In this thesis, we consider two models from physics, which are characterized by the interplay of thermodynamical and fluid mechanical phenomena: demixing (spinodal decomposition) and Rayleigh--Bénard convection. In both models, we investigate the dependencies of certain intrinsic quantities on the system parameters. The first model describes a thermodynamically driven demixing process of a binary viscous fluid. During the evolution, the two components of the mixture separate into two domains of the different equilibrium volume fractions. One observes a clear tendency: Larger domains grow at the expense of smaller ones, and thus, the average domain sizes increases --- a phenomenon called coarsening. It turns out that two mechanisms are relevant for the coarsening process. At an early stage of the evolution, material transport is essentially mediated by diffusion; at a later stage, when the typical domain size exceeds a certain value, due to the viscosity of the mixture, a fluid flow sets in and becomes the relevant transport mechanism. In both regimes, the growth rates of the typical domain size obey certain power laws. In this thesis, we rigorously establish one-sided bounds on these growth rates via a priori estimates. The second model, Rayleigh--Bénard convection, describes the behavior of a fluid between two rigid horizontal plates that is heated from below and cooled from above. There are two competing heat transfer mechanisms in the system: On the one hand, thermodynamics favors a state in which temperature variations are locally minimized. Thus, in our model, the thermodynamical equilibrium state is realized by a temperature with a linearly decreasing profile, corresponding to pure conduction. On the other hand, due to differences in the densities of hot and cold fluid parcels, buoyancy forces act on the fluid. This results in an upward motion of hot parcels and a downward motion of cold parcels. We study the dependence of the average upward heat flux, measured in the so-called Nusselt number, on the temperature forcing encoded by the container height. It turns out that the efficiency of the heat transport is independent of the height of the container, and thus, the Nusselt number is a constant function of height. Using a priori estimates, we prove an upper bound on the Nusselt number that displays this dependency --- up to logarithmic errors. Further investigations on the flow pattern in Rayleigh--Bénard convection show a clear separation of length scales: Along the horizontal top and bottom plates one observes thin boundary layers in which heat is essentially conducted, whereas the large bulk is characterized by a convective heat flow. We give first rigorous results in favor of linear temperature profiles in the boundary layers, which indicate that heat is indeed essentially conducted close to the boundaries.:1 Introduction 2 Coarsening rates in binary viscous fluids 2.1 Background from physics 2.2 Background from mathematics 2.3 The model 2.4 The gradient flow structure 2.5 Heuristics 2.6 Numerical simulations 2.7 Main results 2.8 Preliminaries 2.9 Proof of upper bounds on coarsening rates 2.10 Appendix: Well-posedness and regularity of solutions 3 Scaling of the Nusselt number 3.1 Background from physics 3.2 The model and the Nusselt number 3.3 Heuristics 3.4 Main results 3.5 Scaling law in the linear regime 3.6 Preliminaries and review 3.7 Upper bound using the background field method 3.8 Upper bound using the maximum principle 3.9 Appendix: Some elementary estimates 4 The laminar boundary layer 4.1 Background, model, and motivation 4.2 Main results 4.3 Preparation: Bounds on the velocity field 4.4 On the energy distribution 4.5 Bounds on the second order derivatives of the temperature field 4.6 Bounds on the third order derivatives of the temperature field

Regnvatteninsamling för olika syften är väl utbrett världen över och har blivit allt mer populärt i takt med ett förändrat klimat. Idag används regnvatten på många håll till hushållsanvändning men intresset har även ökat inom industrisektorn. Syftet med examensarbetet var att undersöka möjligheterna för att samla in och lagra regnvatten samt ersätta dricksvatten i Sandvik AB:s kylsystem. Detta genomfördes dels genom att undersöka vilka tillstånd som krävs för att samla in regnvatten, dels genom att föreslå en magasinutformning, storlek samt lokalisering av denna utifrån flödesberäkningar och dels genom att undersöka hur temperaturen förändras hos regnvatten i ett magasin för att bedöma dess funktion som kylvatten. I studien har först flödesberäkningar med avseende på effektivitet (hur mycket regnvatten som kan ersätta dricksvatten) simulerats för en nederbördsfattig, nederbördsrik respektive genomsnittlig tidsperiod. Därefter konstruerades två modeller i HYDRUS-1D, vilka representerade regnvattenmagasin med omgivande jord vid en lodrätt och en horisontell värmetransport. Enligt