The problem of low Mach number (non-Boussin´esq) conjugate laminar natural convection combined with surface radiation in a vertical annulus with a centrally located vertical heat generating rod is studied numerically, taking into account the variable transport properties of the fluid. Such problems arise often in practical applications like spent nuclear fuel casks, cooling of electrical and electronic equipment, convection in ovens, cooling of enclosed vertical bus bars and underground transmission cables. The physical model consists of a vertical heat generating rod, a concentric outer isothermal boundary and adiabatic top and bottom surfaces. The heat generation in the rod drives the natural convection in the annulus. Surface radiation is coupled to natural convection through the solid-fluid interface condition and the adiabatic condition of the top and bottom surfaces. A mathematical formulation is written using the governing equations expressing the conservation of mass, momentum and energy for the fluid as well as the energy balance for the solid heat generating rod. The governing equations are discretized on a staggered mesh and are solved using a pressure-correction algorithm. Steady-state solutions are obtained by time-marching of the time dependent equations. The discretized equations for the dependent variables are solved using the Modified Strongly Implicit Procedure. A global iteration is introduced on the variables at each time step for better coupling. The parameters of the problem are the heat generation and gap width based Grashof number, aspect ratio, radius ratio and the solid-to-fluid thermal conductivity ratio. The coupling of radiation introduces the wall emissivity and the radiation number as the additional parameters and also necessitates the calculation of radiation configuration factors between the elemental surfaces formed by the computational mesh. The radiant heat exchange is calculated using the radiosity matrix method. A parametric study is performed by varying Grashof number from 106 to 1010 , aspect ratio from 1 to 15, radius ratio from 2 to 8, the solid-to-fluid thermal conductivity ratio from 1 to 100, with the Prandtl number 0.7 corresponding to air as the working medium. The characteristic dimension and the outer boundary temperature are fixed. For Radiative calculations, and the emissivity is varied between 0.25 and 0.75. Converged solutions with laminar model could be obtained for high Grashof numbers also as the heat generation based Grashof number is generally two orders of magnitude higher than the temperature difference based Grashof number. Results are presented for the flow and temperature distributions in the form of streamline and isotherm maps. Results are also presented for the variation of various quantities of interest such as the local Nusselt numbers on the inner and outer boundaries, the axial variation of the centerline and interface temperatures, maximum solid, average solid and average interface temperature variations with Grashof number and the average Nusselt number variation for the inner and outer boundaries with Grashof number. The results show that simplification of conjugate problems involving heat generation by the prescription of an isoflux boundary condition on the rod surface is inadequate because a truly isoflux condition cannot be realised on the one hand and because the solid temperature distribution remains unknown with such an approach. The average Nusselt numbers on the inner and outer boundaries show an increasing trend with the Grashof number. For pure natural convection, the Boussin´esq model predicts higher temperatures in the solid and lower average Nusselt numbers on the inner and outer boundaries, compared to the non-Boussin´esq model and the Boussin´esq approximation appears to be adequate roughly upto a Grashof number of 109, beyond which the non-Boussin´esq model is to be invoked. The average pressure in the annulus is found to increase with an increase in the Grashof number. Radiation is found to cause convective drop and homogenize the temperature distribution in the fluid.

