Using the inverse heat conduction problem and thermography for the determination of local heat transfer coefficients and fin effectiveness for longitudinal fins

Heat transfer is a physical process in which energy is exchanged. It occurs in numerous applications, such as production of electricity, building climatisation, food preparation,... Since energy consumption has increased tremendously in the last decades and this trend will continue, the concept of energy efficiency has become omnipresent. In electronics miniaturization has become a trend. Desktops, laptops, dvd-players, mp3-players, televisions,... are getting thinner and/or smaller. Together with the increase in work speed and capacity, these small dimensions cause the energy density of electronic components (chips, processors,. . . ) to intensify significantly. As the electric power supply for these components is converted into heat, the component temperature rises. Hence, large amount of electricity are dissipated in a small surface area and cause high heat fluxes in the electronic components. To prevent overheating (and therefore failure) of electronic components, efficient heat removal is necessary. A cheap and almost universally applicable method for the cooling of electronics uses air as coolant in combination with a heat sink. The heat sinks are placed on the electronic component in order to distribute the heat and to create a better heat transfer. A heat sink mostly consists of longitudinal fins. Fin shape adjustments can improve the heat transfer, without the need for an increase in fin volume. This dissertation is specifically aimed at the research on longitudinal fins. It takes off looking for a measurement method to determine the performance of longitudinal fins as well as possible performance improvements by adjustments to these fins. The developed technique offers a global examination with a performance parameter. Moreover, it creates the possibility to study local heat transfer effects. In this work, the technique is applied to longitudinal fins, specifically fins for the cooling of electronics, but can be extended to other fin types. Chapter one also provides a summary of previous research on longitudinal fins. The number of studies on local heat transfer coefficients is limited and these studies are often inaccurate. A study of different fin performance indicators was also made, which indicated that the widely spread concept of fin efficiency is misleading, and a bad fin performance indicator. Nevertheless, many studies still aim for the highest possible fin efficiency, assuming this would guarantee the maximum heat transfer. A better, more reliable fin performance parameter is the fin effectiveness, or the performance ratio which is derived from it. As high fin effectiveness actually corresponds to a higher heat transfer, fin effectiveness was used as the fin performance indicator in this work. The developed measurement technique should not only be able to determine local heat transfer coefficients, it should also measure the fin effectiveness. To attain those goals, one has to determine the heat flux distribution in the fin. Normally, one does not measure heat fluxes, but temperatures, that make it possible to calculate the heat flux distribution. This requires a technique to accurately measure temperature profiles, and a numerical method to calculate the heat flux distribution from these measurements. This numerical method is developed in the second chapter. Determining heat fluxes from temperatures is known as the inverse heat conduction problem. This kind of problem is solved inversely. Whereas in a direct problem heat fluxes are imposed as boundary conditions and the temperature field is calculated from these conditions, in an inverse conduction problem the solution (temperature field) is known and the boundary conditions (heat fluxes) are determined from these temperatures. An introducing literature survey indicates that the inverse conduction problem is ill-posed and that it therefore can have several solutions. To obtain stable, physically correct solutions, mathematical methods are used. The second chapter offers a summary of the solution methods found in literature, which are all based on the minimization of a temperature functional. The inverse heat conduction problem studied in this work is three-dimensional, linear and steady state. Based on the summary of the different numerical techniques the most suitable methods are chosen. Two methods are taken into consideration: the steepest descent method (SDM) and the conjugate gradient method (CGM). Chapter two mathematically develops both of these similar techniques and writes the complete solution algorithm for both of them. These two solution algorithms are applied to some numerical test cases in chapter 3. The test cases consist of a rectangular longitudinal fin that partly covers a flat primary surface. Different heat transfer coefficient profiles are imposed on the fin walls and the primary surface. Using these boundary conditions, the temperature profiles on the same surfaces are calculated. These temperature profiles are considered as exact temperature measurements and are the boundary conditions for the inverse heat conduction problem. This inverse heat conduction problem is solved with both SDM and CGM. Afterwards, chapter three investigates the influence of measurement errors on the measured temperature profiles for two different measurement accuracies: 0.1°C and 0.5°C. Apparently SDM and CGM have a comparable accuracy, but CGM converges much faster. The introduction of measurement errors gives comparable results as in the ideal case of exact temperature measurements. Only at the edges the deviations increase significantly. Enlarging the measurement error from 0.1°C to 0.5°C does not lead to the expected drastic decrease in accuracy of the estimated profiles. The results are even comparable to the exact results. This indicates that the solution methods are not too sensitive to noise and thus suitable to process experimental measurement data. Relying on the results, CGM was chosen as solution method because of the faster convergence rate. Chapter 4 develops a measurement method using infrared thermography as measurement technique. Infrared thermography has the advantage that it is a noncontacting method. Thus the temperature field and measurement object are not disturbed by the measurement. Moreover, thermography makes it possible to get complete temperature profiles with a single measurement. The first part of the chapter explains some basic notions on radiation and thermography. Calibration methods are drawn up and applied. An error analysis is executed on the parameters that determine the incident radiation energy and on the camera specific properties, resulting in an uncertainty for the measured temperature values. The second part of the chapter explains the measurement setup. First the dimensions of the studied fins are determined based on the Reynolds analogy and on data from literature. Subsequently, the composition of the experimental setup is described. A low speed wind tunnel is used to set the environmental conditions and vary the Reynlods number (Re), which allows examining the influence of Re on the fin effectiveness and local heat transfer coefficients. A heat source is placed at the bottom of the fin, in combination with a guard heater to limit uncontrolled temperature losses. The power of the heat source is based on the fin temperature that should be attained to perform the most accurate temperature measurements with the infrared camera. The end of the chapter presents the different fin forms that will be studied: solid rectangular longitudinal fins and perforated fins with various numbers of perforations. The final chapter accomplishes the data reduction and presents the results. The temperature images, measured with the infrared camera during the experiments, are converted to a matrix with temperature values. This matrix can be used as a boundary condition for the inverse heat conduction problem that is solved with the developed solution method based on CGM. This solution makes it possible to determine the local heat fluxes and fin effectivenesss. The results obtained for the rectangular longitudinal fins agree with data from literature. The local heat transfer coefficients indicate the expected trends, and even show the influence of a horseshoe vortex at the base of the fin. The results for the perforated fins show the influence of the perforations and of restarting the boundary layer: after a perforation higher local heat transfer coefficients are found. The comparison with values from literature confirms the obtained results. The results for fin effectiveness are not accurate enough to draw conclusions for this. To conclude, chapter 6 presents the most important findings and perspectives for future work