studien bedöms verksamheten idag ha alla tillstånd som krävs och behöver inte några ytterligare tillstånd. Valet av magasin blev ett avsättningsmagasin under mark med hänsyn till lokala förutsättningar. Hela anläggningen kan maximalt nå en effektivitet på 44 % under ett nederbördsrikt år med dagens totala förbrukningsdata för dricksvatten i kylsystemet samt totala takytan. Jämförelsen mellan olika lokaliseringar inom anläggningen ledde till att Stålverk 64 föreslogs samt presenterades närmare och utifrån dess effektivitet valdes magasinstorleken 1500 m3 för de 30 000 m2 som Stålverk 64 har i takyta. Effektiviteten för Stålverk 64 blev under ett nederbördsrikt år 77 %, ett genomsnittligt år 64 % och under ett nederbördsfattigt år 54 %. Värmesimuleringarna visade på att det är ytterst få dygn om året som regnvatten som lagras i ett avsättningsmagasin riskerar att vara för varmt för att användas som kylvatten. Slutsatsen är att Sandvik AB har goda möjligheter att samla in regnvatten för att ersätta dricksvatten i kylsystemet men behöver utveckla större lagringsmöjligheter för att uppnå en ännu högre effektivitet. / Rainwater harvesting is used for different purposes all over the world and has increased in popularity in line with climate change. Rainwater is today widely used for households, but interest has also increased within the industrial sector. The aim with this thesis was to investigate rainwater harvesting as a substitute for the use of drinking water in Sandvik´s cooling system. This was examined by investigating legislation concerning rainwater harvesting, different designs and sizes of storage systems and locations that would be suitable for storing rainwater. Also, temperature changes in a rainwater storage system were examined to estimate rainwater´s use for cooling. Firstly, calculations of water flow were simulated with respect to efficiency (how much rainwater that can substitute for drinking water) for three periods with different amounts of precipitation. Secondly, two models were implemented in HYDRUS-1D to represent a storage system for rainwater with surrounding soil with a vertical and horizontal heat transport. The results indicate that the industry has required permits for rainwater harvesting. Taking local conditions into account, an underground storage was chosen to store the rainwater. The entire facility can have a maximum efficiency of 44 % during a year with a high amount of precipitation with the total roof area and today’s consumption of drinking water in the cooling system. A comparison between different locations within the facility resulted in a more specific presentation of Stålverk 64 with respect to its efficiency; 1500 m3 was proposed as the storage size for the roof area of 30 000 m2. The efficiency for Stålverk 64 varied between 54-77 % for years with different amounts of precipitation. Simulated heat transport demonstrated that the risk for excessive water temperatures in an underground storage was low and with elevated temperatures occurring only a couple of days per year. The conclusion is that Sandvik AB has good opportunities for rainwater harvesting to substitute drinking water in the cooling system but need to develop higher capabilities for storage systems to achieve higher efficiency.

Two computational fluid dynamics models are developed to predict the performance of a solid oxide fuel cell stack, a detailed and a simplified model. In the detailed model, the three dimensional momentum, heat, and species transport equations are coupled with electrochemistry. In the simplified model, the diffusion terms in the transport equations are selectively replaced by rate terms within the core region of the stack. This allows much coarser meshes to be employed at a fraction of the computational cost. Following the mathematical description of the problem, results for single-cell and multi-cell stacks are presented. Comparisons of local current density, temperature, and cell voltage indicate that good agreement is obtained between the detailed and simplified models, verifying the latter as a practical option in stack design. Then, the simplified model is used to determine the effects of utilization on the electrochemical performance and temperature distributions of a 10 cell stack. The results are presented in terms of fluid flow, pressure, species mass fraction, temperature, voltage and current density distributions. The effects of species and flow distributions on electrochemical performance and temperature are then analyzed for a 100 cell stack. The discussion highlights the importance of manifold design on performance and thermal management of large stacks. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2013-09-30 15:55:18.627

