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.

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.

Orientador: Carlos Alberto Carrasco Altemani / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-16T09:22:29Z (GMT). No. of bitstreams: 1 Alves_ThiagoAntonini_D.pdf: 12931422 bytes, checksum: b3858d05581229381f7d14684d29e979 (MD5) Previous issue date: 2010 / Resumo: A transferência de calor conjugada por convecção forçada e condução de três aquecedores 2D montados rentes ou protuberantes na placa inferior (substrato) de um canal de placas paralelas foi investigada numericamente em regime permanente. Uma taxa uniforme de geração de calor foi assumida em cada aquecedor e seu resfriamento ocorreu por meio de um escoamento forçado de ar com propriedades constantes em regime laminar. Na entrada do canal, os perfis de velocidade e de temperatura do escoamento eram uniformes. Este problema está relacionado ao resfriamento de componentes eletrônicos montados numa placa de circuito impresso. Para um substrato adiabático, o resfriamento dos aquecedores ocorre apenas por convecção forçada. Para um substrato condutivo, dois mecanismos para a transferência de calor dos aquecedores para o escoamento fluido foram considerados. Um, por convecção forçada, diretamente das superfícies dos aquecedores em contato com o escoamento e outro, por condução através das interfaces substrato-aquecedor. As equações de conservação foram resolvidas dentro de um domínio único, que englobou as regiões sólidas e de fluido, através de um procedimento acoplado. Nesta Tese foi proposto um descritor invariante do processo conjugado de transferência de calor por convecção forçada e condução, por meio de coeficientes de influência conjugados g+, agrupados numa matriz quadrada G+. Com este descritor, a temperatura de cada aquecedor foi determinada a partir de taxas arbitrárias de geração de calor nos aquecedores. Os resultados foram obtidos para números de Reynolds na faixa de 600 a 1900, correspondendo a velocidades médias de entrada do ar no canal na faixa de 0,5 m/s a 1,5 m/s. Os efeitos da razão entre a condutividade térmica do substrato e a do ar foram estudados na faixa de 0 (substrato adiabático) a 80, uma faixa típica de materiais de circuito impresso. A altura dos aquecedores variou entre 0 (aquecedores rentes) e 35% em relação à altura do canal, sendo que em todos os casos o aquecedor possuía uma condutividade térmica 500 vezes maior do que a do ar. / Abstract: The conjugate heat transfer by forced convection and conduction from three 2D heaters either flush mounted or protruding from the lower plate (substrate) of a parallel plates channel was investigated numerically under steady state conditions. A uniform heat generation rate was assumed in each heater and the cooling was performed by means of a forced air flow with constant properties in the laminar regime. At the channel entrance the flow velocity and temperature profiles were assumed uniform. This problem is related to the cooling of electronic components mounted on a circuit board. For an adiabatic substrate, the heaters are cooled only by forced convection. For a conductive substrate, two mechanisms were considered for the heat transfer from the heaters to the fluid flow. One, by forced convection, directly from the heaters surfaces in contact with the flow, and the other, by conduction through the heaters-substrate interfaces. The conservation equations were solved through a coupled procedure within a single calculation domain comprising the solid and fluid regions. In this Thesis an invariant descriptor of the conjugate forced convection and conduction heat transfer was proposed by means of conjugate influence coefficients g+ which were grouped in a square matrix G+. With this descriptor, the temperature of each heater was obtained from an arbitrary distribution of the heat generation rate in the heaters. The results were obtained for Reynolds numbers Re in the range from 600 to 1900, corresponding to average air velocities in the channel entrance from 0.5 m/s to 1.5 m/s. The ratio of the substrate plate thermal conductivity relative to that of the air was considered in the range from 0 (adiabatic substrate) to 80, typical of printed circuit boards. The heaters' height in the channel ranged from 0 (flush mounted) to 35 % of the channel height, while their thermal conductivity was always assumed equal to 500 that of the air. / Doutorado / Termica e Fluidos / Doutor em Engenharia Mecânica

