The power supply for electronic devises is demanded to be lighter and smaller in nowadays market. Therefore, the cooling problem becomes the major design challenge due to reduced heat transfer area. In this thesis, a numerical computation method is employed to numerically simulate the natural convection heat transfer field for a small power supply placed on the ground or table in atmospheric conditions. The effects of parameters are studied including internal heat sink structure, shell structure, heat rate of generation, body size and ground material. The results of the present study can provide design reference.

A parallel numerical method has been implemented for solving the Navier Stokes equations on Cartesian and non-orthogonal meshes. To ensure the accuracy of the code first, second and third order differencing schemes, with and without flux-limiters, have been implemented and tested. The most computationally expensive task in the code is the solution of linear equations, and a number of linear solvers have been tested to determine the most efficient. Krylov space, incomplete factorisation, and other iterative and direct solvers from the literature have been implemented, and have been compared with a novel black-box multigrid linear solver that has been developed both as a solver and as a preconditioner for the Krylov space methods. To further reduce execution time the code was parallelised, after a series of experiments comparing the suitability of different parallelisation techniques and computer architectures for the Navier Stokes solver. The code has been applied to the solution of two classes of problem. Two natural convection flows were studied, with an initial study of two dimensional Rayleigh Benard convection being followed by a study of a transient three dimensional flow, in both cases the results being compared with experiment. The second class of problems modelled were free surface flows. A two dimensional free surface driven cavity, and a two dimensional flume flow were modelled, the latter being compared with analytic theory. Finally a three dimensional ship flow was modelled, with the flow about a Wigley hull being simulated for a range of Reynolds and Froude numbers.

Doctor of Philosophy / Department of Mechanical and Nuclear Engineering / Hitesh Bindra / Helium-cooled, graphite moderated reactors have been considered for a future fleet of high temperature and high efficiency nuclear power plants. Nuclear-grade graphite is used in these reactors for structural strength, neutron moderation, heat transfer and, within a helium environment, has demonstrated stability at temperatures well above HTGR operating conditions. However, in the case of an air ingress accident, the oxygen introduced into the core can affect the integrity of the fuel graphite matrix. In this work a combination of computational models and mixed effects experiments were used to better understand the air ingress process and its potential effects on the heat removal capabilities of an HTGR design following an air-ingress accident. Contributions were made in the understanding of the air-ingress phenomenon, its potential effects on graphite, and in experimental and computational techniques. The first section of this thesis focuses on experimental and computational studies that were undertaken to further the understanding of the Onset of Natural Convection (ONC) phenomenon expected to occur inside of an HTGR following an air ingress accident. The effects of two newly identified factors on ONC – i.e., the existence of the large volume of stagnate helium in a reactor's upper plenum, and the possibility of an upper head leak – were investigated. Mixed-effects experimental studies were performed to determine the changes induced in nuclear grade graphite exposed to high-temperature, oxidizing flow of varying flow rates. Under all scenarios, the thermal diffusivity of the graphite test samples was shown to increase. Thermal conductivity changes due to oxidation were found to be minor in the tested graphite samples – especially compared to the large drop in thermal conductivity the graphite is expected to experience due to irradiation. Oxidation was also found to increase the graphite's surface roughness and create a thin outer layer of decreased density. The effects of thermal contacts on the passive cooling ability of an HTGR were experimentally investigated. Conduction cool down experiments were performed on assemblies consisting of a number of rods packed into a cylindrical tube. Experimental conditions were then modeled using several different methodologies, including a novel graph laplacian approach, and their results compared to the experimentally obtained temperature data. Although the graph laplacian technique shows great promise, the 2–D Finite Element Model (FEM) provided the best results. Finally, a case study was constructed in which a section of a pebble bed reactor consisting of a number of randomly packed, spherical fuel particles was modeled using the validated FEM technique. Using a discrete elements model, a stable, randomly packed geometry was created to represent the pebble bed. A conduction cool down scenario was modeled and the results from the FEM model were compared to best possible results obtainable from a more traditional, homogeneous 1–D approximation. When the graphite in the bed was modeled as both oxided and irradiated, the homogeneous method mispredicted the maximum temperature given by the 3–D, FEM model by more than 100°C.