Cette thèse est consacrée à l’étude de la dynamique et du transport des phonons via la résolution de l’équation de transport de Boltzmann (ETB) pour les Phonons. Un ‘solveur’ Monte Carlo dédié à la résolution de l’ETB des phonons dans l’espace réciproque, prenant en compte tous les processus d’interactions Normaux et Umklapp à trois-phonons, est proposé. Une prise en compte rigoureuse des lois de conservation de l’énergie et de la quantité de mouvement est entreprise. Des relations de dispersion réalistes, intégrant tous les modes de polarisations, sont considérées. Le calcul des taux d’interactions à trois-phonons de tous les processus Normaux et Umklapp est effectué en utilisant l’approche théorique due à Ridley qui ne nécessite qu’un unique paramètre semi-ajustable pour chaque mode de polarisation, nommément : le coefficient de couplage anharmonique représenté par les constantes de Grüneisen. Les taux d’interactions ainsi calculés ne servent pas uniquement à la résolution de l’ETB des phonons, mais ont permis aussi une analyse complète des canaux de relaxation des phonons longitudinaux optiques de centre de zone. Cette analyse a montré que le canal de Vallée-Bogani est négligeable dans le GaAs, et que vraisemblablement les temps de vie des phonons LO de centre de zone dans l’InAs et le GaSb rapportés dans la littérature sont fortement sous-estimés. Pour la première fois à notre connaissance, un couplage de deux solveurs Monte Carlo indépendants l’un dédié aux porteurs de charges (Thèse E. Tea) et l’autre dédié aux phonons, est effectué. Cela permet d’étudier l’effet des phonons chauds sur le transport des porteurs de charges. Cette étude a montré que l’approximation de temps de relaxation surestime souvent l’effet bottleneck des phonons. Le ‘solveur’ Monte Carlo est étendu pour résoudre l’ETB des phonons dans l’espace réel (en plus de l’espace réciproque), cela a permet d’étudier le transport des phonons et ainsi de la chaleur. La théorie généralisée de Ridley est toujours utilisée avec des particules de simulations qui interagissent les unes avec les autres directement. Les règles de conservation de l’énergie et de la quantité de mouvement sont rigoureusement respectées. L’effet des processus Umklapp sur la quantité de mouvement totale des phonons est fidèlement traduit; tout comme l’effet des interactions sur les directions des phonons, grâce à une procédure prenant en compte les directions vectorielles respectives lors d’une interaction, au lieu, de la distribution aléatoire usuellement utilisée. Les résultats préliminaires montrent la limite de l’équation analytique de conduction de la chaleur. / This work is dedicated to the study of phonon transport and dynamics via the solution of Boltzmann Transport Equation (BTE) for phonons. The Monte Carlo stochastic method is used to solve the phonon BTE. A solution scheme taking into account all the different individual types of Normal and Umklapp processes which respect energy and momentum conservation rules is presented. The use of the common relaxation time approximation is thus avoided. A generalized Ridley theoretical scheme is used instead to calculate three-phonon scattering rates, with the Grüneisen constant as the only adjustable parameter. A method for deriving adequate adjustable anharmonic coupling coefficients is presented. Polarization branches with real nonlinear dispersion relations for transverse or longitudinal optical and acoustic phonons are considered. Zone-center longitudinal optical (LO) phonon lifetimes are extracted from the MC simulations for GaAs, InP, InAs, and GaSb. Decay channels contributions to zone-center LO phonon lifetimes are investigated using the calculated scattering rates. Vallée-Bogani’s channel is found to have a negligible contribution in all studied materials, notably GaAs. A comparison of phonons behavior between the different materials indicates that the previously reported LO phonon lifetimes in InAs and GaSb were quite underestimated in the literature. For the first time, to our knowledge, a coupling of two independent Monte Carlo solvers, one for charge carriers [PhD manuscript, E. TEA], and one for phonons, is undertaken. Hot phonon effect on charge carrier dynamics is studied. It is shown that the relaxation time approximation overestimates the phonon bottleneck effect. The phonon MC solver is extended to solve the phonon’s BTE in real space simultaneously with the reciprocal space, to study phonon and heat transport. Ridley’s generalized theoretical scheme is utilized again with simulation particles interacting directly together. Energy and momentum conservation laws are rigorously implemented. Umklapp processes effect on the total phonon momentum is thoroughly reproduced, as for the anharmonic interactions effect on resulting phonon directions. This is thanks to a procedure taking in consideration the respective vector directions during an interaction, instead of the randomization procedure usually used in literature. Our preliminary results show the limit of the analytic macroscopic heat conduction equation.