Orientador: Carlos Alberto C. Altemani / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecanica / Made available in DSpace on 2018-07-22T23:26:55Z (GMT). No. of bitstreams: 1 Martins_EduardoBalster_D.pdf: 10914423 bytes, checksum: ecaf97a75c72546a03b89a1659ad36c3 (MD5) Previous issue date: 1997 / Resumo: Uma investigação do resfriamento conjugado de placas aquecidas suspensas numa cavidade preenchida com ar foi realizada. Duas configurações da cavidade em estudo foram consideradas. Numa delas havia uma única placa, suspensa verticalmente, em posição central, no interior da cavidade. Na outra configuração havia duas placas idênticas suspensas em posições simétricas com relação ao plano médio vertical da cavidade. As paredes laterais e inferior da cavidade eram de material isolante. A parede superior era uma placa isotérmica de material condutor. Um aparato experimental foi construído e a condutância térmica global entre cada placa e o ar ambiente fora da cavidade foi obtida sob condições de regime permanente. O número de Rayleigh da cavidade encontrava-se dentro da faixa de regime laminar para todos os ensaios realizados. Os resultados experimentais foram comparados com os resultados de simulações bidimensionais. Os mecanismos conjugados de condução, convecção e radiação térmica foram incluídos no modelo de análise térmica da cavidade. A solução das equações de conservação foram obtidas numericamente por meio de uma combinação de um método de volumes finitos com o método das radiosidades. Os efeitos de sombreamento provocados pela presença das placas no interior da cavidade foram levados em consideração. Das simulações realizadas foram obtidas as condutâncias térmicas globais para as placas, as frações de contribuição de cada modo de transferência de calor no resfriamento de cada placa e da cavidade e as temperaturas no interior da cavidade / Abstract: An investigation of the conjugate heat transfer tTomheated plates suspended in an air filled enclosure was performed. Two distinct configurations for the enclosure were considered. In the first, there was only one heated plate inside the enclosure, suspended in the central position. In the other configuration, there were two heated plates suspended inside the enclosure. They were symmetrically located with respect to the enclosure's vertical midplane. The side and the bottom walls of the enclosure were insulated, but the top wall was a conductive isothennal plate. An experimental apparatus was built and the global therrnal conductance of the heated plates to the ambient air outside the enclosure was obtained under steady state conditions. The Rayleigh number inside the enclosure was within the larninar range. The experimental results were compared with those of a two-dimensional simulation. The conjugate mechanisms of conduction, convection and therrnal radiation were included in the model for the thennal analysis of the enclosure. The solution of the conservation equations was obtained numerically via a combination of the finite volumes and the radiosities methods. The blockage effect of the heated plate to thermal radiation inside the enclosure was taken into account. From this simulation, the global thermal conductance of the heated plate, the distribution of the heat transfer among the three mechanisms, as well as values of the temperature inside the enclosure were obtained. / Doutorado / Termica e Fluidos / Doutor em Engenharia Mecânica

Orientador: Carlos Alberto Carrasco Altemani / Tese (doutorado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-24T04:10:43Z (GMT). No. of bitstreams: 1 MarchiNeto_Ismael_D.pdf: 4845997 bytes, checksum: b5f466a0bc722eba5f754b6c4ef08357 (MD5) Previous issue date: 2014 / Resumo: O resumo poderá ser visualizado no texto completo da tese digital. / Abstract: The abstract is available with the full electronic document. / Doutorado / Termica e Fluidos / Doutor em Engenharia Mecânica

Numerical simulation is used to investigate the accuracy of a direct-contact device for measuring skin-surface temperature. A variation of thermal conductivity of the foam has greater effect on the error rather than a variation of the blood perfusion rate. For a thermal conductivity of zero, an error of 1.5 oC in temperature was identified. For foam pad conductivities of 0.03 and 0.06 W/m-oC, the errors are 0.5 and 0.15 oC. For the transient study, with k=0 W/m-oC, it takes 4,900 seconds for the temperature to reach steady state compared with k=0.03 W/m-oC and k=0.06 W/m-oC where it takes 3,000 seconds. The configuration without the foam and in presence of an air gap between the skin surface and the sensor gives the most uniform temperature profile.

