Chan Kai Yam. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2001. / Includes bibliographical references (leaves 80-82). / Abstracts in English and Chinese. / Chapter 1 --- Introduction --- p.1 / Chapter 1.1 --- Parameter Identification in Heat Conduction Systems --- p.1 / Chapter 1.2 --- Inverse Problems --- p.3 / Chapter 1.3 --- Challenges in Inverse Problems --- p.6 / Chapter 2 --- Tools in Parameter Identification --- p.9 / Chapter 2.1 --- Output Least Squares Method --- p.10 / Chapter 2.2 --- Tikhonov Regularization --- p.11 / Chapter 2.3 --- Our Approach --- p.14 / Chapter 3 --- Numerical Implementations --- p.20 / Chapter 3.1 --- Finite Element Discretization and Its Convergence --- p.20 / Chapter 3.2 --- Steepest Descent Method --- p.22 / Chapter 3.3 --- Multigrid Techniques --- p.26 / Chapter 4 --- Numerical Experiments --- p.29 / Chapter 4.1 --- One Dimensional Examples --- p.30 / Chapter 4.1.1 --- Selection of mk --- p.31 / Chapter 4.1.2 --- Selection of nk --- p.34 / Chapter 4.1.3 --- Selection of Number of Levels in the Coarse Grid Correction Step --- p.37 / Chapter 4.1.4 --- Convergence with Different Regularization Pa- rameters γ --- p.39 / Chapter 4.1.5 --- Convergence with Different Initial Guesses --- p.42 / Chapter 4.1.6 --- Comparisons between MG and SG Methods --- p.44 / Chapter 4.1.7 --- Comparisons between MG and RMG Methods --- p.46 / Chapter 4.1.8 --- More Examples --- p.49 / Chapter 4.1.9 --- Coarse Grid Correction in Another Approach --- p.60 / Chapter 4.2 --- Two Dimensional Examples --- p.71 / Chapter 4.3 --- Conclusions --- p.78 / Bibliography --- p.80

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Thesis (M.S.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 1979. / MICROFICHE COPY AVAILABLE IN ARCHIVES AND ENGINEERING. / Includes bibliographical references. / by James R. Rinderle. / M.S.

O presente trabalho utiliza o método Design Construtal para desenvolver o estudo numérico de uma configuração de caminhos de alta condutividade de geometria trifurcada que minimiza a resistência ao fluxo de calor, quando a área do caminho trifurcado é mantida constante. O objetivo deste trabalho é o estudo da influência da geometria sobre o desempenho térmico do sistema bem como a otimização do mesmo, assim obtendo uma configuração que minimiza a resistência térmica para cada condição imposta. São apresentadas as considerações e hipóteses utilizadas para a análise, obtendo a equação do calor regente e as condições de contorno do problema, bem como a função objetivo. Para a solução numérica da equação da condução do calor, é utilizado o software MATLAB ®, especificamente as ferramentas PDETOOL, Partial Differential Equations Tool, e GA, Algoritmo Genético. A resistência térmica é minimizada para cada grau de liberdade. A cada nível de otimização, a influência do grau de liberdade em questão é estudada, obtendo um mapeamento da importância de cada grau de liberdade sobre o sistema trifurcado. Também são obtidas as configurações ótimas para diferentes frações de área. Posteriormente, é estudado o comportamento da configuração ótima do sistema para diferentes temperaturas do final das bifurcações do sistema, mostrando que, para as temperaturas estudadas neste trabalho, a configuração ótima não se altera, apenas a resistência térmica, com a alteração na temperatura do sumidouro direito sendo mais influente sobre essa, seguida do sumidouro central e, por fim, do sumidouro esquerdo. Finalmente, este trabalho mostra, com esses resultados, que a geometria ótima é aquela que melhor distribui as imperfeições do sistema, de acordo com o princípio da ótima distribuição das imperfeições e, também, possui robustez quanto às pequenas imperfeições inseridas no sistema. / The present work employs Constructal Design method to develop a numerical study of a triforked high conductivity pathway that minimizes the heat flow resistance when the triforked pathway area is kept constant. The objective of this work is the study of the influence of the geometry over the thermal performance of the system as well as the optimization of the latter, thus obtaining a configuration that minimizes the thermal resistance for each imposed condition. The considerations and hypothesis for the analysis are shown, obtaining a reigning heat equation and boundary conditions for the system, as well as the objetctive function (minimization of the maximum temperature). For the numerical solution of the heat conduction equation, it is utilized MATLAB ® software, specifically the PDETOOL, Partial Differential Equations Tool, and GA, Genetic Algorithm, toolboxes. The thermal resistance is minimized for every degree of freedom. In each level of optimization, the influence of the degree of freedom in question is studied, obtaining a mapping of the importance of each degree of freedom over the performance of the triforked pathway. Optimal configurations are also obtained for different area fractions. Posteriorly, the behavior of the optimal geometry is studied for different temperatures of the branches of the system. Results show that, for the temperatures studied in this work, the optimal configuration does not change, only the thermal resistance, with the increase of temperature of the right sink being more influential over it, followed by the temperature of the middle sink and, at last, the temperature of the left sink. Finally, this work shows, with these results, that the optimal geometry is the one that better distributes the imperfections of the systems, which is in accordance to the principle of the optimal distribution of imperfections, while possessing a certain robustness over small imperfections inserted in the system.