In dieser Arbeit wird erstmalig der Einfluss stochastischer Schwankungen auf endoreversible Modelle untersucht. Hierfür wird die Novikov-Maschine mit drei verschieden Wärmetransportgesetzen (Newton, Fourier, asymmetrisch) betrachtet. Während die maximale verrichtete Arbeit und der dazugehörige Wirkungsgrad recht einfach im Falle konstanter Wärmebadtemperaturen hergeleitet werden können, ändern sich dies, falls die Temperaturen stochastisch fluktuieren können. Im letzteren Fall muss die stochastische optimale Kontrolltheorie genutzt werden, um das Maximum der zu erwartenden Arbeit und die dazugehörige Kontrollstrategie zu ermitteln. Im Allgemeinen kann die Lösung derartiger Probleme auf eine nichtlineare, partielle Differentialgleichung, welche an eine Optimierung gekoppelt ist, zurückgeführt werden. Diese Gleichung wird stochastische Hamilton-Jacobi-Bellman-Gleichung genannt. Allerdings können, wie in dieser Arbeit dargestellt, die Berechnungen vereinfacht werden, wenn man annimmt, dass die Fluktuationen unabhängig von der betrachteten Kontrollvariablen sind. In diesem Fall zeigen analytische Betrachtungen, dass die Gleichungen für die verrichtete Arbeit and den Wirkungsgrad ihre ursprüngliche Form behalten, aber manche Terme müssen durch entsprechende Zeitmittel bzw. Erwartungswerte ersetzt werden, jeweils abhängig von der betrachteten Art der Kontrolle. Basierend auf einer Analyse der Leistungsparameter im Falle einer Gleichverteilung der heißen Temperatur der Novikov-Maschine können Schlussfolgerungen auf deren Monotonieverhalten gezogen werden. Der Vergleich verschiedener, zeitunabhängiger, symmetrischer Verteilungen führt zu einer bis dato unbekannten Erweiterung des Curzon-Ahlborn-Wirkungsgrades im Falle kleiner Schwankungen. Weiterhin wird eine Analyse einer Novikov-Maschine mit asymmetrischen Wärmetransport, bei der das Verhalten der heißen Temperatur durch einen Ornstein-Uhlenbeck-Prozess beschrieben wird, durchgeführt. Abschließend wird eine Novikov-Maschine mit Fourierscher Wärmeleitung, bei der die Dynamik der heißen Temperatur von der Kontrollvariable abhängt, betrachtet. Durch das Lösen der Hamilton-Jacobi-Bellman-Gleichung können neuartige Schlussfolgerungen gezogen werden, wie derartige Systeme optimal zu steuern sind. / In this thesis, the influence of stochastic fluctuations on the performance of endoreversible engines is investigated for the first time. For this, a Novikov-engine with three different heat transport laws (Newtonian, Fourier, asymmetric) is considered. While the maximum work output and corresponding efficiency can be deduced easily in the case of constant heat bath temperatures, this changes, if these temperatures are allowed to fluctuate stochastically. In the latter case, stochastic optimal control theory has to be used to find the maximum of the expected work output and the corresponding control policy. In general, solving such problems leads to a non-linear, partial differential equation coupled to an optimization, called the stochastic Hamilton-Jacobi-Bellman equation. However, as presented in this thesis, calculations can be simplified, if one assumes that the fluctuations are independent of the considered control variable. In this case, analytic considerations show that the equations for performance measures like work output and efficiency keep their original form, but terms have to be replaced by appropriate time averages and expectation values, depending on the considered control type. Based on an analysis of the performance measures in the case of a uniform distribution of the hot temperature of the Novikov engine, conclusions on their monotonicity behavior are drawn. The comparison of several, time independent, symmetric distributions reveals a to date unknown extension to the Curzon-Ahlborn efficiency in the case of small fluctuations. Furthermore, an analysis of a Novikov engine with asymmetric heat transport, where the behavior of the hot temperature is described by an Ornstein-Uhlenbeck process, is performed. Finally, a Novikov engine with Fourier heat transport is considered, where the dynamics of the hot temperature depends on the control variable. By solving the corresponding Hamilton-Jacobi-Bellman equation, new conclusions how to optimally control such systems are drawn.