A Dynamic magnetic resonance imaging (MRI) phantom based on electric field induced residual dipolar couplings

Multi-center functional MRI (fMRI) research studies are advantageous but unavoidably introduce variations in the results due to differences in imager vendor, magnetic field strength, imaging pulse sequences, and many other aspects. These variations make combining data from different MRI centers risky. Even for a single MRI center, temporal variations over the course of a study can make combining data problematic. Therefore, it is necessary in both situations to perform quality assurance (QA) measurements on a regular basis. Unfortunately, there are no dynamic standards or phantoms as they are called in the MRI community, which can mimic the small, rapidly changing fMRI signal at a relatively large field-of-view (FOV) and number of magnetic field strengths. The goal of this research was to develop a dynamic phantom which mimiced the signal change in fMRI and hence could be used for QA procedures related to fMRI. A phantom was developed with a rapidly switchable MRI signal. This phantom consisted of a geometric grid, eight vials with solutions of known proton spin-spin relaxation time (T2) values, and a cylindrical electrical cell filled with a polar liquid, all surrounded by water. An electrical circuit was built to interface the phantom to an imager through the pulse sensor and produce pulsed electric (E) fields during the imaging sequence. The results of spin-echo, echo planar imaging (SE-EPI) imaging sequence showed that the signal changed by approximately 8% with the application of a 11.8 kV/m electric field. This change was found to be based on the residual dipolar couplings induced by the applied E field, directly related to the size of the field, and switchable in 50 μs

