Numerical Simulation of Convective-Radiative Heat Transfer

This book presents numerical, experimental, and analytical analysis of convective and radiative heat transfer in various engineering and natural systems, including transport phenomena in heat exchangers and furnaces, cooling of electronic heat-generating elements, and thin-film flows in various technical systems. It is well known that such heat transfer mechanisms are dominant in the systems under consideration. Therefore, in-depth study of these regimes is vital for both the growth of industry and the preservation of natural resources. The authors included in this book present insightful and provocative studies on convective and radiative heat transfer using modern analytical techniques. This book will be very useful for academics, engineers, and advanced students

Numerical investigation of heat transfer in one-dimensional longitudinal fins

A thesis submitted to the Faculty of Science, University of the Witwatersrand, Johannesburg, in fulfilment of the requirements for the degree of Doctor of Philosophy. Johannesburg, 2014.In this thesis we will establish effective numerical schemes appropriate for the solution of a non-linear partial differential equation modelling heat transfer in one dimensional longitudinal fins. We will consider the problem as it stands without any physical simplification. The main methodology is based on balancing the non-linear source term as well as the application of numerical relaxation techniques. In either approach we will incorporate the no-flux condition for singular fins. By doing so, we obtain appropriate numerical schemes which improve results found in literature. To generalize, we will provide a relaxed numerical scheme that is applicable for both integer and fractional order non-linear heat transfer equations for one dimensional longitudinal fins

Heat Transfer

Over the past few decades there has been a prolific increase in research and development in area of heat transfer, heat exchangers and their associated technologies. This book is a collection of current research in the above mentioned areas and describes modelling, numerical methods, simulation and information technology with modern ideas and methods to analyse and enhance heat transfer for single and multiphase systems. The topics considered include various basic concepts of heat transfer, the fundamental modes of heat transfer (namely conduction, convection and radiation), thermophysical properties, computational methodologies, control, stabilization and optimization problems, condensation, boiling and freezing, with many real-world problems and important modern applications. The book is divided in four sections : "Inverse, Stabilization and Optimization Problems", "Numerical Methods and Calculations", "Heat Transfer in Mini/Micro Systems", "Energy Transfer and Solid Materials", and each section discusses various issues, methods and applications in accordance with the subjects. The combination of fundamental approach with many important practical applications of current interest will make this book of interest to researchers, scientists, engineers and graduate students in many disciplines, who make use of mathematical modelling, inverse problems, implementation of recently developed numerical methods in this multidisciplinary field as well as to experimental and theoretical researchers in the field of heat and mass transfer

Topology optimization for energy problems

The optimal design of energy systems is a challenge due to the large design space and the complexity of the tightly-coupled multi-physics phenomena involved. Standard design methods consider a reduced design space, which heavily constrains the final geometry, suppressing the emergence of design trends. On the other hand, advanced design methods are often applied to academic examples with reduced physics complexity that seldom provide guidelines for real-world applications. This dissertation offers a systematic framework for the optimal design of energy systems by coupling detailed physical analysis and topology optimization. Contributions entail both method-related and application-oriented innovations. The method-related advances stem from the modification of topology optimization approaches in order to make practical improvements to selected energy systems. We develop optimization models that respond to realistic design needs, analysis models that consider full physics complexity and design models that allow dramatic design changes, avoiding convergence to unsatisfactory local minima and retaining analysis stability. The application-oriented advances comprise the identification of novel optimized geometries that largely outperform industrial solutions. A thorough analysis of these configurations gives insights into the relationship between design and physics, revealing unexplored design trends and suggesting useful guidelines for practitioners. Three different problems along the energy chain are tackled. The first one concerns thermal storage with latent heat units. The topology of mono-scale and multi-scale conducting structures is optimized using both density-based and level-set descriptions. The system response is predicted through a transient conjugate heat transfer model that accounts for phase change and natural convection. The optimization results yield a large acceleration of charge and discharge dynamics through three-dimensional geometries, specific convective features and optimized assemblies of periodic cellular materials. The second problem regards energy distribution with district heating networks. A fully deterministic robust design model and an adjoint-based control model are proposed, both coupled to a thermal and fluid-dynamic analysis framework constructed using a graph representation of the network. The numerical results demonstrate an increased resilience of the infrastructure thanks to particular connectivity layouts and its rapidity in handling mechanical failures. Finally, energy conversion with proton exchange membrane fuel cells is considered. An analysis model is developed that considers fluid flow, chemical species transport and electrochemistry and accounts for geometry modifications through a density-based description. The optimization results consist of intricate flow field layouts that promote both the efficiency and durability of the cell