[pt] Neste trabalho é feita uma análise teórica e numérica da evaporação não isotérmica de um líquido contido em um recipiente cilíndrico parcialmente cheio, com paredes adiabáticas. Postula-se que a evaporação acontece em presença de convecção natural impulsionada por diferenças de massa específica, associadas com gradientes de temperatura e composição da mistura. Esta consiste de um gás e o vapor do líquido. Embora a formulação seja geral, o presente trabalho focaliza a evaporação de água para o ar. Estudou-se três situações. Um caso isotérmico, variante do clássico problema de difusão de Stefan, um Caso em que a temperatura do líquido é maior do que a temperatura ambiente e um terceiro caso no qual a temperatura do líquido é menor do que a do ambiente. Duas diferentes condições de contorno foram usadas na abertura do recipiente de modo a explorar a sensibilidade do escoamento às condições no topo. A distância entre a superfície do líquido e o topo variou de duas a dez vezes o raio do recipiente. Duas diferenças de temperatura entre o líquido e o ambiente foram investigadas, 3 graus Celsius e - 2 graus Celsius. O ar ambiente foi considerado como sendo muito seco ou muito úmido. Encontrou-se que, quando a temperatura do líquido é maior do que a temperatura ambiente, a taxa de evaporação alcança valores até quatro vezes maiores do que para o caso isotérmico. Para o caso em que a temperatura do líquido é menor do que a temperatura ambiente, a taxa de evaporação decresce para valores até duas vezes menores do que para o caso isotérmico. / [en] This work reports a theoretical and numerical analysis of the non-isothermal evaporation of a liquid contained in a partially filled cylinder vessel, with adiabatic walls. It is assumed that the evaporation occurs in the presence of natural convection driven by differences in specific mass associated with gradient of temperature and mixture composition. The mixture consist of a gas and the vapor of the evaporating liquid. Although the formulation is general, the specific focus of the present work is on the evaporation of water into air. Three situations were studied. An isothermal case, which is a variant of the classical Stefan diffusion problem, a case where the liquid temperature is higher than the ambient temperature, and a third case in which the liquid temperature is lower than the ambient. Two different boundary conditions were used at the openning of the vessel in a way to explore the sensitivity of the flow to the conditions on the top. The distance between the liquid surface and the top of the vessel varied from two to ten times the vessel radius. Two temperature differences between the liquid and the ambient were investigated, 3 degrees Celsius and - 2 degrees Celsius. The environmental air was considered to be either very dry or very wet. It was found that, when the liquid temperature is higher than the ambient temperature, the rate of evaporation can reach values up to four times larges than that for the isothermal case. For the case where the liquid temperature. is lower than the ambient temperature, the rate of evaporation decreases to values down to half of theisothermal case.

When a gas undergoes an exothermic reaction in a closed vessel, spatial temperature gradients can develop. If these gradients become sufficiently large, the resulting buoyancy forces will move the gas, i.e. there is natural convection. The nature of the resulting flow is determined by the Rayleigh number, Ra = (β g ΔT L^3) / (κ ν). The evolution of such a system will depend on the interactions of natural convection, diffusion of both heat and chemical species, and chemical reaction. This study is concerned with a gas-phase system undergoing Sal'nikov's reaction: P → A → B, in the presence of natural convection. This kinetic scheme is used as a simplified representation of a cool flame, which is a feature of the low temperature combustion of a hydrocarbon vapour. Sal'nikov's reaction is one of the simplest to display thermokinetic oscillations, such as those seen in cool flames. The behaviour of Sal'nikov's reaction in the presence of natural convection was investigated using a combination of analytical and numerical techniques. First, a numerical model was developed to compute the temperature, velocity and concentrations when a simple exothermic reaction occurs in a spherical batch reactor, the results of which could be compared with previous experimental measurements. Subsequently, a scaling analysis of Sal'nikov's reaction proceeding in a spherical reactor was performed. This yielded significant insight into the general behaviour of this and similar systems. The forms of the analytical scales were confirmed through comparison with the results from numerical simulations. These scales were used to predict how the system responds to changes in certain key process variables, such as the pressure and the size of the reactor. It was shown that the behaviour of this system is governed by the ratios of the characteristic timescales for diffusion, reaction and natural convection. These ratios were used to define a regime diagram describing the system. The behaviour in different parts of this regime diagram was characterised and regions in which oscillations occur were identified.

