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 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 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.

This project investigated the manufacturing of large diameter welded PTFE rings.This welding process is time consuming and can take over ten hours for one complete weld cycle. Additionally, the welds can have poor quality in the center of the material due to insufficient heating across the weld face. The goal of this research was to address these two issues by analyzing the current process to determine the root cause of weld failures while also determining the feasibility of reducing the weld cycle time. The scope of this thesis was to develop a model to better understand and simulate the current process which could then be used for design future improvements.<div><br></div><div>A MATLAB model of the current process was developed to simulate the transient heating cycle of the most common weld cycle for PTFE currently used by a manufacturer of PTFE seals. The data for the material properties was gathered from the manufacturer test data as well as from Lau et al. (1984). Temperature dependent material properties were used in the program because the PTFE is heated above its melting point during the weld cycle. Because of the complexity of this heat transfer problem, the heat flux in the model was tuned so that it accurately reflected the current process. This is because the goal of this study was not to determine the exact heat fluxas it was unknown, but to develop an accurate model. Thus, the heat flux was assumed and the model was then verified with process data. Results from the model were compared to validation results from a FLIR thermal camera. The model predicted the compared temperatures to within 3.1% error at both 15-minute and 90-minute intervals. Though there are many potential sources of error in the process and the thermal camera measurement, the model was deemed acceptable as a model of the current process. A semi-infinite heat analysis was calculated to simulate a hot plate welding method on the PTFE. This showed that the temperature of the weld face could be raised by 57.275°C. It is believed that a method similar to hot plate welding applied to PTFE could heat the material faster and more evenly than the current process, reducing the weld failures and cycle time.<br></div>

A parallel domain decomposition Laplace transform Boundary Element Method, BEM, algorithm for the solution of large-scale transient heat conduction problems will be developed. This is accomplished by building on previous work by the author and including several new additions (most note-worthy is the extension to 3-D) aimed at extending the scope and improving the efficiency of this technique for large-scale problems. A Laplace transform method is utilized to avoid time marching and a Proper Orthogonal Decomposition, POD, interpolation scheme is used to improve the efficiency of the numerical Laplace inversion process. A detailed analysis of the Stehfest Transform (numerical Laplace inversion) is performed to help optimize the procedure for heat transfer problems. A domain decomposition process is described in detail and is used to significantly reduce the size of any single problem for the BEM, which greatly reduces the storage and computational burden of the BEM. The procedure is readily implemented in parallel and renders the BEM applicable to large-scale transient conduction problems on even modest computational platforms. A major benefit of the Laplace space approach described herein, is that it readily allows adaptation and integration of traditional BEM codes, as the resulting governing equations are time independent. This work includes the adaptation of two such traditional BEM codes for steady-state heat conduction, in both two and three dimensions. Verification and validation example problems are presented which show the accuracy and efficiency of the techniques. Additionally, comparisons to commercial Finite Volume Method results are shown to further prove the effectiveness.

Proper design of high performance industrial heat transfer equipment relies on accurate knowledge and prediction of the thermal boundary conditions. In order to enhance the overall gas turbine efficiency, advancements in cooling technology for gas turbines and related applications are continuously investigated to increase the turbine inlet temperature without compromising the durability of the materials used. For detailed design, local distributions are needed in addition to bulk quantities. Detailed local distributions require advanced experimental techniques whereas they are readily available using numerical tools. Numerical predictions using a computational fluid dynamics approach with popular turbulence models are benchmarked against a semi-empirical correlation for the friction in a circular channel with repeated-rib roughness to demonstrate some shortcomings of the models used. Numerical predictions varied widely depending on the turbulence modelling approach used. The need for a compatible experimental dataset to accompany numerical simulations was discussed. An exact, closed-form analytical solution to the enhanced lumped capacitance model is derived. The temperature evolution in a representative 2D turbulated surface is simulated using Fluent to validate the model and its exact solution. A case including an interface contact resistance was included as well as various rib sizes to test the validity of the model over a range of conditions. The analysis was extended to the inter-rib region to investigate the extent and magnitude of the influence of the metallic rib features on the apparent heat transfer coefficients in the inter-rib region. It was found that the thermal contamination is limited only to the regions closest to the base of the rib feature. An experimental setup was developed, capable of measuring the local heat transfer distributions on all four channel walls of a rectangular channel (with aspect ratios between 1 and 5) at Reynolds numbers up to 150,000. The setup utilizes a transient thermochromic liquid crystals technique using narrow band crystals and a four camera setup. The setup is used to test a square channel with ribs applied to one wall. Using the transient thermochromic liquid crystals technique and applying it underneath high conductivity, metallic surface features, it is possible to calculate the heat transfer coefficient using a lumped heat capacitance approach. The enhanced lumped capacitance model is used to account for heat conduction into the substrate material. Rohacell and aluminum ribs adhered to the surface were used to tandem to validate the hybrid technique against the standard technique. Local data was also used to investigate the effect of thermal contamination. Thermal contamination observed empirically was more optimistic than numerical predictions. Traditional transient thermochromic liquid crystals technique utilizes the time-to-arrival of the peak intensity of the green color signal. The technique has been extended to utilize both the red and green color signals, increasing the throughput by recovering unused data while also allowing for a reduction in the experimental uncertainty of the calculated heat transfer coefficient. The over-determined system was solved using an un-weighted least squares approach. Uncertainty analysis of the multi-color technique demonstrated its superior performance over the single-color technique. The multi-color technique has the advantage of improved experimental uncertainty while being easy to implement.