Résumé: Les mécanismes de perfectionnement du transfert thermique des nanofluids sont encore peu clairs. Les études précédentes au sujet des nanofluids ont essayé de résoudre certains des nombreux défis au sujet de la performance thermique et hydrodynamique des nanofluides et de leurs propriétés ; toutefois il reste beaucoup de problèmes non résolus et questions sans réponse certaine. Par conséquent, plus d'études sont nécessaires, qui peuvent être expérimentales, numériques ou théoriques. Dans la présente étude, des nanofluides sont étudiés intensivement en utilisant des approches numériques et analytiques. La partie numérique se compose de trois chapitres et couvre un éventail de problèmes de transfert thermique, incluant; laminaire et turbulente, monophasique et diphasique, aussi bien que, convection mixte et convection forcée. Plusieurs concentrations volumétriques de nanoparticules et nombres de Reynolds sont considérés. Le deuxième chapitre est consacré à la convection laminaire mixte de nanofluide d'Al[indice inférieur 2]O[indice inférieur 3]-eau à l'intérieur d'un tube horizontal. Le flux uniforme de chaleur est appliqué au mur. Deux nombres de Reynolds et trois concentrations volumétriques de nanoparticules sont utilisés, et finalement les résultats numériques thermiques et hydrodynamiques de trois différents modèles diphasiques et du modèle monophasique sont comparés aux données expérimentales. On démontre que les résultats de ces différentes approches sont extrêmement différents. Pour un régime de convection laminaire mixte, les modèles diphasiques sont en meilleur accord avec des données expérimentales. Les résultats de modèles diphasiques sont proches mais loin des résultats du modèle monophasique. Le troisième chapitre évalue la sensibilité de la formulation laminaire sur des combinaisons choisies des expressions pour la conductivité et la viscosité des nanofluids. Deux expressions pour la conductivité et trois pour la viscosité sont choisis, ce qui donne six combinaisons. Ces choix s'avèrent avoir des effets très importants sur les résultats finals. Par conséquent, chaque étude numérique devrait d'abord justifier son choix des corrélations de viscosité-conductivité. En outre, une liste des modèles les plus importants pour la conductivité et la viscosité des nanofluids est recueillie et incluse dans ce chapitre. Le quatrième chapitre évalue les résultats du modèle monophasique et trois différents modèles diphasiques pour la convection forcée turbulente de nanofluide dans un tube horizontal. Le flux uniforme de la chaleur est appliqué au mur. Le modèle turbulent "Realizable k-[epsilon]" est employé, qui est un modèle à deux équations. Deux ensembles de données expérimentales pour différents nanofluides (Al[indice inférieur 2]O[indice inférieur 3]-eau et Cu-eau) sont employés, qui couvrent un éventail des concentrations volumétriques de nanoparticules et de nombres de Reynolds. L'exactitude monophasique des résultats est confirmée avec un choix approprié de combinaisons de conductivité-viscosité. Les résultats des différents modèles diphasiques sont proches; cependant, ils sont très loin des résultats monophasique [i.e. monophasiques] et des données expérimentales. Les modèles diphasiques ne pourraient pas satisfaire les données expérimentales pour le régime convection forcée turbulente de deux nanofluides différents par deux différentes études expérimentales, alors que l'approche monophasique le fait bien. Dans la partie analytique de l'étude, de nouveaux modèles pour la conductivité thermique des nanofluides et le nombre de Nusselt de l'écoulement autour des nanoparticules sont dérivés. Ces modèles tiennent compte de l'effet du mouvement Brownien, de la résistance thermique surfacique, du groupement des particules, de la distribution de taille de ces groupements et de la micro-convection aussi bien que de la concentration des particules, de la dimension particulaire et de la température. Le groupement des particules et la distribution de leur taille sont analysés à l'aide de la théorie fractale. Le modèle proposé pour la conductivité des nanofluides est comparé aux données expérimentales de plusieurs études pour cinq nanofluides différents et différentes concentrations volumétriques de nanoparticules. Ce modèle est également comparé à deux modèles semblables. II montre une très bonne concordance avec l'expérience et une meilleure performance comparé à ces modèles choisis.||Abstract: The mechanisms of nanofluids heat transfer enhancement are still unclear. Previous studies about nanofluids have tried to solve some of many challenges about the thermal and hydrodynamic performance of nanofluids and their properties; however still there are many problems unsolved and questions without a certain answer. Hence, more studies are necessary, which can be experimental, numerical and theoretical. In the present study, nanofluids are investigated intensively using numerical and analytical approaches. The numerical part consists of three chapters and covers a wide range of heat transfer problems, including; laminar and turbulent, single-phase and two-phase as well as mixed convection and forced convection flows. Several particle volume fractions and a large number of Reynolds numbers are considered. Chapter two is dedicated to laminar mixed convection flow of Al 2 O 3 -water nanofluid inside a horizontal tube. Uniform heat flux is applied at the wall. Two Reynolds numbers and three particle volume fractions are used, and finally the thermal and hydrodynamic numerical results from three different two-phase models and the single phase model are compared with experimental data. It is shown that the predictions of these different approaches are extremely different. For a laminar mixed convection flow, two-phase models are in better agreement with a given experimental data. The two-phase models predictions are close but far from single-phase. Chapter three evaluates the sensitivity of the laminar formulation on selected combinations of models for the conductivity and viscosity of nanofluids. Two models for the conductivity and three for the viscosity are chosen, which make six combinations. These choices are found to have very important effects on the final results. Therefore, every numerical study should first justify their choice of viscosity-conductivity correlations. Also, a list of the most important models for the conductivity and viscosity of nanofluids are gathered and included in this chapter. Chapter four evaluates the predictions of single-phase and three different two-phase models for turbulent forced convection inside a horizontal tube. Uniform heat flux is applied at the wall. Realizable k-[varepsilon] turbulent model is used, which is a two-equation model. Two sets of experimental data for different nanofluids (Al 2 O3 -water and Cu-water) are used, which cover a wide range of volume fractions and Reynolds numbers. The single-phase results accuracy is confirmed with an appropriate selection of conductivity-viscosity combination. The results from different two-phase models are found to be very close; however, they were too far from the single-phase predictions and the experimental data. Two-phase models could not satisfy the experimental data for turbulent forced convection flow of two different nanofluids from different experimental studies, while single-phase approach does it well. In the analytical part of the study, new models for the thermal conductivity of nanofluids and the Nusselt number of the flow around the nanoparticles are derived. These models take into account the effect of Brownian motion, interfacial thermal resistance, particles clustering, clusters size distribution and micro-convection as well as particles concentration, particles size and temperature. The clusters size and size distribution are analyzed based on the fractal theory. The proposed model for the conductivity of nanofluids is compared with experimental data from several studies for five different nanofluids and various magnitudes of volume fractions. This model is also compared with two similar models. It shows very good agreement with experiment and better performance compared to those selected models.[symboles non conformes]

