Gaussian estimates for the density of the non-linear stochastic heat equation in any space dimension

In this paper, we establish lower and upper Gaussian bounds for the probability density of the mild solution to the stochastic heat equation with multiplicative noise and in any space dimension. The driving perturbation is a Gaussian noise which is white in time with some spatially homogeneous covariance. These estimates are obtained using tools of the Malliavin calculus. The most challenging part is the lower bound, which is obtained by adapting a general method developed by Kohatsu-Higa to the underlying spatially homogeneous Gaussian setting. Both lower and upper estimates have the same form: a Gaussian density with a variance which is equal to that of the mild solution of the corresponding linear equation with additive noise.

Nuclear phenotype changes after heat shock in Panstrongylus megistus (Burmeister)

The nuclear phenotypes of Malpighian tubule epithelial cells of male nymphs of the blood-sucking insect, Panstrongylus megistus, subjected to short- and long-duration heat shocks at 40ºC were analyzed immediately after the shock and 10 and 30 days later. Normal nuclei with a usual heterochromatic body as well as phenotypes indicative of survival (unravelled heterochromatin, giants) and death (apoptosis, necrosis) responses were observed in control and treated specimens. However, all nuclear phenotypes, except the normal ones, were more frequent in shocked specimens. Similarly altered phenotypes have also been reported in Triatoma infestans following heat shock, although at different frequencies. The frequency of the various nuclear phenotypes observed in this study suggests that the forms of cell survival observed were not sufficient or efficient enough to protect all of the Malpighian tubule cells from the deleterious effects of stress. In agreement with studies on P. megistus survival following heat shock, only long-duration shock produced strongly deleterious effects.

Anomalous specific-heat jump in a two-component ultracold Fermi gas

The thermodynamic functions of a Fermi gas with spin population imbalance are studied in the temperature-asymmetry plane in the BCS limit. The low-temperature domain is characterized by an anomalous enhancement of the entropy and the specific heat above their values in the unpaired state, decrease of the gap and eventual unpairing phase transition as the temperature is lowered. The unpairing phase transition induces a second jump in the specific heat, which can be measured in calorimetric experiments. While the superfluid is unstable against a supercurrent carrying state, it may sustain a metastable state if cooled adiabatically down from the stable high-temperature domain. In the latter domain the temperature dependence of the gap and related functions is analogous to the predictions of the BCS theory.

Heat fluctuations in Brownian transducers

The heat fluctuation probability distribution function in Brownian transducers operating between two heat reservoirs is studied. We find, both analytically and numerically, that the recently proposed fluctuation theorem for heat exchange [C. Jarzynski and D. K. Wojcik, Phys. Rev. Lett. 92, 230602 (2004)] has to be applied carefully when the coupling mechanism between both baths is considered. We also conjecture how to extend such a relation when an external work is present.

Magnetization versus heat treatment in rapidly solidified NdFeB alloys

NdFeB melt-spun amorphous or partially amorphous alloys of four compositions were prepared. Their crystallization kinetics induced by thermal treatment was studied by differential scanning calorimetry and scanning and transmission electron microscopy. Scanning electron microscopy demonstrated that heterogeneous nucleation occurs preferentially at the ribbon surface which was in contact with the wheel. The explicit form of the kinetic equation that best describes the first stage of crystallization under high undercooling conditions was obtained for each alloy. From the crystallization results, the lower part of the experimental time-temperature-transformation curves was deduced for each alloy and extrapolated up to the high-temperature limit of their validity. Microstructural observations showed a typical size of the microcrystals obtained by heat treatment of ~100 nm. From the magnetic properties measured with a vibrating sample magnetometer, the same magnetic behavior of partially crystallized alloys is observed regardless of the temperature of annealing provided the same crystallization fraction, x, is achieved, at least for small values of x (typically ~10%).

Simulation of Boundary Layers and Heat Transfer in the Entrance Region of Pipes

The study of fluid flow in pipes is one of the main topic of interest for engineers in industries. In this thesis, an effort is made to study the boundary layers formed near the wall of the pipe and how it behaves as a resistance to heat transfer. Before few decades, the scientists used to derive the analytical and empirical results by hand as there were limited means available to solve the complex fluid flow phenomena. Due to the increase in technology, now it has been practically possible to understand and analyze the actual fluid flow in any type of geometry. Several methodologies have been used in the past to analyze the boundary layer equations and to derive the expression for heat transfer. An integral relation approach is used for the analytical solution of the boundary layer equations and is compared with the FLUENT simulations for the laminar case. Law of the wall approach is used to derive the empirical correlation between dimensionless numbers and is then compared with the results from FLUENT for the turbulent case. In this thesis, different approaches like analytical, empirical and numerical are compared for the same set of fluid flow equations.

