyking ten einde ossilasies in die drukveld in die nie-verspringde roosters te vermy. Die rekenaarkode vir die oplossing van die drie dimensionele termo-vloeiveld is ontwikkel in FORTRAN 77. Die kode is geevalueer teen eenvoudige toetsprobleme waarvoor analitiese en eksperimentele resultate bestaan. Die kode IS ook gebruik om die termo-vloeiveld binne 'n radiale son kollekteerder te analiseer. SLEUTELWOORDE: NUMERIESE METODE, EINDIGE VOLUME, NIE-ORTOGONAAL, k - E TURBULENSIE MODEL, SIP

University of Macau / Faculty of Science and Technology / Department of Mathematics