By using the finite element method to solve the appropriate momentum and energy equations the friction factors and Nusselt numbers for fully developed laminar flow were determined for one- and two-dimensional flow systems. The Nusselt numbers were determined for domain boundaries subjected to a constant heat flux (H1) or a constant surface temperature (T) around the computational boundaries and in the axial directions. C++ programs, that were rewritten and extended from previous programs, were used to solve the laminar flow and to determine the values. The required wall shear stresses and heat fluxes were directly obtained for a duct as part of the primary finite-element solution; these values were then used to determine the Nusselt number and friction factor for the specific duct. The computations were performed for circular-, annular-, trapezoidal-, rectangular- and triangular ducts. Special emphasis was placed on trapezoidal ducts since only a limited number of studies have been performed on trapezoidal duct shapes and none of these studies employed the finite element method. Excellent agreement was found when the determined values were compared with the values reported in the literature. In general, the agreement of the values improved as the number of elements was increased. It was, therefore, concluded that the methods used in this study yielded friction factors and Nusselt numbers that are very accurate and usable. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.

By using the finite element method to solve the appropriate momentum and energy equations the friction factors and Nusselt numbers for fully developed laminar flow were determined for one- and two-dimensional flow systems. The Nusselt numbers were determined for domain boundaries subjected to a constant heat flux (H1) or a constant surface temperature (T) around the computational boundaries and in the axial directions. C++ programs, that were rewritten and extended from previous programs, were used to solve the laminar flow and to determine the values. The required wall shear stresses and heat fluxes were directly obtained for a duct as part of the primary finite-element solution; these values were then used to determine the Nusselt number and friction factor for the specific duct. The computations were performed for circular-, annular-, trapezoidal-, rectangular- and triangular ducts. Special emphasis was placed on trapezoidal ducts since only a limited number of studies have been performed on trapezoidal duct shapes and none of these studies employed the finite element method. Excellent agreement was found when the determined values were compared with the values reported in the literature. In general, the agreement of the values improved as the number of elements was increased. It was, therefore, concluded that the methods used in this study yielded friction factors and Nusselt numbers that are very accurate and usable. / Thesis (M.Ing. (Mechanical Engineering))--North-West University, Potchefstroom Campus, 2009.

