We consider the design of finite element methods for inverse problems with full-field data governed by elliptic forward operators. Such problems arise in applications in inverse heat conduction, in mechanical property characterization, and in medical imaging. For this class of problems, novel finite element methods have been proposed (Barbone et al., 2010) that give good performance, provided the solutions are in the H^1(Ω) function space. The material property distributions being estimated can be discontinuous, however, and therefore it is desirable to have formulations that can accommodate discontinuities in both data and solution. Toward this end, we present a mixed variational formulation for this class of problems that handles discontinuities well. We motivate the mixed formulation by examining the possibility of discretizing using a discontinuous discretization in an irreducible finite element method, and discuss the limitations of that approach. We then derive a new mixed formulation based on a least-square error in the constitutive equation. We prove that the continuous variational formulations are well-posed for applications in both inverse heat conduction and plane stress elasticity. We derive a priori error bounds for discretization error, valid in the limit of mesh refinement. We demonstrate convergence of the method with mesh refinement in cases with both continuous and discontinuous solutions. Finally we apply the formulation to measured data to estimate the elastic shear modulus distributions in both tissue mimicking phantoms and in breast masses from data collected in vivo.

The subject of diploma thesis is design of a testing cabin for high pressure pump testing under low temperature. The objective is to project a cooling system and a cooled testing cabin. Suggested cooling system must be sized to cool down the estimated power and the cabin is supposed to be located inside the existing testbench. There was peroformed an analytical calculation of thermic evaluation, several parts of calculation were verified using ANSYS program simulation. The second section of the thesis is focused mainly on the design, especially on design of testing cabin. The result of diploma thesis is prepared for utilization in Bosch Diesel s.r.o. Jihlava.

Light curve inversion is a standard method to determine shapes, rotation periods and spin axis orientations of asteroids. This method can be extended to determine the size, albedo, thermal inertia and surface roughness parameters of an asteroid by including observations in thermal infrared. A solution of the Heat Conduction Equation (HCE) is necessary to model infrared flux from the asteroid. We analyse the accuracy requirements of the extended method for numerical solution of the HCE. We show that current implementation leads to errors in flux that are substantial. We recommend changes in the current implementation of the HCE solving approach to address the accuracy issues. We discuss uniqueness and stability of the solutions produced by the extended method as well as the accuracy of the determined parameters and their stability. Shapes of asteroids are produced and their physical attributes are determined based on light curve and infrared data.

Modernas empresas buscam a melhoria dos seus sistemas de produção a fim de aumentar a produtividade e a qualidade de produtos. A tecnologia de usinagem com alta velocidade de corte (HSC – High Speed Cutting) permite aumentar as taxas de remoção de material, as tolerâncias dimensionais das partes, assim como a melhoria do acabamento superficial. Esta tecnologia tem sido muito utilizada na área de moldes e matrizes, pois minimiza o problema de tempos de usinagem longos na produção e facilita a obtenção de elevada qualidade, normalmente requerida em produtos injetados/estampados. Atualmente diversos estudos em HSC buscam a compreensão de todos os fatores envolvidos nesta nova tecnologia, a qual ainda apresenta diversas lacunas para o seu domínio completo. Este trabalho apresenta um estudo teórico-experimental da condução de calor nos materiais utilizados na fabricação de moldes e matrizes, submetidos à usinagem com altas velocidades de corte. Os materiais utilizados foram os aços AISI D2 e AISI H13, muito utilizados nas indústrias de moldes e matrizes. Os ensaios foram realizados com fresas de ponta esférica (Ball-Nose) com e sem angulação de hélice e com ângulo de saída neutro, com revestimento de ('TI'AL')N e com uma ferramenta com uma placa de PcBN soldada. A geometria dos corpos-de-prova foi projetada para aproximar-se dos casos reais encontrados na indústria, casos em que superfícies complexas e paredes finas são comumente usinadas em matrizes e moldes. Dois sistemas de resfriamento foram utilizados o ar comprimido e o ar gelado utilizando o princípio de vórtice. Os resultados demonstraram uma pequena variação da temperatura em função dos materiais empregados e das ferramentas utilizadas em todos os testes. Os dois sistemas de resfriamento alternativos à usinagem sem sistema de resfriamento, o ar comprimido e o ar frio, também se mostraram influentes na variação da temperatura, apresentando-se como sistemas capazes de remover o calor no processo durante a usinagem. Os desvios de forma encontrados nos corpos-de-prova devem ser considerados na usinagem de perfis muito precisos. Foram encontrados valores da ordem de 0,05 mm, oriundos da combinação de distorções térmicas e tensões residuais, os quais podem ser signifcativos, por exemplo, na área de matrizaria / Modern industries improve their production systems aiming at increasing productivity and product quality. The high speed cutting (HSC) technology allows increasing material removal rates, workpiece dimensional tolerance and surface finishing as well. Such technology has been extensively used in mold and dies areas, since it minimizes long lead time problems and facilitates high quality machining, normally required in injected/formed products. Nowadays, several studies in HSC search for understanding all aspects involved in that new technology, which still presents many blanks for its complete knowledge. The present work shows a theoretical and experimental study on heat conduction flux in materials applied to mold and die manufacturing, submitted to HSC. It was used AISI D2 and AISI H13, which are very common in mold and die industry. Two types of cylindrical ball nose end milling tool were used in the experiments: coated with ('TI'AL')N and tipped with PcBN. The workpiece geometry was conceived to simulate real cases found in industry, in which complex surfaces and slim walls are commonly machined in molds and dies. Two cooling systems were used in the tests, compressed air and frozen air using vortex principle. Results indicated a small temperature variation as a function of machined materials and tools throughout the tests. Both alternative cooling systems, besides dry machining, compressed air and cool air, also demonstrated to affect temperature variation. They presented themselves as capable of remove heat from the process during the cutting operation. The form deviation found in the workpiece after machining must be considered when machining very precise profiles. Variation values of around 0.05 mm were found, coming from a combination of thermal distortion and residual stress, which could be significant, for example, in die manufacturing area