Thermal-Aware Networked Many-Core Systems

Advancements in IC processing technology has led to the innovation and growth happening in the consumer electronics sector and the evolution of the IT infrastructure supporting this exponential growth. One of the most difficult obstacles to this growth is the removal of large amount of heatgenerated by the processing and communicating nodes on the system. The scaling down of technology and the increase in power density is posing a direct and consequential effect on the rise in temperature. This has resulted in the increase in cooling budgets, and affects both the life-time reliability and performance of the system. Hence, reducing on-chip temperatures has become a major design concern for modern microprocessors. This dissertation addresses the thermal challenges at different levels for both 2D planer and 3D stacked systems. It proposes a self-timed thermal monitoring strategy based on the liberal use of on-chip thermal sensors. This makes use of noise variation tolerant and leakage current based thermal sensing for monitoring purposes. In order to study thermal management issues from early design stages, accurate thermal modeling and analysis at design time is essential. In this regard, spatial temperature profile of the global Cu nanowire for on-chip interconnects has been analyzed. It presents a 3D thermal model of a multicore system in order to investigate the effects of hotspots and the placement of silicon die layers, on the thermal performance of a modern ip-chip package. For a 3D stacked system, the primary design goal is to maximise the performance within the given power and thermal envelopes. Hence, a thermally efficient routing strategy for 3D NoC-Bus hybrid architectures has been proposed to mitigate on-chip temperatures by herding most of the switching activity to the die which is closer to heat sink. Finally, an exploration of various thermal-aware placement approaches for both the 2D and 3D stacked systems has been presented. Various thermal models have been developed and thermal control metrics have been extracted. An efficient thermal-aware application mapping algorithm for a 2D NoC has been presented. It has been shown that the proposed mapping algorithm reduces the effective area reeling under high temperatures when compared to the state of the art.Siirretty Doriast

Evaluation of the thermal design of a liquid-lens cooling system for projection picture tubes

The thermal design of a liquid-lens system for cooling picture tubes in projection television receivers is evaluated using an experimentally benchmarked numerical model. Because of the intense brightness in the visual image, excessive waste heat is generated as the by-product of light emission fi‘om the phosphor screen as the electron beam sweeps across the raster region at the back of the face panel. Projection tube specifications indicate a maximum allowable temperature at the face-panel center and a maximum allowable temperature differential between the center and perimeter points. To cool the tube’s face, an optical liquid (liquid lens) fills the space between the face panel and a meniscus lens directly in front of it. A metallic enclosure frame serves as support for the meniscus lens and a container for the liquid. Heat is transferred by natural convection from the face panel to the enclosure frame and from there to the interior environment of the television cabinet by convection and radiation

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

IEA ECES Annex 31 Final Report - Energy Storage with Energy Efficient Buildings and Districts: Optimization and Automation

At present, the energy requirements in buildings are majorly met from non-renewable sources where the contribution of renewable sources is still in its initial stage. Meeting the peak energy demand by non-renewable energy sources is highly expensive for the utility companies and it critically influences the environment through GHG emissions. In addition, renewable energy sources are inherently intermittent in nature. Therefore, to make both renewable and nonrenewable energy sources more efficient in building/district applications, they should be integrated with energy storage systems. Nevertheless, determination of the optimal operation and integration of energy storage with buildings/districts are not straightforward. The real strength of integrating energy storage technologies with buildings/districts is stalled by the high computational demand (or even lack of) tools and optimization techniques. Annex 31 aims to resolve this gap by critically addressing the challenges in integrating energy storage systems in buildings/districts from the perspective of design, development of simplified modeling tools and optimization techniques