Cooking is an integral part of each and every human being as food is one of the basic necessities for living. Commonly used sources of energy for cooking are firewood, crop residue, cow dung, kerosene, electricity, liquefied petroleum gas(LPG), biogas etc. Half of the world’s population is exposed to indoor air pollution, mainly the result of burning solid fuels for cooking and heating. Wood cut for cooking purpose contributes tothe16 million hectares(above4% of total area of India) of forest destroyed annually. The World Health Organization(WHO) reports that in 23 countries 10% of deaths are due to just two environmental risk factors: unsafe water, including poor sanitation and hygiene; and indoor air pollution due to solid fuel usage for cooking. In under-developed countries, women have to walk 2kms on average and spend significant amount of time for collecting the firewood for cooking. The cooking energy demand in rural areas of developing countries is largely met with bio-fuels such as fuel wood, charcoal, agricultural residues and dung cakes, whereas LPG or electricity is predominantly used in urban areas. India has abandon amount of solar energy in most of the regions making it most ideal place for harvesting solar energy. With almost 300 sunny days each year, one can confidently relay on this source of energy. India’s geographical location is in such a way that theoretically it receives 5x1015 kWh/ year of solar energy. Solar cooking is the simplest, safest, environmental friendly and most convenient way to cook. It is a blessing for those who cook using firewood or cow dung, who walk for miles to collect wood, who suffer from indoor air pollution. Hence solar cooking is going to play major role in solving future energy problem. Solar based cooking has never been a strong contender in the commercial market or even close to being a preferred method of cooking. They have been relegated to demonstration appliances to show case the solar based concepts. In this mode, cooking is no longer a time independent activity that can be performed at any time of day. One is forced to cook only at certain times when there is sufficient insolation. The geography of the cooking activity also shifts away from the kitchen. The kitchen is no longer the hearth of the home as the actual cooking activity shifts to the roof tops or high insolation platforms. This further adds to the inconvenience apart from being unable to cook at night or during cloudy conditions or during most of the winter days. Another issue of significant inconvenience is the general social structure in most families of the developing countries wherein the cooking activity is carried out by the senior ladies of the home. They are generally not athletic enough to be moving to and from the kitchen and the roof top to carry out the cooking exercise. As the solar cookers are enclosed spaces, interactive cooking is not possible let alone having any control on the rate of cooking. These are some of the more significant issues in the social psyche that has abundantly impeded the acceptance of solar thermal based cooking appliances. These issues and problems are in fact the motivating factors for this thesis. Based on these motivating factors, this thesis aims to propose solutions keeping the following points as the major constraints. cooking should be performed in the kitchen. one should be able to perform the cooking activity independent of the time of day or insolation. the cooking activity should be interactive the time taken for cooking should be comparable with the conventional methods in vogue. there should be a reduction in the use of conventional energy. Using the constraints and the motivating factors discussed above as the central theme, this thesis proposes a method to transfer solar thermal energy to the kitchen and act as a supplement to the conventional source of energy like the LPG or other sources that are traditionally being used in the households. The method proposed is in fact a hybrid scenario wherein the solar thermal is used to supplement the traditional source. Solar photovoltaic cells are also used to power the electronics and apparatus proposed in this thesis. This thesis addresses in detail the issues in analysis, modeling, designing and fabrication of the proposed hybrid solar cooking topology. The main goal of the proposed system is to transfer heat from sun to the cooking load that is located in the kitchen. The topology includes an additional feature for storing the energy in a buffer. The heat is first transferred from the solar thermal collector to a heat storage tank(that acts as the buffer) by circulating the heat transfer fluid at a specific flow rate that is controlled by a pump. The stored heat energy that is collected in the buffer is directed into the kitchen by circulating the heat transfer fluid into the heat exchanger, located in the kitchen. This is accomplished by controlling the flow rate using another pump. The solar thermal collector raises the temperature of the thermic fluid. The collector can be of a concentrating type in order to attain high temperatures for cooking. Concentrating collector like linear parabolic collector or parabolic dish collector is used to convert solar energy into heat energy. Absorption of energy from the incident solar insolation is optimized by varying the flow rate of circulating thermic fluid using a pump. This pump is energized from a set of photovoltaic panels(PV cell) which convert solar energy into electrical energy. The