Saving clubs or stokvels have been around in many parts of the World, under different names, for many years and they have been instrumental in teaching people how to save. This research sets to investigate the possible use of stokvels as vehicles, channels or conduits for wealth accumulation among migrant population living in the inner city of Johannesburg. Participants’ contributions and the extent this translates into wealth accumulation among members were critically examined. Furthermore, the study explored whether gender plays any role in terms of stokvels membership and the reasons thereof. The hypothesis of this research was that incomes from stokvels contribute to wealth accumulation of migrants in the inner city of Johannesburg. This study used both quantitative and qualitative research methods to address the research questions and gather relevant data. The use of a mixed approach was adopted as it allows a deeper exploration of the different research objectives and questions of the study. Thematic content analysis was used to analyse the data. The findings of this study have revealed that there is a positive relationship between membership to stokvels and wealth accumulation. Moreover, trust and social capital were found to be pivotal in ensuring success of these groups in terms of who should be accepted into the group. However, many other factors, such as the level of education, the length of stay in South Africa and the marital status of participants could have an impact on wealth status of participants.

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Rigorous bounds on heat transfer in rapidly rotating convection have existed for several years in the case of free-slip or stress-free boundary conditions. No-slip boundary conditions result in a phenomenon known as Ekman pumping, which significantly impacts the heat transport. A recent collaborative effort in which the author was involved significantly sharpened the bound on heat transfer in the presence of Ekman pumping. The resulting publication was targeted for an audience consisting primarily of physicists and other non-mathematicians. This work stems from the same effort, but is intended for a mathematical audience. Two additional, new results are presented that provide a more solid mathematical footing. These are firstly, a rigorous justification of the infinite Prandtl limit relied on in the referenced work, and secondly, a maximum principle for the temperature field, which provides the needed justification for the application of the background method.

Les instabilités hydrodynamiques en cavité chauffée latéralement jouent un rôle important dans certains processus de fabrication de matériaux tels que le procédé de Bridgman horizontal. En effet, le fluide (métal liquide qui va se solidifier) est le siège d’une circulation thermoconvective due à l’existence d’un gradient de température horizontal qui est susceptible de devenir instationnaire via des instabilités oscillatoires. La connaissance et la maîtrise de ces instabilités sont donc primordiales afin de pouvoir améliorer la qualité des cristaux obtenus par cette technique. Dans cette thèse, nous nous sommes intéressés en premier aux instabilités affectant la circulation convective dans une cavité tridimensionnelle de dimensions 4×2×1. (longueur × largeur × hauteur). Grâce aux techniques numériques de continuation, nous avons pu obtenir les solutions stationnaires et oscillatoires, ainsi que leur stabilité, jusqu’à l’apparition de la quasi-périodicité en fonction du nombre de Grashof Gr et pour un nombre de Prandtl allant de 0 à 0,025. Ensuite, pour un éventuel contrôle des instabilités, nous nous sommes intéressés aux effets induits par la rotation de la cavité. Nous avons tout d’abord considéré un modèle monodimensionnel que nous avons développé durant cette thèse. Ce modèle analytique, bien que simplifié, est en très bon accord avec les observations en dynamique des écoulements atmosphériques (déviation des masses fluides vers la droite de la composante de vitesse dominante et vents thermiques). La stabilité linéaire de cet écoulement est ensuite effectuée en fonction du taux de rotation donné par le nombre de Taylor et du nombre de Grashof pour un nombre de Prandtl allant de 0 à 10. Nous avons pu montrer à travers ce modèle que la rotation possède un caractère stabilisant vis-à-vis de ce type d’écoulement. Enfin, nous nous sommes focalisés sur les effets de la rotation sur l’écoulement pleinement tridimensionnel dans la cavité de dimensions 4×2×1. Nous avons mis en évidence deux régimes d’écoulements : un régime dominé par la convection, où la circulation du fluide est déviée par la rotation dans la diagonale de la cavité, et un deuxième régime dominé par la rotation où la circulation du fluide est concentrée dans les couches limites dites d’Ekman et de Stewartson. Un très bon accord est observé entre le modèle analytique simplifié et la simulation numérique tridimensionnelle. / Hydrodynamic instabilities in laterally heated cavities play an important role in some material processing techniques such as the horizontal Bridgman process. Indeed, the fluid (liquid metal to be solidified) is the seat of a thermoconvective circulation due to the existence of a horizontal temperature gradient which is likely to become unsteady via oscillatory instabilities. The knowledge and the control of these instabilities are thus essential in order to be able to improve the quality of the crystals obtained by this technique. In this thesis, we are first interested in the instabilities of the convective circulation in a three-dimensional cavity of dimensions 4×2×1 (length × width × height). Thanks to the numerical continuation techniques, we were able to obtain the stationary and oscillatory solutions, as well as their stability, until the appearance of the quasi-periodicity according to the Grashof number Gr and for a Prandtl number Pr ranging from 0 to 0.025.Then, the effects induced by a rotation of the cavity around the vertical axis parallel to gravity (for a possible control of the instabilities) are studied and a one-dimensional model developed during this thesis was first considered. This analytical model, although simplified, is in very good agreement with the observations of the atmospheric flows (deviation of the fluid masses towards the right of the component of the dominant velocity and thermal winds). The linear stability of this flow as well as an energy analysis at the thresholds are then performed as a function of the rotation rate given by the Taylor number Ta and the Grashof number Gr for a Prandtl number Pr ranging from 0 to 10. Through this model, we have been able to show that the rotation has a stabilizing effect on this type of flow.We finally focused on the effects of this type of rotation on the steady fully threedimensional flow observed in the cavity 4×2×1 at low Grashof numbers.We have highlighted two flow regimes: a regime dominated by convection where the fluid circulation, deviated by the rotation, occurs in the diagonal of the cavity, and a second regime dominated by rotation where the fluid circulation is concentrated in the so-called Ekman and Stewartson boundary layers. A very good agreement is observed between the simplified analytical model and the three-dimensional numerical simulation.