Stochastic Inverse Methods to Identify non-Gaussian Model Parameters in Heterogeneous Aquifers

La modelación numérica del flujo de agua subterránea y del transporte de masa se está convirtiendo en un criterio de referencia en la actualidad para la evaluación de recursos hídricos y la protección del medio ambiente. Para que las predicciones de los modelos sean fiables, estos deben de estar lo más próximo a la realidad que sea posible. Esta proximidad se adquiere con los métodos inversos, que persiguen la integración de los parámetros medidos y de los estados del sistema observados en la caracterización del acuífero. Se han propuesto varios métodos para resolver el problema inverso en las últimas décadas que se discuten en la tesis. El punto principal de esta tesis es proponer dos métodos inversos estocásticos para la estimación de los parámetros del modelo, cuando estos no se puede describir con una distribución gausiana, por ejemplo, las conductividades hidráulicas mediante la integración de observaciones del estado del sistema, que, en general, tendrán una relación no lineal con los parámetros, por ejemplo, las alturas piezométricas. El primer método es el filtro de Kalman de conjuntos con transformación normal (NS-EnKF) construido sobre la base del filtro de Kalman de conjuntos estándar (EnKF). El EnKF es muy utilizado como una técnica de asimilación de datos en tiempo real debido a sus ventajas, como son la eficiencia y la capacidad de cómputo para evaluar la incertidumbre del modelo. Sin embargo, se sabe que este filtro sólo trabaja de manera óptima cuándo los parámetros del modelo y las variables de estado siguen distribuciones multigausianas. Para ampliar la aplicación del EnKF a vectores de estado no gausianos, tales como los de los acuíferos en formaciones fluvio-deltaicas, el NSEnKF propone aplicar una transformación gausiana univariada. El vector de estado aumentado formado por los parámetros del modelo y las variables de estado se transforman en variables con una distribución marginal gausiana.Zhou ., H. (2011). Stochastic Inverse Methods to Identify non-Gaussian Model Parameters in Heterogeneous Aquifers [Tesis doctoral no publicada]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/12267Palanci

Multidisciplinary Research Program in Atmospheric Science

A theoretical analysis of the vertical resolving power of the High resolution Infrared Radiation Sounder (HIRS) and the Advanced Meteorological Temperature Sounder (AMTS) is carried out. The infrared transmittance weighting functions and associated radiative transfer kernels are analyzed through singular value decomposition. The AMTS was found to contain several more pieces of independent information than HIRS when the transmittances were considered, but the two instruments appeared to be much more similar when the temperature sensitive radiative transfer kernels were analyzed. The HIRS and AMTS instruments were also subjected to a thorough analysis. It was found that the two instruments should have very similar vertical resolving power below 500 mb but that AMTS should have superior resolving power above 200 mb. In the layer 200 to 500 mb the AMTS showed badly degraded spread function

Space-time sampling strategies for electronically steerable incoherent scatter radar