The overall goal of this work is to provide a systematic methodology by which the difficulties associated with the inverse heat conduction problem (IHCP) can be resolved. To this end, two inverse heat conduction methods are presented. First, a space-marching IHCP method (discrete space, discrete time) utilizing a Gaussian low-pass filter for regularization is studied. The stability and accuracy of this inverse prediction is demonstrated to be more sensitive to the temporal mesh than the spatial mesh. The second inverse heat conduction method presented aims to eliminate this feature by employing a global time, discrete space inverse solution methodology. The novel treatment of the temporal derivative in the heat equation, combined with the global time Gaussian low-pass filter provides the regularization required for stable, accurate results. A physical experiment used as a test bed for validation of the numerical methods described herein is also presented. The physics of installed thermocouple sensors are outlined, and loop-current step response (LCSR) is employed to measure and correct for the delay and attenuation characteristics of the sensors. A new technique for the analysis of LCSR data is presented, and excellent agreement is observed between this model and the data. The space-marching method, global time method, and a new calibration integral method are employed to analyze the experimental data. First, data from only one probe is used which limits the results to the case of a semi-infinite medium. Next, data from two probes at different depths are used in the inverse analysis which enables generalization of the results to domains of finite width. For both one- and two-probe analyses, excellent agreement is found between the actual surface heat flux and the inverse predictions. The most accurate inverse technique is shown to be the calibration integral method, which is presently restricted to one-probe analysis. It is postulated that the accuracy of the global time method could be improved if the required higher-time derivatives of temperature data could be more accurately measured. Some preliminary work in obtaining these higher-time derivatives of temperature from a voltage-rate interface used in conjunction with the thermocouple calibration curve is also presented.

The heat dissipation and thermal performance of ventilated brake discs strongly depends on the aerodynamic characteristics of the air flow through the rotor passages. In this thesis, the thermal convection is analyzed using an analytical method, and the velocity distribution, temperature contours and Nusselt number are determined. Then numerical models for different rotors, pillar post rotors and vane rotors are generated and numerical simulations are conducted to determine the desired parameters. To analyze more realistic vane and pillar post rotor models, commercial CFD software packages, Fluent and Gambit, are used to simulate the heat flux rate, air flow rate, velocity distributions, temperature contours, and pressure distributions inside the rotors. Furthermore, sensitivity studies have been performed, to determine the effects of a different number of vanes or pillar posts, inner and outer radii and various angles of vanes. To automate the tedious and repetitive design process of the disc rotor, a design synthesis framework, iSIGHT, is used to integrate the geometrical modeling using GAMBIT and numerical simulations based on FLUENT. Through this integrated design synthesis process, the disc rotor geometrical optimization is performed using design of experiment studies. / UOIT