Orientador: Carlos Alberto Carrasco Altemani / Dissertação (mestrado) - Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica / Made available in DSpace on 2018-08-24T09:07:23Z (GMT). No. of bitstreams: 1 Loiola_BrunaRafaella_M.pdf: 2801156 bytes, checksum: 0bbef2296c5a3a938f63b6246554ab2d (MD5) Previous issue date: 2013 / Resumo: A transferência de calor conjugada por convecção forçada-condução de dois aquecedores protuberantes montados na parede inferior (substrato) de um duto retangular foi investigada através de medidas experimentais em laboratório. Potência elétrica era dissipada em resistências embutidas nos aquecedores feitos de alumínio, que eram resfriados em regime permanente por um escoamento forçado de ar no duto. Cada aquecedor transferia calor por convecção diretamente das suas superfícies em contato com o escoamento e por condução para a placa do substrato através da interface comum. Esta condução de calor espalhava na placa do substrato e era transferida por convecção da placa para o escoamento de ar no duto. O resfriamento conjugado dos aquecedores na placa de substrato foi descrito por uma matriz de coeficientes conjugados obtidos por meio de testes experimentais realizados com um aquecedor ativo por vez, em uma faixa do número de Reynolds do escoamento entre 1600 e 6400. Foram utilizadas duas montagens experimentais praticamente idênticas, uma com a placa do substrato de acrílico e a outra, de alumínio. O número de Nusselt adiabático, que é um descritor invariante do processo convectivo de troca de calor, também foi avaliado nos testes com o substrato de acrílico. Os coeficientes conjugados obtidos nestes testes foram então utilizados para prever as temperaturas dos aquecedores em testes adicionais com os dois simultaneamente ativos, sob condições variadas de escoamento e aquecimento. A concordância dessas temperaturas indicou que esses coeficientes são descritores invariantes do resfriamento conjugado dos aquecedores discretos no duto. Simulações numéricas do escoamento e da transferência de calor no duto considerado foram efetuadas com o pacote computacional PHOENICS em um domínio tridimensional semelhante ao duto experimental. Os resultados numéricos obtidos foram comparados com as medidas experimentais / Abstract: Conjugate heat transfer by forced convection-conduction of two protruding heaters mounted on the lower wall (substrate) of a rectangular duct was investigated through experiments in laboratory. Electric power dissipation in the Aluminum heaters¿ embedded resistances was transferred under steady state conditions to forced airflow in the duct. Heat losses from each heater included direct convection from its surfaces in contact with the airflow and conduction to the substrate plate through their common interface. This heat conduction was spread in the substrate plate and eventually transferred by convection from the plate to the airflow in the duct. The heaters¿ conjugate cooling was described by a conjugate matrix with coefficients obtained from experimental tests with a single active heater at a time, in the range of the airflow Reynolds number from 1,600 to 6,400. Two almost identical assemblies were used, one with a Plexiglas plate and the other with Aluminum. The adiabatic Nusselt number, an invariant descriptor of the convective heat transfer, was also evaluated in the tests with the Plexiglas plate. The conjugate coefficients were used to predict the heaters¿ temperatures from additional tests with both active heaters, for arbitrary airflow rates and heaters¿ power dissipation. An agreement of these temperatures indicated that the conjugate coefficients are invariant descriptors of their conjugate cooling. Numerical CFD simulations were performed using the PHOENICS software in a three dimensional domain similar to the experimental assembly. The numerical results were compared to those of the experiments / Mestrado / Termica e Fluidos / Mestra em Engenharia Mecânica