No description available.

The mass and thermal transport in porous media play an important role in many engineering and geological processes. The hydrodynamic and thermal effects are two interesting aspects arising in the research of porous media. This thesis is concerned with numerical investigations of double-diffusive natural convective heat and mass transfer in saturated porous cavities with Soret and Dufour effects. An in-house FORTRAN code, named ALFARHANY, was developed for this study. The Darcy-Brinkman-Forchheimer (generalized) model with the Boussinesq approximation is used to solve the governing equations. In general, for high porosity (more than 0.6), Darcy law is not valid and the effects of inertia and viscosity force should be taken into account. Therefore, the generalized model is extremely suitable in describing all kinds of fluid flow in a porous medium. The numerical model adopted is based on the finite volume approach and the pressure velocity coupling is treated using the SIMPLE/SIMPLER algorithm as well as the alternating direction implicit (ADI) method was employed to solve the energy and species equations. Firstly, the model validation is accomplished through a comparison of the numerical solution with the reliable experimental, analytical/computational studies available in the literature. Additionally, transient conjugate natural convective heat transfer in two-dimensional porous square domain with finite wall thickness is investigated numerically. After that the effect of variable thermal conductivity and porosity investigated numerically for steady conjugate double-diffusive natural convective heat and mass transfer in two-dimensional variable porosity layer sandwiched between two walls. Then the work is extended to include the geometric effects. The results presented for two different studies (square and rectangular cavities) with the effect of inclination angle. Finally, the work is extended to include the Soret and Dufour effects on double-diffusive natural convection heat and mass transfer in a square porous cavity. In general, the results are presented over wide range of non-dimensional parameters including: the modified Rayleigh number (100 ≤ Ra* ≤ 1000), the Darcy number (10-6 ≤ Da ≤ 10-2), the Lewis number (0.1 ≤ Le ≤ 20), the buoyancy ratio (-5 ≤ N ≤ 5), the thermal conductivity ratio (0.1 ≤ Kr ≤ 10), the ratio of wall thickness to its height (0.1 ≤ D ≤ 0.4), the Soret parameter (-5 ≤ Sr ≤ 5), and the Dufour parameter (-2 ≤ Df ≤ 2).