energy absorbed from the solar thermal collector is stored in a buffer tank which is thermally insulated. Whenever cooking has to be carried out, the high temperature fluid from the buffer tank is circulated through a heat exchanger that is located in the kitchen. The rate of cooking can be varied by controlling both the flow rate of fluid from the buffer tank to heat exchanger and also by controlling the amount of energy drawn from the auxiliary source. If the available stored energy is not sufficient, the auxiliary source of energy is used for cooking in order to ensure that cooking is in-dependent of time and solar insolation. In the proposed hybrid solar cooking system, the thesis addresses the issues involved in optimization of energy extracted from sun to storage tank and its subsequent transfer from the storage tank to the load. The flow rate at which maximum energy is extracted from sun depends on many parameters. Solar insolation is one of the predominant parameters that affect the optimum flow rate. Insolation at any location varies with time on a daily basis (diurnal variations) and also with day on a yearly basis(seasonal variation). This implies that the flow rate of the fluid has to be varied appropriately to maximize the energy absorbed from sun. In the proposed system, flow rate control plays a very significant role in maximizing the energy transfer from the collector to the load. The flow rate of the thermic fluid in the proposed system is very small on the order of 0.02kg/s. It is very difficult to sense such low flows without disrupting the operating point of the system. Though there are many techniques to measure very low flow rates, they invariably disrupt the system in which flow rate has to be measured. Further, the low flow sensors are far too expensive to be included in the system. A reliable, accurate and inexpensive flow measuring technique has been proposed in this thesis which is non-disruptive and uses a null-deflection technique. The proposed measuring method compensates the pressure drop across the flow meter using a compensating pump. The analysis, modeling, design and fabrication of this novel flow meter are addressed. The design and implementation of different subsystems that involves the selection and design of solar concentrating collector and tracking are explained. Finally, it is essential to know the economic viability of the proposed system that is designed and implemented. To understand the economics, the life cycle cost analysis of the proposed system is presented in this thesis. The major contributions of this thesis are: Energy transport: Major challenge in energy transport is to bring heat energy obtained from the sun to the kitchen for cooking. Energy transferred from solar insolation to the cooking load has to be optimized to maximize the overall efficiency. This can be split in to two parts,(a) optimizing efficiency of energy transferred from the collect or to the energy buffer tank,(b) optimizing efficiency of energy transferred from the buffer tank to the load. The optimization is performed by means of a maximum power point tracking(MPPT) algorithm for a specific performance index. Modeling of the cooking system: There are several domains that exist in the solar cooking system such as electrical domain, thermal domain, and hydraulic domain. The analysis of power/energy flow across all these domains presents a challenging task in developing a model of the hybrid cooking system. A bond graph modeling approach is used for developing the mathematical model of the proposed hybrid cooking system. The power/energy flow across different domains can be seamlessly integrated using the bond graph modeling approach. In this approach, the various physical variables in the multi-domain environment are uniformly de-fined as generalized power variables such as effort and flow. The fundamental principle of conservation of power/energy issued in describing the flow of power/energy across different domains and thus constructing the dynamic model of the cooking system. This model is validated through experimentation and simulation. Flow measurement: A novel method of low fluid mass flow measurement by compensating the pressure drop across the ends of measuring unit using a compensating pump has been proposed. The pressure drop due to flow is balanced by feedback control loop. This is a null-deflection type of measurement. As insertion of such a measuring unit does not affect the functioning of the systems, this is also a non-disruptive flow measurement method. This allows the measurement of very low flow rate at very low resolution. Implementation and design of such a unit are discussed. The system is modeled using bond graph technique and then simulated. The flow meter is fabricated and the model is experimentally validated. Design Toolbox: Design of hybrid cooking system involves design of multi domain systems. The design becomes much more complex if the energy source to operate the system is hybrid solar based. The energy budget has to be evaluated considering the worst case conditions for the availability of the solar energy. The design toolbox helps in assessing the user requirement and help designing the cooking system to fulfill the user requirement. A detailed toolbox is proposed to be developed that can be used in designing/selecting sub-systems like collector, concentrator, tracking system, buffer tank, heat exchanger, PV panel, batteries etc. The toolbox can also be used for performing life cycle costing.