The low thermal conductivity of gallium arsenide compared to silicon results in self-heating effects in GaAs MESFETs that limit the electrical performance of such devices for high power applications. To date, analytical thermal models of self heating in GaAs MESFETs are based on the assumption of a uniformly heated channel. This thesis presents a two dimensional analysis of the electrothermal effect of this device based on the two dimensional power density distribution in the channel under various bias conditions. The numerical simulation is performed using the finite difference technique. The results of the simulation of an isothermal MESFET without heat effects is compared with various one dimensional analytical models in the literature. Electro thermal effects into the two-dimensional isothermal MESFET model allowed close examination of the temperature profile within the MESFET. The large gradient in power distribution results in a localized heat source within the channel which increases the overall channel temperature, which shows that the assumption of a uniformly heated channel is erroneous, and may lead to an underestimation of the maximum channel temperature. / Graduation date: 1992

The performance of some polymeric materials is profoundly affected by long-term exposure to moisture during service. This poses problems for high precision and/or load bearing components in engineering applications where moisture-induced changes in mechanical properties and dimensional stability could compromise the reliability of the device or structure. In addition to external factors such as moisture, the material properties are also evolving due to inherent structural relaxation within the polymeric material through a process known as physical aging. Based on the current knowledge of both mechanisms, they have opposite effects on material properties. The common approach to studying the effects of moisture is to expose the polymeric material to combined moisture and heat, also referred to as hygrothermal conditions. The application of heat not only increases the rate of moisture diffusion but also accelerates physical aging processes which would otherwise be very slow. In spite of this coupled response, nearly all hygrothermal studies ignore physical aging in their investigations due to the complexity of the coupled problem. The goal of this work is to develop a numerical model for simulating the interactive effects of moisture diffusion and physical aging in a glassy polymer. The intent is to develop a capability that would also allow one to model these effects under various mechanical loading and heat transfer conditions. The study has chosen to model the response of polycarbonate/acrylonitrile-butadiene-styrene (PC/ABS), which is a glassy polymer blend that has very similar behaviour to polycarbonate. In this study, a comprehensive approach which considers four physical mechanisms – structural mechanics, moisture diffusion, heat conduction, and physical aging – has been applied. The most current analytical models in the literature usually attempt to model two or three coupled physical phenomena. To develop the four coupled phenomena model, the current work has undertaken an extensive scope of work involving experimental characterization and finite element modeling. In the experimental part of this work, seven sets of different tests were conducted to characterize the behaviour of PC/ABS exposed to moisture diffusion and accelerated physical aging. These experiments provided a comparative study between the effects of physical aging and moisture diffusion on the material’s behaviour; and at the same time, provided data for the numerical modeling. The dual glass transition temperatures (Tg) of the material were determined using two techniques: dynamic mechanical analysis (DMA) and thermo-mechanical analysis (TMA). The DMA tests provided data for studying the effects of hygrothermal aging on the Tg’s of the material and were also useful for mechanical tests such as creep and stress relaxation performed using the DMA. The Tg’s obtained using the TMA were also required for physical aging experiments using the dilatometry mode of TMA. Structural relaxation of the blend was studied by aging the material at 80 °C for 7 aging times in the TMA. These experiments gave an insight into the volume relaxation behaviour of the blend at a constant temperature. Specific heat capacity of the PC/ABS blend was also measured using another thermal analysis technique; i.e., differential scanning calorimeter (DSC), before and after test specimens were exposed to hygrothermal aging for 168 hours. The interactive effects of physical aging and moisture diffusion on the moisture uptake of the material were studied using gravimetric experiments performed at 5 different hygrothermal conditions. The experimental results were used to determine the coefficient of diffusion as well as the equilibrium moisture uptake of the samples. Furthermore, the effects of both moisture diffusion and physical aging on the mechanical behaviour of the polymer blend were investigated using stress relaxation tests. The comparison of the results of the tests performed on un-aged specimens with those of thermally and hygrothermally aged samples showed how physical aging effects competed with moisture diffusion. Also, the coefficient of hygroscopic expansion of the PC/ABS blend was determined using a so-called TMA/TGA technique. The numerical modeling of the four-coupled physics was achieved using the governing equations in the form of partial differential equations. Modeling was performed using the commercial finite element software package, COMSOL Multiphysics®. First, the uncoupled physical mechanisms of structural mechanics, moisture diffusion, and heat conduction were modeled separately to investigate the validity of the PDEs for each individual phenomenon. The modeling of the coupled physics was undertaken in two parts. The three coupled physics of structural mechanics, moisture diffusion, and heat conduction was first simulated for a gas pipe having a linear elastic behaviour. The comparison of the results with similar analysis available in the literature showed the capability of the developed model for the analysis of the triple coupled mechanisms. The second part modeled the four coupled phenomena by incorporating the experimentally determined coupling coefficients. In the developed numerical model, the material behaviour was considered to be linear viscoelastic, which complicated the model further but provided more realistic results for the behaviour of the polymer blend. Moreover, an approximation method was proposed for estimating the coupling coefficients that exist between different coupled physics in this study. It was also suggested that the anomalous moisture diffusion in the material can be modeled using a time varying boundary condition. Finally, the model was successfully verified and demonstrated using test case studies with thin thermoplastic plates. The proposed four-coupled physics model was able to predict with good accuracy the deflection of thin thermoplastic plates under bending for a set of hygorthermal test condition.