The main objective of this thesis is to design blades for the axial pump with two counter-rotating rotors for design point. Then compare results with the standard concept with one runner and guide blades.

This diploma thesis deals with hydraulic design and optimization of the blades of the axial pump. Main objective of the thesis is to design two stage pump with counter-rotating rotors meeting conditions of design point. In addition to the design solution the thesis includes theoretical part which deals with dividing and function description of hydrodynamic pumps.

This work deals with the determination of the heat transfer coefficient in small channels with a rotating wall. The research part of the thesis is focused on specific geometry, namely labyrinth seals used in rotary machines. Existing criteria equations determining heat transfer coefficients and other parameters in these specific geometries are described. The central part describes the built experimental device for the determination of values of heat flows and heat transfer coefficients on both stator and rotor for given airflow and rotor speed. The following section is devoted to presenting the results of the performed experiments with the corresponding criteria equations. The next part describes the basic mathematical models of inverse heat conduction problems. Calculations of heat flux using these inverse methods are performed and compared with reference heat flux sensors.

The diploma thesis deals with a design of a rotating part of a crane trolley of a scrap crane with a load capacity of 110,000 kg, which is situated in an exterior environment. The aim of the diploma thesis is a design and calculation verified design of the lifting mechanism, rotation mechanism and the design of a spacious traverse, which is used for the manipulation of the scrap trough and casting ladle.

