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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.

Advances in microelectronics and nanotechnology have generated tremendous interest in the non-Fourier regimes of heat conduction, where the conventional theories based on local equilibrium no longer apply. The non-Fourier regimes include small length scales, where the medium can no longer be treated using bulk properties due to ballistic transport, and short time scales, on the order of the relaxation time of heat carriers, such as in short pulse laser heating. One of the objectives of this thesis is to clarify some misunderstandings in hyperbolic heat equation (HHE), commonly thought as a remedy of Fourier's law at small time scales. The HHE is analyzed from the stand point of statistical mechanics with an emphasis on the consequences of assumptions applied to the Boltzmann transport equation (BTE) when deriving the HHE. In addition, some misperceptions of the HHE, caused by a few experiments and confusion with other physical phenomena, are clarified. It is concluded that HHE should not be interpreted as a more general equation governing heat transport because of several fundamental limitations. The other objective of this thesis is to introduce radiation entropy to the equation of phonon radiative transport (EPRT) for understanding the heat transfer mechanism on a fundamental level which can be applied to both diffusion and ballistic heat conduction in dielectric solids. The entropy generation due to phonon transport is examined along with the definition of a phonon brightness temperature, which is direction and frequency dependent. A better understanding of non-Fourier heat conduction will help researchers and engineers to choose appropriate theories or models in analyzing thermal transport in nanodevices.

[pt] Em geral, as varetas combustíveis de reatores do tipo LMFBR consistem de pastilhas de combustível encapsuladas em tubos de revestimento. Externamente ao tubo de revestimento, um arame é enrolado, na forma de um helicoidal, para atuar como espaçador. Distorções nas distribuições da temperatura na vareta e fluxo de calor no revestimento podem ser provocadas por variações angulares nos coeficientes de troca de calor entre a pastilha e a superfície interna do revestimento e entre o revestimento, ovalização do tubo de revestimento e presença do arame espaçador. Estas distribuições podem ser afetadas, ainda, por efeitos operacionais, tais como densificação, reestruturação e inchamento do combustível. O presente trabalho consiste no desenvolvimento de um programa para análise dos fatores geométricos, acoplados aos fatores operacionais, no desempenho térmico de varetas combustíveis nucleares, em regime permanente. / [en] Generally, LMFBR fuel rods consist of fuel pellets encapsulated in cladding tubes. These tubes are wrapped by a helical wire, working as a spacer. Distortions in the rod temperature distribution and in the external heat flux can be generated by angular variations in the local heat transfer coefficients due to the wire, by excentricity between pellet and clad or by’ovalization of the cladding tube. Also, the temperature distribuitions can be affected by fuel desensification, reestructuring and swelling. The present work consists of the development of a computer code in order to analyse the fuel rod performance as function of geometrical and operational effects, in steady state regime.

Neste trabalho apresenta-se uma discussão geral sobre problemas inversos, problemas mal-postos c técnicas de regularização, visando sua aplicabilidade em problemas térmicos. Métodos numéricos especiais são discutidos para a solução de problemas que apresentam instabilidade em relação aos dados. Tais métodos baseiam-se na utilização de restrições ou informações adicionais sobre a solução procurada. O problema de determinação da condição inicial da equação do calor é resolvido numericamente através destas técnicas, particularmente a regularização de Tikhonov e o príncipio da máxima entropia conectados ao príncipio da discrepância de Morozov são utilizados. / In this work we present a general discussion on invcrse problems, ill-posed problems and regularization techniqucs, applying these techniques to thermal problcms. Special numerical methods are discusscd in order to solve problerns for which the solution is unstable under data perturbations. Such methods are based on the utilization of restrictions or additional information on thc solution. The problern of determining the initial condition of thc heat equation is numerically solved beyond thesc techniques, particularly thc T ikhonov regularization and thc maximum entropy principie connected to thc Morozov's discrepancy principie are used.