Baigiamajame magistro darbe nagrinėjamos OpenMP, UPC, MPI ir BSP lygiagrečiojo programavimo technologijos sprendžiant dvimatį šilumos laidumo uždavinį lygiagrečiuoju Jakobio iteraciniu metodu. Kiekvienai technologijai sudaromi lygiagretieji algoritmai, aptariamas jų realizacijos sudėtingumas programuotojo požiūriu ir efektyvumas skirtingose kompiuterių architektūrose. Dabą sudaro 6 dalys: įvadas, technologijų apžvalga, šilumos laidumo uždavinys, programų realizacija, rezultatų palyginimas, išvados, literatūra. Darbo apimtis – 38 p. teksto be priedų, 9 paveikslėliai, 3 lentelės, 10 bibliografinių šaltinių. / In this thesis, we consider OpenMP, UPC, MPI and BSP parallel programming technologies - solving two dimensional heat equation, using parallel Jacobi iterative method. Parallel algorithms are constructed and implemented for each technology. Their effectiveness in different computer architectures is discussed as well as the complexity of different implementations from programmer’s point of view. Thesis consists of 6 parts: introduction, technology overview, heat conduction problem, program implementations, comparison of the results, conclusions and references. Thesis consist of: 38 p. text without appendixes, 9 pictures, 3 tables, 10 bibliographical entries.

Study of pseudotachylytes (PT) (frictional melts) can provide information on the physical and chemical conditions at the earthquake source. This study examines the influence of asperityscale fault dynamics on asperity temperature distribution, and therefore, the potential for frictional melting to occur. Frictional melting occurs adiabatically, and is initiated between opposing asperity tips during fault slip. Our model considers 2-D heat conduction in elastic, isotropic, hemispherical asperities, with temperature dependent thermal properties. The only heat source is a point heat flux pulse at the asperity tip. The non-linear problem was solved using the -form of Newton-Kantorovich procedure coupled with the -form of Douglas-Gunn two level finite difference scheme, while the linear problem required only the latter method. Results for quartz and feldspar indicate that peak temperatures can reach melting point values for typical asperity sizes (1-100 mm), provided that contact (frictional) shear stress is sufficiently high. For any asperity size, the temperature distribution peak becomes insignificant by the time it reaches the asperity center. These results imply that much of asperity scale melting is highly localized, which may explain why most PT veins in the field are usually very thin. However, in some cases, successive asperity encounters may generate temperature increases large enough to trigger the massive melting inferred from typical PT exposures. Significant differences were observed between the results of the linear and nonlinear models.