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This thesis was aimed developing a fundamental understanding of the boundary layer response to arbitrary motion. In this context arbitrary motion was defined as the unsteady translation and rotation of an object. Research objectives were developed from the gaps in knowledge as defined during the literature survey. The objectives were divided into three main activities; mathematical formulations for non-inertial bulk flow and boundary layer equations, implementation of said formulations in a numerical solver and simulations for various applications in arbitrary motion. Mathematical formulations were developed for the bulk flow and boundary layer equations in arbitrary motion. It was shown that the conservation of momentum and energy equations remains invariant in the non-inertial forms. The conservations of momentum equation can at most have six fictitious terms for unsteady arbitrary motion. The origin of the terms were found to be from transformation of the material derivative to the non-inertial frame. All fictitious terms were found to be present in the boundary layer equations, none could be eliminated during an order of magnitude analysis. The vector form of the non-inertial equations were implemented in a novel OpenFOAM solver. The non-inertial solver requires prescribed motion input and operate on a stationary mesh. Validation of the solver was done using analytical solutions of a steady, laminar flat plate and rotating disk respectively. Numerical simulation were done for laminar flow on a translating plate, rotating disk and rotating cone in axial flow. A test matrix was executed to investigated various cases of acceleration and deceleration over a range of 70 g to 700 000g. The boundary layer profiles, boundary layer parameters and skin friction coefficients were reported. Three types of boundary layer responses to arbitrary motion were defined. Response Type I is viscous dominant and mimics the steady state velocity profile. In Response Type II certain regions of the boundary layer are dominated by viscosity and others by momentum. Response Type III is dominated by momentum. In acceleration the near-wall velocity gradient increases with increasing acceleration. In deceleration separation occurs at a result of momentum changes in the flow. The mechanism that causes these responses have been identified using the developed boundary layer equations. In acceleration the relative frame fictitious terms become a momentum source which results in an increase in velocity gradient at the wall. In deceleration the relative frame fictitious terms become a momentum sink that induced an adverse pressure gradient and subsequently laminar separation. / Hierdie tesis is gerig op die ontwikkeling van 'n fundamentele begrip aangaande die grenslaag reaksie op arbitrêre beweging. In hierdie konteks word arbitrêre beweging gedefinieer as die ongestadigde translasie en rotasie van 'n voorwerp. Navorsingsdoelwitte is ontwikkel uit die gapings soos omskryf in die literatuuroorsig. Die doelwitte is verdeel in drie hoof aktiwiteite; wiskundige formulerings vir ongestadigde vloei en grenslaag vergelykings, implementering van hierdie formulerings in 'n numeriese kode en simulasies vir verskeie gevalle van arbitrêre beweging. Wiskundige formulerings is ontwikkel vir die vloei en grenslaag vergelykings in arbitrêre beweging. Daar is bewys dat die behoud van massa en energie vergelykings onveranderd in die nie-inertiële vorms bly. Die behoud van momentum vergelyking kan hoogstens ses fiktiewe terme vir ongestadigde, arbitrêre beweging hê. Die oorsprong van die terme is vanuit die transformasie van die ongestadigde en adveksie terme (aan die linker kant van die momentum vergelyking) na die nie-inertiële raam. Alle fiktiewe terme is teenwoordig in die grenslaag vergelykings. Die vektor vorm van die nie-inertiële vergelykings is in 'n nuwe OpenFOAM oplosser geïmplementeer. Die nie-inertiële oplosser vereis voorgeskrewe beweging insette en werk op 'n stilstaande rooster. Die oplosser is getoets teen analitiese oplossings van 'n gestadigde, laminêre plaat plaat en 'n roterende skyf, onderskeidelik. Numeriese simulasies is gedoen vir laminêre vloei op 'n translerende plaat, roterende skyf en roterende konus in aksiale vloei. 'n Toets matriks is gebruik om ondersoek in te stel na gevalle van versnelling en vertraging oor 'n verskeidenheid van 70 g tot 700 000 g. Die grenslaag profiele, grenslaag parameters en oppervlak wrywingskoëffisiënte is aangemeld nie. Drie tipes grenslaag reaksies op arbitrêre beweging is gedefinieer. Reaksie Tipe I is viskeus dominant en boots die bestendige snelheidsprofiel na. In reaksie Tipe II sekere dele van die grenslaag is oorheers deur viskositeit en ander deur momentum. Reaksie Tipe III word in totaliteit oorheers deur momentum. In versnelling die snelheid helling teen die objek neem toe met toenemende versnelling. In vertraging is 'n negatiewe snelheidsprofiel waargeneem as gevolg van momentum veranderinge in die vloei. Die meganisme wat hierdie reaksies veroorsaak is geïdentifiseer deur die grenslaag vergelykings. In versnelling word die fiktiewe terme 'n bron van momentum. Dit lei tot 'n toename in snelheid helling op die objek. In vertraging word die fiktiewe terme 'n momentum gebruiker wat 'n negatiewe drukgradiënt veroorsaak en gevolglik laminêre vloei wegbreking veroorsaak. / Thesis (PhD)--University of Pretoria, 2016. / Mechanical and Aeronautical Engineering / PhD / Unrestricted