The topic of this doctoral thesis is to study the thermal properties of PCM materials and discussion of their use for cooling of photovoltaic systems. The aim of the study is to measure and characterize the thermal properties of commercial PCM materials (Micronal®), their practical use is related to the phase transitions. The behavior of bulk materials at different temperatures is well described theoretically and experimentally verified. For the application use it is necessary to examine and determine the thermal properties of PCM materials depending on the phase transitions during heating and cooling. To study the thermal properties of materials the known transient methods of measuring are used which give full information about the behavior of the materials investigated in dependence on the temperature and thus allow the determination of the thermo-physical parameters of the system. For the transient measurements there are used especially pulse transient and step wise method. Newly is used also combination of linear temperature rise (the ramp wise) and the step wise method. The principle is based on the generation of a small amount of heat inside the studied sample and it is measured the thermal response of the system from which it may be then determined the necessary thermo-physical parameters. The theoretical part of this thesis focuses on characterization of methods for the determination of thermo-physical parameters of the investigated material. In the experimental part of the approached process of experiment, the results, the method of evaluation of the obtained data and also the discussion of results from the viewpoint of potential applications are presented.

In dieser Arbeit wird erstmalig der Einfluss stochastischer Schwankungen auf endoreversible Modelle untersucht. Hierfür wird die Novikov-Maschine mit drei verschieden Wärmetransportgesetzen (Newton, Fourier, asymmetrisch) betrachtet. Während die maximale verrichtete Arbeit und der dazugehörige Wirkungsgrad recht einfach im Falle konstanter Wärmebadtemperaturen hergeleitet werden können, ändern sich dies, falls die Temperaturen stochastisch fluktuieren können. Im letzteren Fall muss die stochastische optimale Kontrolltheorie genutzt werden, um das Maximum der zu erwartenden Arbeit und die dazugehörige Kontrollstrategie zu ermitteln. Im Allgemeinen kann die Lösung derartiger Probleme auf eine nichtlineare, partielle Differentialgleichung, welche an eine Optimierung gekoppelt ist, zurückgeführt werden. Diese Gleichung wird stochastische Hamilton-Jacobi-Bellman-Gleichung genannt. Allerdings können, wie in dieser Arbeit dargestellt, die Berechnungen vereinfacht werden, wenn man annimmt, dass die Fluktuationen unabhängig von der betrachteten Kontrollvariablen sind. In diesem Fall zeigen analytische Betrachtungen, dass die Gleichungen für die verrichtete Arbeit and den Wirkungsgrad ihre ursprüngliche Form behalten, aber manche Terme müssen durch entsprechende Zeitmittel bzw. Erwartungswerte ersetzt werden, jeweils abhängig von der betrachteten Art der Kontrolle. Basierend auf einer Analyse der Leistungsparameter im Falle einer Gleichverteilung der heißen Temperatur der Novikov-Maschine können Schlussfolgerungen auf deren Monotonieverhalten gezogen werden. Der Vergleich verschiedener, zeitunabhängiger, symmetrischer Verteilungen führt zu einer bis dato unbekannten Erweiterung des Curzon-Ahlborn-Wirkungsgrades im Falle kleiner Schwankungen. Weiterhin wird eine Analyse einer Novikov-Maschine mit asymmetrischen Wärmetransport, bei der das Verhalten der heißen Temperatur durch einen Ornstein-Uhlenbeck-Prozess beschrieben wird, durchgeführt. Abschließend wird eine Novikov-Maschine mit Fourierscher Wärmeleitung, bei der die Dynamik der heißen Temperatur von der Kontrollvariable abhängt, betrachtet. Durch das Lösen der Hamilton-Jacobi-Bellman-Gleichung können neuartige Schlussfolgerungen gezogen werden, wie derartige Systeme optimal zu steuern sind. / In this thesis, the influence of stochastic fluctuations on the performance of endoreversible engines is investigated for the first time. For this, a Novikov-engine with three different heat transport laws (Newtonian, Fourier, asymmetric) is considered. While the maximum work output and corresponding efficiency can be deduced easily in the case of constant heat bath temperatures, this changes, if these temperatures are allowed to fluctuate stochastically. In the latter case, stochastic optimal control theory has to be used to find the maximum of the expected work output and the corresponding control policy. In general, solving such problems leads to a non-linear, partial differential equation coupled to an optimization, called the stochastic Hamilton-Jacobi-Bellman equation. However, as presented in this thesis, calculations can be simplified, if one assumes that the fluctuations are independent of the considered control variable. In this case, analytic considerations show that the equations for performance measures like work output and efficiency keep their original form, but terms have to be replaced by appropriate time averages and expectation values, depending on the considered control type. Based on an analysis of the performance measures in the case of a uniform distribution of the hot temperature of the Novikov engine, conclusions on their monotonicity behavior are drawn. The comparison of several, time independent, symmetric distributions reveals a to date unknown extension to the Curzon-Ahlborn efficiency in the case of small fluctuations. Furthermore, an analysis of a Novikov engine with asymmetric heat transport, where the behavior of the hot temperature is described by an Ornstein-Uhlenbeck process, is performed. Finally, a Novikov engine with Fourier heat transport is considered, where the dynamics of the hot temperature depends on the control variable. By solving the corresponding Hamilton-Jacobi-Bellman equation, new conclusions how to optimally control such systems are drawn.

