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