The company Kanthal produces electric heating elements that require high temperature treatment in one production step. In this process step, called sintering, the amount of heat received by the sintered material is in direct correlation to the product’s outcome.  It is therefore of interest for the company to gather information about how heat transfer happens in an electrical furnace. This study examines two different possible scenarios of how the heat transfer in the furnace could look like and which amount of heat the sintered material would receive. The relation between a gaseous ambience at a certain temperature and the temperature an object submerged into this ambience is assuming is studied in the process called "transient heat conduction".  Two models were built in Matlab, representing transient heat conduction effects on two different geometries: a plane wall and a short cylinder.  It could be shown that transient heat conduction effects turned out differently for the two models. The conclusion drawn from the results was that the wall model was susceptible to horizontal heat transfer effects, whereas the cylinder model was affected from all directions equally. Further, an analysis of the heat transfer channels within the furnace revealed that the heat leakage through the furnace muffle edges, which are in contact with air, causes a multiple in heat loss compared to the overall heat leakage.

Optically-transparent solids have a significant role in many emerging topics of fundamental and applied research, in areas related to Applied Optics and Photonics. In the functional devices based on them, the presence of ‘time-varying temperature fields’ critically limit their achievable performance, when used particularly for high power laser-related tasks such as light-generation, light-amplification, nonlinear-harmonic conversion etc. For optimization of these devices, accurate knowledge of the material thermal parameters is essential. Many optical and non-optical methods are currently in use, for the reliable estimation of the thermal parameters. The thermal diffusivity is a key parameter for dealing with ‘transient heat transport’ related problems. Although its importance in practical design for thermal management is well understood, its physical meaning however continues to be esoteric. The present effort concerns with a few investigations on the “Optical interrogation of ‘transient thermal conduction’ in dielectric solids”. In dielectric solids, the current understanding is that the conductive heat transport occurs only through phonons relevant to microscopic lattice vibrations. Introducing for the first time, a virtual linear translator motion as the basis for heat conduction in dielectric materials, the present investigation discusses an alternative physical mechanism and a new analytical model for the transient heat conduction in dielectric solids. The model brings into limelight a ‘new law of motion’ and a ‘new quantity’ which can be defined at every point in the material, through which time-varying heat flows resulting in time-varying temperature. Physically, this quantity is a measure for the linear translatory motion resulting from transient heat conduction. For step-temperature excitation it bears a simple algebraic relation to the thermal diffusivity of the material. This relationship helps to define the thermal diffusivity of a dielectric solid as the “translatory motion speed” measured at unit distance from the heat source. A novel two-beam interferometric technique is proposed and corroborated the proposed concept with significant advantages. Two new approaches are introduced to estimate thermal diffusivity of optically transparent dielectric solid; first of them involves measurement of the position dependent velocity of isothermal surface and second one depend on the measurement of position dependent instantaneous velocity of normalized moving intensity points. A ‘new mechanism’ is proposed and demonstrated to visualize, monitor and interrogate optically, the ‘linear translatory motion’ resulting from the transient heat flow due to step- temperature excitation. Two new approaches are introduced, first one is ‘mark’ and ‘track’ approach, it involves a new interaction between sample supporting unsteady heat flow with its ambient and produces optical mark. Thermal diffusivity is estimated by tracking the optical mark. Second one involves measurement of instantaneous velocity of optical mark for different step-temperature at a fixed location to estimate thermal diffusivity. A new inverse method is proposed to estimate thermal diffusivity and thermal conductivity from the volumetric specific heat capacity alone through thought experiment. A new method is proposed to predict volumetric specific heat capacity more accurately from thermal diffusivity.