O presente trabalho trata da modelagem da condução de calor transiente com geração de calor em meios heterogêneos, e tem o objetivo de desenvolver um modelo multiescala adequado a esse fenômeno. Já existem modelos multiescala na literatura relacionados ao problema proposto, e que são válidos para os seguintes casos: (a) o elemento de volume representativo tem tamanho desprezível quando comparado ao comprimento característico macroscópico (e como consequência, a microescala tem inércia térmica desprezível); ou (b) a geração de calor é homogênea na microescala. Por outro lado, o modelo proposto nesta tese, o qual é desenvolvido utilizando uma descrição variacional do problema, pode ser aplicado a elementos de volume representativos finitos e em condições em que a geração de calor é heterogênea na microescala. A discretização temporal (diferenças finitas) e as discretizações espaciais na microescala e na macroescala (método dos elementos finitos) são apresentadas em detalhes, juntamente com os algoritmos necessários para implementar a solução do problema. Nesta tese são apresentados casos numéricos simples, procurando verificar não só o modelo teórico multiescala desenvolvido, mas também a implementação feita. Para tanto, são analisados, por exemplo, (a) casos em que considera-se a microescala um material homogêneo, tornando possível a comparação da solução multiescala com a solução convencional (uma única escala) pelo método dos elementos finitos, e (b) um caso em um material heterogêneo para o qual a solução completa, isto é, modelando diretamente os constituintes no corpo macroscópico, é obtida, tornando possível a comparação com a solução multiescala. A solução na microescala para vários casos analisados nesta tese sofre grande influência da inércia térmica da microescala. Para demonstrar o potencial de aplicação do modelo multiescala, simula-se a cura de um elastômero carregado com negro de fumo. Embora a simulação demonstre que a inércia térmica não precise ser considerada para esse caso em particular, a aplicação da presente metodologia torna possível modelar a cura do elastômero diretamente sobre a microescala, uma abordagem até então não utilizada no contexto de métodos multiescala. Essa metodologia abre a possibilidade para futuros aperfeiçoamentos da modelagem do estado de cura. / This work deals with the modeling of transient heat conduction with heat generation in heterogeneous media, and its objective is to develop a proper multiscale model for this phenomenon. There already exist multiscale models in the literature related to this proposed problem, and which are valid for the following cases: (a) the representative volume element has a negligible size when compared to the characteristic macroscopic size (and, as a consequence, the microscale has a negligible thermal inertia); or (b) the heat generation is homogeneous at the microscale. On the other hand, the model proposed in this thesis, which is developed using a variational description of the problem, can be applied to finite representative volume elements and in conditions in which the heat generation is heterogeneous at the microscale. The time discretization (finite difference) and the space discretizations at both the microscale and the macroscale (finite element method) are presented in details, together with the algorithms needed for implementing the solution of the problem. In this thesis, simple numerical cases are presented, aiming to verify not only the theoretical multiscale model developed, but also its implementation. For this, it is analyzed, for instance, (a) cases in which the microscale is taken as a homogeneous material, making it possible the comparison of the multiscale solution with the conventional solution (one single scale) by the finite element method, and (b) a case in a heterogeneous material for which the full solution, that is, modeling all constituents directly on the macroscale, is obtained, making it possible the comparison with the multiscale solution. The solution at the microscale for several cases analyzed in this thesis suffers a large influence of the microscale thermal inertia. To demonstrate the application potential of the multiscale model, the cure of a carbon black loaded elastomer is simulated. Although the simulation shows that the thermal inertia does not have to be considered for this case in particular, the application of the present methodology makes it possible to model the cure of the elastomer directly at the microscale, an approach not used in multiscale methods context until now. This methodology opens the possibility for future improvements of the state of cure modeling.

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.

Made available in DSpace on 2014-06-11T19:35:41Z (GMT). No. of bitstreams: 0 Previous issue date: 2007-01Bitstream added on 2014-06-13T18:48:27Z : No. of bitstreams: 1 correa_va_dr_guara.pdf: 949805 bytes, checksum: 5d0ebae9cf9395efc83588da395f5ab9 (MD5) / Universidade Estadual Paulista (UNESP) / Com a evolução dos sistemas de computação simbólica ampliou-se a capacidade de modelagem e análise de problemas provenientes de equações diferenciais. Propõe-se a resolução da equação da condução de calor em regimes permanente e transiente para uma geometria cilíndrica com condições de contorno convectivas de forma analítica e numérica utilizando o software de computação simbólica Maple. Para este propósito serão empregados para a resolução analítica, o método de separação de variáveis e para a resolução numérica, o método das diferenças finitas com o esquema Crank- Nicolson e explícito. Os resultados obtidos das resoluções analíticas e numéricas, para algumas situações avaliadas são comparadas. As vantagens computacionais da utilização do software Maple são apresentadas. / The evolution of symbolic computation systems enlarges the capacity of modeling and analysis of problems by differential equations. The aim is the resolution of the conduction heat equation in unsteady and steady state for the cylindrical geometry with convective boundary conditions with analytical and numerical solutions using the Maple software. To this results will be used the separated variables method and finite differences to numerical solutions with Crank-Nicolson and explicit schemes. The results obtained for numerical and analytical solutions for some situations it will available and compared. The computational advantages of the Maple software are showed too.

Resumo: Com a evolução dos sistemas de computação simbólica ampliou-se a capacidade de modelagem e análise de problemas provenientes de equações diferenciais. Propõe-se a resolução da equação da condução de calor em regimes permanente e transiente para uma geometria cilíndrica com condições de contorno convectivas de forma analítica e numérica utilizando o software de computação simbólica Maple. Para este propósito serão empregados para a resolução analítica, o método de separação de variáveis e para a resolução numérica, o método das diferenças finitas com o esquema Crank- Nicolson e explícito. Os resultados obtidos das resoluções analíticas e numéricas, para algumas situações avaliadas são comparadas. As vantagens computacionais da utilização do software Maple são apresentadas. / Abstract: The evolution of symbolic computation systems enlarges the capacity of modeling and analysis of problems by differential equations. The aim is the resolution of the conduction heat equation in unsteady and steady state for the cylindrical geometry with convective boundary conditions with analytical and numerical solutions using the Maple software. To this results will be used the separated variables method and finite differences to numerical solutions with Crank-Nicolson and explicit schemes. The results obtained for numerical and analytical solutions for some situations it will available and compared. The computational advantages of the Maple software are showed too. / Orientador: Luiz Roberto Carrocci / Coorientador: Marcio Abud Marcelino / Banca: Petronio Masanobu Tanisho / Banca: Rubens Alves Dias / Banca: Carlos Alberto Chaves / Banca: José Rui Camargo / Doutor

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.