In the present thesis turbulent natural convection of air within different challenging test cases are investigated numerically by means of an unstructured finite volume code, Code_Saturne. First, flow within both two-dimensional vertical and inclined differentially heated rectangular cavities at 60° and 15° to the horizontal for an aspect ratio of H/L=28.6 and Rayleigh number of 0.86×10e6 is computed using several high and low-Re models. Here the effectiveness of the RANS models in Code_Saturne is assessed through comparisons with a range of available experimental data. After some tests of thermal field inside vertical cavity, the “two-velocity-scale wall function” is chosen to be used with high-Re models. In both vertical and inclined cases the overall flow pattern appears similar, with a single circulation cell, and a boundary layer at the wall. The levels of turbulence energy are generally slightly lower in the inclined case. Most models give a reasonable prediction of measured Nusselt number, with the two low-Re approaches generally being closer to the data than the schemes employing wall functions. For the 15° inclined cavity, a multi cellular motion is shown by the high-Re models. Nevertheless, all the model predictions disagree with experimental data due to the presence in real flow of 3-D unsteady structures as found in Benard convection problems. These cannot, definitely, be reproduced using a 2-D geometry. Both highly resolved LES and unsteady RANS computations are then conducted, for turbulent natural convection of air inside 15° unstably and stably stratified cavities. In accordance with recent experimental data, the LES computations for both enclosures returned three-dimensional time-averaged flow fields. In the case of the unstably stratified enclosure, the flow is highly unsteady with coherent turbulent structures in the core of the enclosure. Results of LES computations show close agreement with the measured data. Subsequent comparisons of different URANS schemes with the present LES are used in order to explore to what extent these models are able to reproduce the large-scale unsteady flow structures. All URANS schemes have been found to be able to reproduce the 3-D unsteady flow features present in the 15° unstable cavity. However, the low-Re model tested as well as requiring a high resolution near-wall grid, also needed a finer grid in the core region than the high-Re models, thus making it computationally very expensive. Flow within the 15° stable cavity also shows some 3-D features, although it is significantly less unsteady, and the URANS models tested here have been less successful in reproducing this flow pattern. Finally, natural convection of CO2 inside a horizontal annular penetration enclosure, which can be found in AGR's, has been performed using a highly resolved LES and a set of RANS models. The Rayleigh number is 1.5×10e9. RANS models agree with the present LES on the fact that the flow is unsteady and there are large-scale oscillations present which decrease in amplitude as one moves from the open towards the closed end of the annular enclosure. Overall heat transfer and thermal quantitative and dynamic results show that RANS schemes are in close agreement with the current LES data except some discrepancies shown by the high-Re model which can be returned to the limitation of the simple wall function used to predict such complex flow.

This dissertation focuses on the effects of superhydrophobic (SHPo) surfaces on thermal transport. The work is divided into two main categories: thermal transport without phase change and thermal transport with phase change. Thermal transport without phase change is the topic of four stand-alone chapters. Three address jet impingement at SHPo surfaces and the fourth considers natural convection at a vertical, SHPo wall. Thermal transport with phase change is the topic of a single stand-alone chapter exploring pool boiling at SHPo surfaces.Two chapters examining jet impingement present analytical models for thermal transport; one considered an isothermal wall and the other considered an isoflux wall. The chapter considering the isothermal scenario has been archivally published. Conclusions are presented for both models. The models indicated that the Nusselt number decreased dramatically as the temperature jump length increased. Further, the influence of radial position, jet Reynolds number, Prandtl number and isoflux versus isothermal heating become negligible as temperature jump length increased. The final chapter concerning jet impingement reports an experimental exploration of jet impingement at post patterned SHPo surfaces with varying microfeature pitch and cavity fraction. The empirical results show a decrease in Nusselt number relative to smooth hydrophobic surfaces for small pitch and cavity fraction and the isoflux model agrees well with this data when the ratio of temperature jump length to slip length is 3.1. At larger pitch and cavity fractions, the empirical results have higher Nusselt numbers than the SHPo surfaces with small pitch and cavity fraction but remain smaller than the smooth hydrophobic surface. We attribute this to the influence of small wetting regions. The chapter addressing natural convection presents an analytical model for buoyant flow at a vertical SHPo surface. The Nusselt number decreased dramatically as temperature jump length increased, with greater decrease occurring near the lower edge and at higher Rayleigh number. Thermal transport with phase change is the topic of the final stand-alone chapter concerning pool boiling, which has been archivally published. Surface heat flux as a function of surface superheat was reported for SHPo surfaces with rib and post patterning at varying microfeature pitch, cavity fraction, and microfeature height. Nucleate boiling is more suppressed on post patterned surfaces than rib patterned surfaces. At rib patterned surfaces, transition superheat decreases as cavity fraction increases. Increasing microfeature height modestly increases the transition superheat. Once stable film boiling is achieved, changes in surface microstructure negligibly influence thermal transport.