Do changes in how cross-equatorial energy transport is partitioned between the ocean and atmosphere impact the hemispheric climate response to forcing? To find out, we alter the cross-equatorial ocean heat transport in a state-of-the-art GCM and ascertain how changes in energy transport and its partitioning impact hemispheric climate and precipitation sensitivity following abrupt CO2-doubling. We further evaluate the applicability our results in CMIP6-class ESMs, where AMOC facilitates the northward cross-equatorial ocean heat transport. In our experiments, changes in ocean cross-equatorial energy transport trigger compensating changes in atmospheric energy transport through changes in the Hadley cells and a shift in the Intertropical Convergence Zone. However, the climate sensitivity in each hemisphere is linearly related to the ocean heat transport convergence, not atmospheric energy transport convergence, due to the impact of ocean heating on evaporation and atmospheric specific humidity. Similarly, we also find that ocean heat transport convergence controls the hemispheric precipitation sensitivity through the impact of ocean heating on surface evaporation. This relationship is also evident in CMIP6 models, where we find differences in hemispheric precipitation sensitivity to be related to the Atlantic Meridional Overturning Circulation (AMOC). Changes in the AMOC control hemispheric differences in upper ocean heat content, which then affect how the hydrologic cycle responds to CO2 forcing in each hemisphere. These results suggest that ocean dynamics impact the hemispheric climate response to CO2 forcing, particularly how much regional precipitation changes with warming. / Graduate

The need to consider groundwater and surface water as a single resource has fostered the interest of the scientific community on the interactions between surface water and groundwater. The region below and alongside rivers where surface hydrology and subsurface hydrology concur is the hyporheic zone. This is the region where water exchange determines many biogeochemical and ecological processes of great impact on the functioning of rivers. However, the complex processes taking place in the hyporheic zone require a multidisciplinary approach. The combination of innovative point and distributed techniques originally developed in separated disciplines is of great advantage for the indirect identification of water exchange in the hyporheic zone. Distributed techniques using temperature as a tracer such as fiber-optic distributed temperature sensing can identify the different components of groundwater-surface water interactions based on their spatial and temporal thermal patterns at the sediment-water interface. In particular, groundwater, interflow discharge and local hyporheic exchange flows can be differentiated based on the distinct size, duration and sign of the temperature anomalies. The scale range and resolution of fiber-optic distributed temperature sensing are well complemented by geophysics providing subsurface structures with a similar resolution and scale. Thus, the use of fiber-optic distributed temperature sensing to trace flux patterns supported by the exploration of subsurface structures with geophysics enables spatial and temporal investigation of groundwater-surface water interactions with an unprecedented level of accuracy and resolution. In contrast to the aforementioned methods that can be used for pattern identification at the interface, other methods such as point techniques are required to quantify hyporheic exchange fluxes. In the present PhD thesis, point methods based on hydraulic gradients and thermal profiles are used to quantify hyporheic exchange flows. However, both methods are one-dimensional methods and assume that only vertical flow occurs while the reality is much more complex. The study evaluates the accuracy of the available methods and the factors that impact their reliability. The applied methods allow not only to quantify hyporheic exchange flows but they are also the basis for an interpretation of the sediment layering in the hyporheic zone. For upscaling of the previous results three-dimensional modelling of flow and heat transport in the hyporheic zone combines pattern identification and quantification of fluxes into a single framework. Modelling can evaluate the influence of factors governing groundwater-surface water interactions as well as assess the impact of multiple aspects of model design and calibration of high impact on the reliability of the simulations. But more importantly, this modelling approach enables accurate estimation of water exchange at any location of the domain with unparalleled resolution. Despite the challenges in 3D modelling of the hyporheic zone and in the integration of point and distributed data in models, the benefits should encourage the hyporheic community to adopt an integrative approach comprising from the measurement to the upscaling of hyporheic processes.