Modernas empresas buscam a melhoria dos seus sistemas de produção a fim de aumentar a produtividade e a qualidade de produtos. A tecnologia de usinagem com alta velocidade de corte (HSC – High Speed Cutting) permite aumentar as taxas de remoção de material, as tolerâncias dimensionais das partes, assim como a melhoria do acabamento superficial. Esta tecnologia tem sido muito utilizada na área de moldes e matrizes, pois minimiza o problema de tempos de usinagem longos na produção e facilita a obtenção de elevada qualidade, normalmente requerida em produtos injetados/estampados. Atualmente diversos estudos em HSC buscam a compreensão de todos os fatores envolvidos nesta nova tecnologia, a qual ainda apresenta diversas lacunas para o seu domínio completo. Este trabalho apresenta um estudo teórico-experimental da condução de calor nos materiais utilizados na fabricação de moldes e matrizes, submetidos à usinagem com altas velocidades de corte. Os materiais utilizados foram os aços AISI D2 e AISI H13, muito utilizados nas indústrias de moldes e matrizes. Os ensaios foram realizados com fresas de ponta esférica (Ball-Nose) com e sem angulação de hélice e com ângulo de saída neutro, com revestimento de ('TI'AL')N e com uma ferramenta com uma placa de PcBN soldada. A geometria dos corpos-de-prova foi projetada para aproximar-se dos casos reais encontrados na indústria, casos em que superfícies complexas e paredes finas são comumente usinadas em matrizes e moldes. Dois sistemas de resfriamento foram utilizados o ar comprimido e o ar gelado utilizando o princípio de vórtice. Os resultados demonstraram uma pequena variação da temperatura em função dos materiais empregados e das ferramentas utilizadas em todos os testes. Os dois sistemas de resfriamento alternativos à usinagem sem sistema de resfriamento, o ar comprimido e o ar frio, também se mostraram influentes na variação da temperatura, apresentando-se como sistemas capazes de remover o calor no processo durante a usinagem. Os desvios de forma encontrados nos corpos-de-prova devem ser considerados na usinagem de perfis muito precisos. Foram encontrados valores da ordem de 0,05 mm, oriundos da combinação de distorções térmicas e tensões residuais, os quais podem ser signifcativos, por exemplo, na área de matrizaria / Modern industries improve their production systems aiming at increasing productivity and product quality. The high speed cutting (HSC) technology allows increasing material removal rates, workpiece dimensional tolerance and surface finishing as well. Such technology has been extensively used in mold and dies areas, since it minimizes long lead time problems and facilitates high quality machining, normally required in injected/formed products. Nowadays, several studies in HSC search for understanding all aspects involved in that new technology, which still presents many blanks for its complete knowledge. The present work shows a theoretical and experimental study on heat conduction flux in materials applied to mold and die manufacturing, submitted to HSC. It was used AISI D2 and AISI H13, which are very common in mold and die industry. Two types of cylindrical ball nose end milling tool were used in the experiments: coated with ('TI'AL')N and tipped with PcBN. The workpiece geometry was conceived to simulate real cases found in industry, in which complex surfaces and slim walls are commonly machined in molds and dies. Two cooling systems were used in the tests, compressed air and frozen air using vortex principle. Results indicated a small temperature variation as a function of machined materials and tools throughout the tests. Both alternative cooling systems, besides dry machining, compressed air and cool air, also demonstrated to affect temperature variation. They presented themselves as capable of remove heat from the process during the cutting operation. The form deviation found in the workpiece after machining must be considered when machining very precise profiles. Variation values of around 0.05 mm were found, coming from a combination of thermal distortion and residual stress, which could be significant, for example, in die manufacturing area