Directional solidification has a wide interest due to its importance to the iron and steel industry. Examples of further application can be found in the aerospace industry regarding the manufacture of turbine blades and the semiconductor industry regarding single-crystal growth applications. Solute convection in the solidification process results in channel formation, which has a freckle-like appearance in cross-section and has a critical effect on the mechanical strength of a casting. For a solidification process that occurs via planar solidification from a solid boundary, one may consider the presence of three distinct regions often identified as horizontal layers, i.e. a fluid binary mixture (the melt), the solid layer and a two-phase (fluid-solid) mushy layer, separating the other two. The mushy layer is practically a porous medium consisting of an interconnected solid phase having its voids filled with the melt binary fluid. Channelling in the mushy layer and the creating of freckles are being considered the main reasons for non-homogeneous solidification and production of defects in the resulting solid product. The production of defects adversely affects the mechanical properties of the solid product leading to undesirable constraints on its industrial use. The purpose of this study is to evaluate the effect the vibrations have on the heat transfer during the solidification process as well as on the average density of the solid product and void formation. Experimental as well as theoretical investigations related to the solidification process were undertaken. Two effects that have been observed in previous experimental studies when metals and metal alloys are vibrated during solidification are a decrease in dendritic spacing, which directly affects density, and faster cooling rates and associated solidification times. Because these two effects happen simultaneously during solidification it is challenging to determine the one effect independently from the other. Most previous studies were on metals and metal alloys. In these studies, the one effect, i.e. the decrease in dendritic spacing, might influence the other, i.e. the faster cooling rates, and vice versa. The direct link between vibration and heat transfer has not yet been studied independently. The purpose of this study was to experimentally investigate the effect of vibration only on heat transfer and thus solidification rate. Experiments were conducted on paraffin wax, because it had a clearly defined macroscopic crystal structure consisting of mostly large straight-chain hydrocarbons. The advantage of the large straight-chain hydrocarbons was that the dendritic spacing was not affected by the cooling rate. Experiments were done with paraffin wax inside hollow plastic spheres of 40 mm diameter with 1 mm wall thickness. The paraffin wax was initially in a liquid state at a uniform temperature of 60°C and then submerged into a thermal bath at a uniform constant temperature of 15°C, which was approximately 20°C below the mean solidification temperature of the wax. Experiments were conducted in approximately 300 samples, with and without vibration at frequencies varying from 10 – 300 Hz. The first set of experiments were conducted to determine the solidification times. In the second set of experiments, the mass of wax solidified was determined at discrete time steps, with and without vibration. The results showed that paraffin wax had vibration independent of solid density contrary to other materials, eg. metals and metal alloys. Enhancement of heat transfer resulted in quicker solidification times and possible control over the heat transfer rate. The increase in heat transfer leading to faster solidifcation times was observed to first occur, as frequency increased and then to decrease. Experimental results showed that paraffin wax had vibration independent of solid density contrary to other materials, eg. metals and metal alloys. Enhancement of heat transfer resulted in quicker solidification times and possible control over the heat transfer rate. The increase in heat transfer leading to faster solidifcation times was observed to first occur, as frequency increased and then to decrease. Theoretical results of heat convection in a porous layer heated from below and subject to vibrations are presented by using a truncated spectral method in space. The partial differential equations governing the mass, momentum, heat, and solute transport were tranformed into a set of ordinary differential equations via a truncated modal expansion. Then the resutling equations were solved to identify the variety of regimes, and transitionbetween them, i.e. from steady convection, via periodic and quasi-periodic convection, towards chaotic or weak turbulent convection. The theoretcial results show that the heat convection subject to vibration is generally reduced when compared with the corresponding convection without vibrations. The exception for a certain frequency range shows about a 10% enhancement in the weak turbulent regime of convection, however, a 10% enhancement is still lower than the heat transfer prior to the transition to weak turbulence. Therefore, the heat transfer mechanism can be excluded as the main reason behind the improvement in solidification when vibrations are applied. Both experimental and theoretical results show an enhancement in heat transfer which correlate qualitativally. / Thesis (PhD)--University of Pretoria, 2014. / tm2015 / Mechanical and Aeronautical Engineering / PhD / Unrestricted