Incoherent scatter radar (ISR) systems allow researchers to peer into the ionosphere via remote sensing of intrinsic plasma parameters. ISR sensors have been used since the 1950s and until the past decade were mainly equipped with a single mechanically steerable antenna. As such, the ability to develop a two or three dimensional picture of the plasma parameters in the ionosphere has been constrained by the relatively slow mechanical steering of the antennas. A newer class of systems using electronically steerable array (ESA) antennas have broken the chains of this constraint, allowing researchers to create 3-D reconstructions of plasma parameters. There have been many studies associated with reconstructing 3-D fields of plasma parameters, but there has not been a systematic analysis into the sampling issues that arise. Also, there has not been a systematic study as to how to reconstruct these plasma parameters in an optimum sense as opposed to just using different forms of interpolation. The research presented here forms a framework that scientists and engineers can use to plan experiments with ESA ISR capabilities and to better analyze the resulting data. This framework attacks the problem of space-time sampling by ESA ISR systems from the point of view of signal processing, simulation and inverse theoretic image reconstruction. We first describe a physics based model of incoherent scatter from the ionospheric plasma, along with processing methods needed to create the plasma parameter measurements. Our approach leads to development of the space-time ambiguity function, forming a theoretical foundation of the forward model for ISR. This forward model is novel in that it takes into account the shape of the antenna beam and scanning method along with integration time to develop the proper statistics for a desired measurement precision. Once the forward model is developed, we present the simulation method behind the Simulator for ISR (SimISR). SimISR uses input plasma parameters over space and time and creates complex voltage samples in a form similar to that produced by a real ISR system. SimISR allows researchers to evaluate different experiment configurations in order to efficiently and accurately sample specific phenomena. We present example simulations using input conditions derived from a multi-fluid ionosphere model and reconstructions using standard interpolation techniques. Lastly, methods are presented to invert the space-time ambiguity function using techniques from image reconstruction literature. These methods are tested using SimISR to quantify accurate plasma parameter reconstruction over a simulated ionospheric region

Analisis Performansi Precoding Regularized Channel Inversion (RCI) Pada Sistem Multiuser MIMO-GFDM Untuk Kanal Downlink 5G

Pada penelitian ini, dianalisis kinerja teknik precoding linier regularized channel inversion (RCI) yang dikombinasikan dengan salah satu kandidat waveform 5G, yaitu generalized frequency division multiplexing (GFDM), pada sistem multiuser MIMO downlink. RCI merupakan precoding linier paling sederhana berdasarkan kriteria MMSE. Pada penelitian sebelumnya, RCI menunjukkan kinerja yang baik pada sistem MU-MIMO saat dikombinasikan dengan orthogonal frequency division multiplexing (OFDM), waveform yang saat ini digunakan pada teknologi 4G. Penggunaan RCI pada sistem MU-MIMOOFDM dapat menurunkan efek inter user interference (IUI) tanpa meningkatkan kompleksitas sistem secara signifikan. Di dalam penelitian