<p> The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a  mathematical point of view, the entire situation leads to a non-characteristic Cauchy problem, where by using recorded temperature one can solve a well-posed nonlinear problem in the finite region for computing heat flux, and consequently obtain the Cauchy data [u, u_x]. Further by using these data and by performing an appropriate method, e.g. a space marching method, one can eventually achieve the desired temperature at x = 0.</p><p>The problem is severely ill-posed in the sense that the solution does not depend continuously on the data. The problem solved by two different methods, and for both cases we stabilize the computations by replacing the time derivative in the heat equation by a bounded operator. The first one, a spectral method based on finite Fourier space is illustrated to supply an analytical approach for approximating the time derivative. In order to get a better accuracy in the numerical computation, we use cubic spline function for approximating the time derivative in the least squares sense.</p><p>The inverse problem we want to solve, by using Cauchy data, is a nonlinear heat conduction problem in one space dimension. Since the temperature data u = g(t) is recorded, e.g. by a thermocouple, it usually contains some perturbation in the data. Thus the solution can be severely ill-posed if the Cauchy data become very noisy. Two experiments are presented to test the proposed approach.</p>

The inverse heat conduction problem also frequently referred as the sideways heat equation, in short SHE, is considered as a mathematical model for a real application, where it is desirable for someone to determine the temperature on the surface of a body. Since the surface itself is inaccessible for measurements, one is restricted to use temperature data from the interior measurements. From a  mathematical point of view, the entire situation leads to a non-characteristic Cauchy problem, where by using recorded temperature one can solve a well-posed nonlinear problem in the finite region for computing heat flux, and consequently obtain the Cauchy data [u, ux]. Further by using these data and by performing an appropriate method, e.g. a space marching method, one can eventually achieve the desired temperature at x = 0. The problem is severely ill-posed in the sense that the solution does not depend continuously on the data. The problem solved by two different methods, and for both cases we stabilize the computations by replacing the time derivative in the heat equation by a bounded operator. The first one, a spectral method based on finite Fourier space is illustrated to supply an analytical approach for approximating the time derivative. In order to get a better accuracy in the numerical computation, we use cubic spline function for approximating the time derivative in the least squares sense. The inverse problem we want to solve, by using Cauchy data, is a nonlinear heat conduction problem in one space dimension. Since the temperature data u = g(t) is recorded, e.g. by a thermocouple, it usually contains some perturbation in the data. Thus the solution can be severely ill-posed if the Cauchy data become very noisy. Two experiments are presented to test the proposed approach.