Nonlinear Dynamic Analysis and Control of Chemical Processes Using Dynamic Operability

Nonlinear dynamic analysis serves an increasingly important role in process systems engineering research. Understanding the nonlinear dynamics from the mathematical model of a process helps to find the boundaries of all achievable process conditions and identify the system instabilities. The information on such boundaries is beneficial for optimizing the design and formulating a control structure. However, a systematic approach to analyzing nonlinear dynamics of chemical processes considering such boundaries in a quantifiable and adaptable way is yet to exist in the literature. The primary aim of this work is to formulate theoretical concepts for dynamic operability, as well as develop the practical implementation methods for the analysis of dynamic performance in chemical processes. Process operability is a powerful tool for analyzing the relationships between the input variables, the output variables, and the disturbances via the geometric computation of variable sets. The operability sets are described by unions of polyhedra, which can be translated to sets of inequality constraints, so the results of the operability analysis can be used for process optimization and advanced process control. Nonetheless, existing process operability approaches in the literature are currently limited for steady-state processes and a generalized definition of dynamic operability that retains the core principles of steady-state operability as a controllability measure. A unified dynamic operability concept is proposed in this dissertation with two different adaptations to represent the complex relationships between the design, control structure, and control law of a given process. The existing operability mapping methods discretize the input space by partitioning the ranges of each input variable evenly, and all possible input combinations are simulated to achieve the output sets. The procedure is repeated for each value in the expected disturbance set to find the output regions that are guaranteed to be achieved regardless of the disturbance scenario. However, for dynamic systems, the same set of manipulated inputs can take different values at different time intervals, so the number of possible input combinations, which is also the number of simulations required, increases exponentially with the number of time intervals. This tractability challenge motivates the development of novel dynamic operability mapping approaches. A linear time-invariant dynamic system is first considered to tackle the dynamic mapping of achievable output sets. For a linear system, the achievable output set (AOS) at a fixed predicted time is the smallest convex hull that contains all the images of the extreme points of the available input set (AIS) when propagated through the dynamic model. Given a collection of AOS’s at all predicted times, referred to as the achievable funnel, a set of output constraints is infeasible if its intersection with the achievable funnel is empty. Under the influence of a stochastic disturbance, the achievable funnel is shifted according to the definition of the expected disturbance set (EDS). If the EDS is bounded, the intersection of all achievable funnels at each disturbance realization is the tightest set of transient output constraints that is operable. Additionally, given a fixed setpoint, an AOS is referred to as a feasible AOS if a series of inputs from the AIS always brings any output to the setpoint regardless of the realization of the disturbance within the EDS. Thus, novel developed theories and algorithms to update the dynamic operability mapping according to the current state variables and the disturbance propagations are proposed to reduce the online computational time of the constraint calculation task. Dynamic operability mapping for nonlinear processes is an expansion of the above linear mapping. A novel state-space projection mapping is proposed by taking advantage of the discrete-time state-space structure of the dynamic model to reduce the number of input mapping combinations. This method augments the AIS at the current step to include the AOS of the state variables from the previous time step. The nonlinear dynamic operability mapping framework consists of three components: the AOS inspector, the AIS divider, and the merger of the AOS from the previous time with the AIS. Specifically, the AOS inspector evaluates if the current input-output combinations are approximately accurate to the real AOS when all input combinations are mapped to the output space. If the AOS inspector gauges that the current AOS is not sufficiently precise, the AIS divider systematically generates more input-output combinations based on the current AOS. This feedback process is repeated until an accuracy tolerance is reached. Finally, a novel grey-box model identification algorithm for process control is developed by integrating dynamic operability mapping and Bayesian calibration. The proposed dynamic discrepancy reduced-order model-based approach calibrates the rates of changes of the grey-box model to match the plant instead of compensating for the time-varying output differences. The model reduction framework is divided into three steps: formulating the dynamic discrepancy terms, calibrating the hyperparameters, and selecting the least complex model that is neither underfitted nor overfitted. To demonstrate the effectiveness of the reduced-order model, the developed approach is implemented into a model predictive controller for a high-fidelity model as the simulated plant