ini, kinerja RCI pada sistem yang diusulkan, yaitu MU-MIMO-GFDM, dibandingkan dengan performansi RCI pada sistem sebelumnya, yaitu MU-MIMO-OFDM. Khusus untuk sistem MU-MIMO-GFDM, dibuat dua sistem MU-MIMO-GFDM yang menggunakan mapper berbeda, yaitu 16-QAM dan 16-OQAM untuk masingmasing sistem. Dari hasil simulasi dan analisis, RCI pada MU-MIMO-GFDM mencapai kinerja yang sama baik seperti kinerja RCI pada saat diimplementasikan di MU-MIMO-OFDM, dalam hal bit error rate (BER). Bahkan, berdasarkan kurva CCDF, sistem MU-MIMO-GFDM-QAM memiliki nilai PAPR paling baik,dengan rata-rata selisih sebesar 0.794 atau -1 dB dari PAPR yang dihasilkan pada MU-MIMO-OFDM-QAM. Sedangkan MU-MIMO-GFDM-OQAM memiliki rata-rata selisih nilai PAPR sebesar 0,806 atau -0,9 dB dari MU-MIMO-OFDMQAM. Di sisi OOB, rata-rata nilai OOB antara MU-MIMO-GFDM-QAM dengan MU-MIMO-OFDM-QAM adalah sebesar 4,38 dBW atau 2,78 W. Untuk perbandingan rata-rata nilai OOB dari sistem MU-MIMO-GFDM-OQAM dengan MU-MIMO-OFDM-QAM adalah sebesar 3,18 dBW atau 2,07 W. Penggunaan RCI pada sistem yang diusulkan tidak dapat menghilangkan pengaruh IUI secara total, namun sinyal yang diinginkan dengan sinyal penginterferensi masih dapat dibedakan. Jika dibandingkan dengan sistem lain yang menggunakan precoding berbeda, yaitu block diagonalization, kinerja sistem masih lebih rendah daripada sistem lain tersebut sehingga masih membutuhkan pengenbangan lebih lanjut. ======================================================================================= In this research, it is analyzed the performance of regularized channel inversion (RCI) technique combined with one of 5G waveform candidate, generalized frequency division multiplexing (GFDM), in multiuser MIMO (MU-MIMO)downlink system. RCI is the simplest linear precoding based on MMSE criteria. In previous research, RCI showed good performance on MU-MIMO system when it is combined with orthogonal frequency division multiplexing (OFDM), a waveform currently used in 4G technology. The use of RCI in the MU-MIMOOFDM system can reduce the inter-user interference (IUI) effect without significantly increasing system complexity. In this study, the performance of RCI in the proposed system, i.e. MU-MIMO-GFDM, will be compared to the performance of RCI in the previous system, ie MU-MIMO-OFDM. Especially for the MU-MIMO-GFDM, two MU-MIMO-GFDM systems are created using different mapper, 16-QAM and 16-OQAM respectively. From the simulation and analysis results, the RCI on MU-MIMO-GFDM achieves the same performance as RCI performance when it is implemented on MU-MIMO-OFDM, in terms of bit error rate (BER). In fact, based on the CCDF curve, the MU-MIMO-GFDMQAM system has the best PAPR value, with an average difference of 0.794 or -1 dB from the PAPR generated at MU-MIMO-OFDM-QAM. While MU-MIMOGFDM-OQAM has an average difference of PAPR value of 0.806 or -0.9 dB from MU-MIMO-OFDM-QAM. On the OOB side, the average OOB value between MU-MIMO-GFDM-QAM and MU-MIMO-OFDM-QAM is 4.38 dBW or 2.78 W. For a comparison of the average OOB values of the MU-MIMOGFDM-OQAM system with MU-MIMO-OFDM-QAM is 3.18 dBW or 2.07 W. The use of RCI in the proposed system can not eliminate totally influence from other user's channels. However, the desired signals and its the interference signal can still be distinguished. If it is compared to other systems using other linear precoding, ie, block diagonalization, its performance is still lower than that other system so that it is still enhancement further