L'étude des jets impactants a fait l'objet d'une multitude de travaux depuis plusieurs dizaines d'années en raison de la variété des domaines d'applications. Il existe une grande diversité de jets tels que les jets axisymétriques et les jets bidimensionnels pour les plus classiques ou tels que les jets à géométrie lobée, c'est à dire des jets axisymétriques sur lesquels il a été appliqué un contrôle passif, pour les plus complexes. Dans nos travaux, nous avons réalisé une étude fondamentale des jets plans confinés pour une gamme de faibles nombres de Reynolds. Nous avons étudié la stabilité des jets d'un fort confinement à un faible confinement. Nous avons ainsi pu établir une multitude d'interaction entre les modes de jets instationnaires et les modes de cavités. L'utilisation d'un outil de mesure permettant un suivi temporel des écoulements nous a permis d'extraire ces différents modes globaux. Dans le cadre d'études visant à optimiser les transferts thermiques sur la paroi impactée par le jet, nous avons réalisé plusieurs études sur l'influence des jets à géométrie lobée (contrôle passif) sur la dynamique en amont de la paroi d'impact et sur les transferts thermiques de la paroi impactée. Une première étude fondamentale avait pour objectif de mettre en lumière les mécanismes en jeu dans la dynamique des jets et de mieux comprendre le lien entre les transferts thermiques et l'écoulement proche paroi. Nous avons été en mesure d'extraire les modes globaux de certains mécanismes et de montrer les capacités de transferts thermiques de plusieurs buses lobées face à ceux d'une buse axisymétrique. Deux études paramétriques des buses à géométrie lobée nous ont permis d'évaluer dans un premier temps, les effets des nombres de lobes et un second temps les effets de la forme des lobes sur les transferts thermiques. Ces études ont été menées à la fois sur les distances d'impact et sur les nombres de Reynolds. Nous avons ainsi pu émettre des hypothèses sur les mécanismes à l'origine de l'amélioration des transferts thermiques. / Impacting jets has been widely studied by the scientific community since several decades. The main reason is the great variety of industrial application of these jets. This study concerns a wide variety of jets such as the axisymmetric jets and two-dimensional slotted jets for the more classic configurations or for a more complex situation, such as lobed jet geometry, i.e. axisymmetric jets on which a passive control has beed applied. In our study, we performed a fundamental study of confined slot jets within a low Reynolds number range. The stability of confined slot jets has been studied with various confinement levels. We were able to observe multiple interactions between the unsteady jet modes and the cavity modes. Time-resolved measurement enabled us to extract these various global modes. Regarding the studies performed to optimize heat transfer on impacted jets, we aimed at showing the influence of the lobed jet geometry (passive control) on the dynamic upstream of the impacted wall and the heat transfer associated to it. A first fundamental study aimed at highlighting the mechanism involved in the dynamics of these lobed jets and at understanding the relationship between heat transfer and flow. We were able to extract global modes of some mechanisms and demonstrated the heat transfer capabilities of various lobed jet nozzle compared to those of an axisymmetric nozzle. Two parametric studies of lobed geometry enabled us evaluate (i) the effects of the number of lobes present and (ii) the effects of the shape of these lobes on heat transfer. These studies were conducted both at several impacting distance and for several Reynolds numbers. We were able to emit hypothesis about the mechanisms behind the enhancement of heat transfer.

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.