Probability theory is the study of random phenomena. Many dynamical systems with random influence, in nature or artificial complex systems, are better modeled by equations incorporating the intrinsic stochasticity involved. In probability theory, stochastic partial differential equations (SPDEs) generalize partial differential equations through random force terms and coefficients, while stochastic differential equations (SDEs) generalize ordinary differential equations. They are both abound in models involving Brownian motion throughout science, engineering and economics. However, Brownian motion is just one example of a random noisy input. The goal of this thesis is to make contributions in the study and applications of stochastic dynamical systems involving a wider variety of stochastic processes and noises. This is achieved by considering different models arising out of applications in thermal engineering, population dynamics and mathematical finance.<br><div><br></div><div>1. Power-type non-linearities in SDEs with rough noise: We consider a noisy differential equation driven by a rough noise that could be a fractional Brownian motion, a generalization of Brownian motion, while the equation's coefficient behaves like a power function. These coefficients are interesting because of their relation to classical population dynamics models, while their analysis is particularly challenging because of the intrinsic singularities. Two different methods are used to construct solutions: (i) In the one-dimensional case, a well-known transformation is used; (ii) For multidimensional situations, we find and quantify an improved regularity structure of the solution as it approaches the origin. Our research is the first successful analysis of the system described under a truly rough noise context. We find that the system is well-defined and yields non-unique solutions. In addition, the solutions possess the same roughness as that of the noise.<br></div><div><br></div><div>2. Parabolic Anderson model in rough environment: The parabolic Anderson model is one of the most interesting and challenging SPDEs used to model varied physical phenomena. Its original motivation involved bound states for electrons in crystals with impurities. It also provides a model for the growth of magnetic field in young stars and has an interpretation as a population growth model. The model can be expressed as a stochastic heat equation with additional multiplicative noise. This noise is traditionally a generalized derivative of Brownian motion. Here we consider a one dimensional parabolic Anderson model which is continuous in space and includes a more general rough noise. We first show that the equation admits a solution and that it is unique under some regularity assumptions on the initial condition. In addition, we show that it can be represented using the Feynman-Kac formula, thus providing a connection with the SPDE and a stochastic process, in this case a Brownian motion. The bulk of our study is devoted to explore the large time behavior of the solution, and we provide an explicit formula for the asymptotic behavior of the logarithm of the solution.<br></div><div><br></div><div>3. Heat conduction in semiconductors: Standard heat flow, at a macroscopic level, is modeled by the random erratic movements of Brownian motions starting at the source of heat. However, this diffusive nature of heat flow predicted by Brownian motion is not observed in certain materials (semiconductors, dielectric solids) over short length and time scales. The thermal transport in these materials is more akin to a super-diffusive heat flow, and necessitates the need for processes beyond Brownian motion to capture this heavy tailed behavior. In this context, we propose the use of a well-defined Lévy process, the so-called relativistic stable process to better model the observed phenomenon. This process captures the observed heat dynamics at short length-time scales and is also closely related to the relativistic Schrödinger operator. In addition, it serves as a good candidate for explaining the usual diffusive nature of heat flow under large length-time regimes. The goal is to verify our model against experimental data, retrieve the best parameters of the process and discuss their connections to material thermal properties.<br></div><div><br></div><div>4. Bond-pricing under partial information: We study an information asymmetry problem in a bond market. Especially we derive bond price dynamics of traders with different levels of information. We allow all information processes as well as the short rate to have jumps in their sample paths, thus representing more dramatic movements. In addition we allow the short rate to be modulated by all information processes in addition to having instantaneous feedbacks from the current levels of itself. A fully informed trader observes all information which affects the bond price while a partially informed trader observes only a part of it. We first obtain the bond price dynamic under the full information, and also derive the bond price of the partially informed trader using Bayesian filtering method. The key step is to perform a change of measure so that the dynamic under the new measure becomes computationally efficient.</div>

In this thesis an equation of heat conduction including phase and structural changes is derived, involving various boundary conditions. It seems to be the most suitable to calculate the equation by enthalpy method. In this equation not only enthalpy occurs, but also the temperature, and in consequence the relationship between these variables is quite complicated. In this paper I use the values measured or calculated using solidifcation models. The calculation is implemented in Matlab Simulink, which is a very popular blocks scheme in common practice of regulation. The calculation is based on steady state set up with help of experts and as a result, the program could be put into practice. The program calculates the intensity of cooling according to the initial casting speed, casting inlet temperature and the desired temperature curves. The rate of inuence of cooling can be changed according to the given criteria. The thesis compares the surface temperatures and cooling in the case of a predictive controller is or is not applied in the program.