Reduction of conductivity uncertainty propagations in the inverse problem of EEG source analysis

In computer simulations, the response of a system under study depends on the input parameters. Each of these parameters can be assigned a fixed value or a range of values within the input parameter space for system performance evaluations. Starting from values of the input parameters and a certain given model, the so-called forward problem can be solved that needs to approximate the output of the system. Starting from measurements related to the output of the system model it is possible to determine the state of the system by solving the so-called inverse problem. In the case of a non-linear inverse problem, non-linear minimization techniques need to be used where the forward model is iteratively evaluated for different input parameters. The accuracy of the solution in the inverse problem is however decreased due to the noise available in the measurements and due to uncertainties in the system model. Uncertainties are parameters for which their values are not exactly known and/or that can vary in time and/or depend on the environment. These uncertainties have, for given input parameter values, an influence on the forward problem solution. This forward uncertainty propagation leads then to errors in the inverse solutions because the forward model is iteratively evaluated for recovering the inverse solutions. Until now, it was assumed that the recovery errors could not be reduced. The only option was to either quantify the uncertain parameter values as accurate as possible or to reflect the uncertainty in the inverse solutions, i.e. determination of the region in parameter space wherein the inverse solution is likely to be situated. The overall aim of this thesis was to develop reduction techniques of inverse reconstruction errors so that the inverse problem is solved in a more robust and thus accurate way. Methodologies were specifically developed for electroencephalography (EEG) source analysis. EEG is a non-invasive technique that measures on the scalp of the head, the electric potentials induced by the neuronal activity. EEG has several applications in biomedical engineering and is an important diagnostic tool in clinical neurophysiology. In epilepsy, EEG is used to map brain areas and to receive source localization information that can be used prior to surgical operation. Starting from Maxwell’s equations in their quasi-static formulation and from a physical model of the head, the forward problem predicts the measurements that would be obtained for a given configuration of current sources. The used headmodels in this thesis are multi-layered spherical head models. The neural sources are parameterized by the location and orientation of electrical dipoles. In this thesis, a set of limited number of dipole sources is used as source model leading to a well posed inverse problem. The inverse problem starts from measured EEG data and recovers the locations and orientations of the electrical dipole sources. A loss in accuracy of the recovered neural sources occurs because of noise in the EEG measurements and uncertainties in the forward model. Especially the conductivity values of scalp, skull and brain are not well known since these values are difficult to measure. Moreover, these uncertainties can vary from person to person, in time, etc. In this thesis, novel numerical methods are developed so to provide new approaches in the improvement of spatial accuracy in EEG source analysis, taking into account model uncertainties. Nowadays, the localization of the electrical activity in the brain is still a current and challenging research topic due to the many difficulties arising e.g. in the process of modeling the head and dealing with the not well known conductivity values of its different tissues. Due to uncertainty in the conductivity value of the head tissues, high values of errors are introduced when solving the EEG inverse problem. In order to improve the accuracy of the solution of the inverse problem taking into account the uncertainty of the conductivity values, a new mathematical approach in the definition of the cost function is introduced and new techniques in the iterative scheme of the inverse reconstruction are proposed. The work in this thesis concerns three important phases. In a first stage, we developed a robust methodology for the reduction of errors when reconstructing a single electrical dipole in the case of a single uncertainty. This uncertainty concerns the skull to soft tissue conductivity ratio which is an important parameter in the forward model. This conductivity ratio is difficult to quantify and depends from person to person. The forward model that we employed is a three shell spherical head model where the forward potentials depend on the conductivity ratio. We reformulated the solution of the forward problem by using a Taylor expansion around an actual value of the conductivity ratio which led to a linear model of the solution for the simulated potentials. The introduction of this expanded forward model, led to a sensitivity analysis which provided relevant information for the reconstruction of the sources in EEG source analysis. In order to develop a technique for reducing the errors in inverse solutions, some challenging mathematical questions and computational problems needed to be tackled. We proposed in this thesis the Reduced Conductivity Dependence (RCD) method where we reformulate the traditional cost function and where we incorporated some changes with respect to the iterative scheme. More specifically, in each iteration we include an internal fitting procedure and we propose selection of sensors. The fitting procedure makes it possible to have an as accurate as possible forward model while the selection procedure eliminates the sensors which have the highest sensitivity to the uncertain skull to brain conductivity ratio. Using numerical experiments we showed that errors in reconstructed electrical dipoles are reduced using the RCD methodology in the case of no noise in measurements and in the case of noise in measurements. Moreover, the procedure for the selection of electrodes was thoroughly investigated as well as the influence of the use of different EEG caps (with different number of electrodes). When using traditional reconstruction methods, the number of electrodes has not a high influence on the spatial accuracy of the reconstructed single electrical dipole. However, we showed that when using the RCD methodology the spatial accuracy can be even more increased. This because of the selection procedure that is included within the RCD methodology. In a second stage, we proposed a RCD method that can be applied for the reconstruction of a limited number of dipoles in the case of a single uncertainty. The same ideas were applied onto the Recursively Applied and Projected Multiple Signal Classification (RAP-MUSIC) algorithm. The three shell spherical head model was employed with the skull to brain conductivity ratio as single uncertainty. We showed using numerical experiments that the spatial accuracy of each reconstructed dipole is increased, i.e. reduction of the conductivity dependence of the inverse solutions. Moreover, we illustrated that the use of the RCD-based subspace correlation cost function leads to a high efficiency even for high noise levels. Finally, in a third stage, we developed a RCD methodology for the reduction of errors in the case of multiple uncertainties. We used a five shell spherical head model where conductivity ratios with respect to skull, cerebrospinal fluid, and white matter were uncertain. The cost function as well as the fitting and selection procedure of the RCD method were extended. The numerical experiments showed reductions in the reconstructed electrical dipoles in comparison with the traditional methodology and also compared to the RCD methodology developed for dealing with a single uncertainty