In the past, steam turbines were mostly used for base load operation. Nowadays, with the increased development of variable renewable technologies, these same steam turbines are withstanding higher cyclic operational regimes with more frequent start-ups and fast changing loads. As such, improving the operational flexibility of installed and future designed steam turbines is a key aspect to be considered by equipment manufacturers. Steam turbine start-up is a phase of particular interest since is considered to be the most intricate of transient operations. During this phase, the machine can potentially be subjected to excessive thermal stresses and axial rubbing due to differential thermal expansion. These two thermal phenomena either consume component lifetime or can lead to machine failure if not carefully controlled. As such, there is a balance to be considered between increasing turbine start-up speed while ensuring the safe operation and life preservation of these machines. In order to improve the transient operation of steam turbines, it becomes important to examine their thermal behavior during start-up operation. To do that, it is important to have tools able to predict the thermal response of the machine. In this thesis work the impact of different aspects and boundary conditions on the results of ST3M, a KTH in-house tool, were investigated with the aim of understanding how large was their impact on the way to capture the thermal behavior of the turbine in terms of metal temperature and differential expansion. A small industrial high pressure turbine was validated against measured data and implemented on a sensitivity study; this analysis showed that the geometrical approximation introduce errors in the results, that the use of empirical Nusselt correlations give similar results to the validated model and that the cavity assumptions have a large impact on the trend of the differential expansion. Lastly, a strategy to validate any other similar turbine to the one of the study case was proposed in order to give a guide to future works in how to validate a model and what are the most influent parameters to take care of.

One approach recently proposed for reducing the frictional resistance to liquid flow in microchannels is the patterning of micro-ribs and cavities on the channel walls. When treated with a hydrophobic coating, the liquid flowing in the microchannel wets only the top surfaces of the ribs, and does not penetrate into the cavities, provided the pressure is not too high. The net result is a reduction in the surface contact area between channel walls and the flowing liquid. For micro-ribs and cavities that are aligned normal to the channel axis (principal flow direction), these micropatterns form a repeating, periodic structure. This thesis presents numerical results of a study exploring the momentum and thermal transport in a parallel plate microchannel with such microengineered walls. The liquid-vapor interface (meniscus) in the cavity regions is approximated as flat in the numerical analysis. Two conditions are explored with regard to the cavity region: 1) The liquid flow at the liquid-vapor interface is treated as shear-free (vanishing viscosity in the vapor region), and 2) the liquid flow in the microchannel core and the vapor flow within the cavity are coupled through the velocity and shear stress matching at the interface. Predictions reveal that significant reductions in the frictional pressure drop (as large as 80%) can be achieved relative to the classical smooth channel Stokes flow. In general, reductions in the friction factor-Reynolds number product (fRe) are greater as the cavity-to-rib length ratio is increased (increasing shear-free fraction), as the relative module length (length of a rib-cavity module over the channel hydraulic diameter) is increased, as the Reynolds number decreases, and as the vapor cavity depth increases. The thermal transport results predict lower average Nusselt (Nu) numbers as the cavity-to-rib length ratio is increased (increasing shear-free fraction), as the relative module length (is increased, and as the Reynolds number decreases with little dependence on cavity depth. The ratio of Nu to fRe was evaluated to characterize the relative change in heat transfer with respect to the reduction in driving pressure. Results show that the benefits of reduction in driving pressure outweigh the cost of reduction in heat transfer at higher Reynolds numbers and narrower relative channel widths.

A Laser Inertial Fusion Energy (LIFE) target’s flight through a low Reynolds number and high Mach number regime was analyzed with computational fluid dynamics software. This regime consisted of xenon gas at 1,050 K and approximately 6,670 Pa. Simulations with similar flow conditions were performed over a sphere and compared with experimental data and published correlations for validation purposes. Transient considerations of the developing flow around the target were explored. Simulations of the target at different velocities were used to determine correlations for the drag coefficient and Nusselt number as functions of the Reynolds number. Simulations with different target angles of attack were used to determine the aerodynamic coefficients of drag, lift, Magnus moment, and overturning moment as well as target stability. The drag force, lift force, and overturning moment changed minimally with spin. Above an angle of attack of 15°, the overturning moment would be destabilizing. At angles of attack less than 15°, the overturning moment would tend to decrease the target’s angle of attack, indicating the lack of a need for spin for stability at these small angles. This stabilizing moment would cause the target to move in a mildly damped oscillation about the axis parallel to the free-stream velocity vector through the target’s center of gravity.

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