The main objective of this industrially important work was to gain an increasing understanding of the properties of some industrially important materials such as CMSX-4 nickel base super alloy, 90Ti.6Al.4V alloy, 25Cr:6Ni stainless steel, 0.7% carbon steel, AISI 304 stainless steel-alumina composites, mould powder used in continuous casting of steel as well as coke used in blast furnace with special reference to the thermal diffusivities. The measurements were carried out in a wide temperature range covering solid, liquid, glassy and crystalline states. For CMSX-4 alloy, the thermal conductivities were calculated from the experimental thermal diffusivities. Both the diffusivities and conductivities were found to increase with increasing temperature. Microscopic analysis showed the presence of intermetallic phases γ´ such as Ni3Al below 1253 K. In this region, the mean free path of the electrons and phonons is likely to be limited by scattering against lattice defects. Between 1253 K and solidus temperature, these phases dissolved in the alloy adding to the impurities in the matrix, which, in turn, caused a decrease in the thermal diffusivity. This effect was confirmed by annealing the samples at 1573 K. The thermal diffusivities of the annealed samples measured at 1277, 1403 and 1531 K were found to be lower than the thermal diffusivities of non-annealed samples and the values did not show any noticeable change with time. It could be related to the attainment of equilibrium with the completion of the dissolution of γ´ phase during the annealing process. Liquid CMSX-4 does not show any change of thermal diffusivity with temperature. It may be attributed to the decrease of the mean free path being shorter than characteristic distance between two neighbouring atoms. Same tendency could be observed in the case of 90Ti.6Al.4V alloy. Since the thermal diffusivity increases with increasing temperature below 1225 K and shows slight decrease or constancy at higher temperature. For 25Cr:6Ni stainless steel, the thermal diffusivity is nearly constant up to about 700 K. Beyond that, there is an increase with temperature both during heating as well as cooling cycle. On the other hand, the slope of the curve increases above 950 K, which can be due to the increase of bcc phase in the structure. 0.7% carbon steel shows a decrease in the thermal diffusivity at temperature below Curie point, where the structure contains bcc+ fcc phases. Above this point the thermal diffusivity increases, where the structure contains only fcc phase. The experimental thermal conductivity values of these alloys show good agreement with the calculated values using Mills model. Thermal diffusivity measurements as a function of temperature of sintered AISI 304 stainless steel-alumina composites having various composition, viz, 0.001, 0.01, 0.1, 1, 2, 3, 5, 7, 8 and 10 wt% Al2O3 were carried out in the present work. The thermal diffusivity as well as the thermal conductivity were found to increase with temperature for all composite specimens. The thermal diffusivity/conductivity decreases with increasing weight fraction of alumina in the composites. The experimental results are in good agreement with simple rule of mixture, Eucken equation and developed Ohm´s law model at weight fraction of alumina below 5 wt%. Beyond this, the thermal diffusivity/ conductivity exhibits a high discrepancy probably due to the agglomeration of alumina particles during cold pressing and sintering. On the other hand, thermal diffusivities of industrial mould flux having glassy and crystalline states decrease with increasing temperature at lower temperature and are constant at higher temperature except for one glassy sample. The thermal diffusivity is increased with increasing crystallisation degree of mould flux, which is expected from theoretical considerations. Analogously, the thermal diffusivity measurements of mould flux do not show any significant change with temperature in liquid state. It is likely to be due to the silicate network being largely broken down. In the case of coke, the sample taken from deeper level of the pilot blast furnace is found to have larger thermal diffusivity. This can be correlated to the average crystallite size along the structural c-axis, Lc, which is indicative of the higher degree of graphitisation. This was also confirmed by XRD measurements of the different coke samples. The degree of graphitisation was found to increase with increasing temperature. Further, XRD and heat capacity measurements of coke samples taken from different levels in the shaft of the pilot blast furnace show that the graphitisation of coke was instantaneous between 973 and 1473 K. / QC 20100629

Das thermische Raummodell THERAKLES berechnet das dynamische Verhalten eines Raumes und seiner Umschließungsflächen in Abhängigkeit von realistischen Klimarandbedingungen, sowie Nutzer- und Anlagenverhalten. Neben Energieverbrauchswerten werden die operative Temperatur sowie weitere Kriterien zur Beurteilung der Behaglichkeit berechnet. Schwerpunkt der Anwendung liegt auf Optimierung der thermischen Behaglichkeit im Sommerfall, sowie energetischer Optimierung der Regelung von Heizungsanlagen unter Ausnutzung der Dynamik schwerer Baukonstruktionen und Massivbauwände. Das Modell beschreibt das dynamische Verhalten der Umfassungskonstruktionen durch instationäre, räumlich aufgelöste Simulation der Wand-, Fußboden-, und Decken- bzw. Dachflächen. Dadurch werden in der Konstruktion enthaltene Phasenwechselmaterialien (PCM) berücksichtigt und die zeitliche Verfügbarkeit der zusätzlichen Wärmespeicherfähigkeit abgebildet.

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