Numerical and ExperimentalModelling of Gas Flow and Heat Transfer in the Air Gap of An Electric Machine

This work deals with the cooling of high-speed electric machines, such as motors and generators, through an air gap. It consists of numerical and experimental modelling of gas flow and heat transfer in an annular channel. Velocity and temperature profiles are modelled in the air gap of a high-speed testmachine. Local and mean heat transfer coefficients and total friction coefficients are attained for a smooth rotor-stator combination at a large velocity range. The aim is to solve the heat transfer numerically and experimentally. The FINFLO software, developed at Helsinki University of Technology, has been used in the flow solution, and the commercial IGG and Field view programs for the grid generation and post processing. The annular channel is discretized as a sector mesh. Calculation is performed with constant mass flow rate on six rotational speeds. The effect of turbulence is calculated using three turbulence models. The friction coefficient and velocity factor are attained via total friction power. The first part of experimental section consists of finding the proper sensors and calibrating them in a straight pipe. After preliminary tests, a RdF-sensor is glued on the walls of stator and rotor surfaces. Telemetry is needed to be able to measure the heat transfer coefficients at the rotor. The mean heat transfer coefficients are measured in a test machine on four cooling air mass flow rates at a wide Couette Reynolds number range. The calculated values concerning the friction and heat transfer coefficients are compared with measured and semi-empirical data. Heat is transferred from the hotter stator and rotor surfaces to the coolerair flow in the air gap, not from the rotor to the stator via the air gap, althought the stator temperature is lower than the rotor temperature. The calculatedfriction coefficients fits well with the semi-empirical equations and precedingmeasurements. On constant mass flow rate the rotor heat transfer coefficient attains a saturation point at a higher rotational speed, while the heat transfer coefficient of the stator grows uniformly. The magnitudes of the heat transfer coefficients are almost constant with different turbulence models. The calibrationof sensors in a straight pipe is only an advisory step in the selection process. Telemetry is tested in the pipe conditions and compared to the same measurements with a plain sensor. The magnitudes of the measured data and the data from the semi-empirical equation are higher for the heat transfer coefficients than thenumerical data considered on the velocity range. Friction and heat transfer coefficients are presented in a large velocity range in the report. The goals are reached acceptably using numerical and experimental research. The next challenge is to achieve results for grooved stator-rotor combinations. The work contains also results for an air gap with a grooved stator with 36 slots. The velocity field by the numerical method does not match in every respect the estimated flow mode. The absence of secondary Taylor vortices is evident when using time averagednumerical simulation.

In-Vessel Penetrator -käärmerobotin mallinnus ADAMS-ohjelmistolla

Työn tavoitteena oli muodostaa virtuaaliprototyyppi fuusioreaktorin huollossa käytettävästä IVP-robotista. Työssä mallinnettiin robotin mekaniikka joustavana sekä toimilaitteiden ja käyttöjen dynaamiset ominaisuudet valmistajien esitietojen ja mitoitustietojen perusteella. Käyttöjen ja mekaniikan mallit yhdistettiin ADAMS-ohjelmistossa. Mekaanisten joustojen mallinnuksessa sekä verifioinnissa käytettiin apuna ANSYS –ohjelmistoa. Virtuaaliprototyypin toimivuudesta varmistuttiin vertaamalla sitä robotin suunnittelutietoihin ja fyysiseen prototyyppiin. Robotin ohjauksessa käytettävän P-säätäjän vaikutusta tutkittiin eri vahvistuksen arvoilla sekä verrattiin mekaanisia vasteita fyysisen prototyypin dynaamisiin testeihin. Esimerkkinä robotin käyttäytymisestä todellisessa tilanteessa simuloitiin sen ajoa reaktoriin. Toteutetun simulointimallin todettiin vastaavan rakenteeltaan sekä siinä esiintyvien voimien osalta suunnitelmien mukaista konstruktiota. Käytetyillä parametreilla se toteutti hyvin robotille asetetut nopeusvaatimukset.

Hydrodynamics and Heat Transfer in an Airlift Reactor

Työn teoriaosassa esitetään kirjallisuudessa esiintyviä teoreettisia ja kokeellisia yhtälöitä nesteen nopeuden, kaasun tilavuusosuuden, painehäviön ja lämmönsiirron laskemiseksi. Lisäksi käsitellään airlift-reaktoreiden toimintaa, rakennetta ja teollisia sovelluksia, sekä sekoitusta ja geometrian vaikutusta airlift-reaktoreiden hydrodynaamisiin ominaisuuksiin. Kokeellisessa osassa kuvataan käytetty koelaitteisto ja mittausmenetelmät sekä esitetään saadut koetulokset. Koelaitteisto on viidellä nousuputkella varustettu ulkoisen kierron airlift-reaktori. Kokeellisessa osassa pyritään ratkaisemaan tällaisessa reaktorissa mahdollisesti esiintyviä ongelmia, kuten "slug flown" muodostuminen nousuputkissa sekä fluidien epätasainen jakautuminen nousuputkiin. Lisäksi tutkitaan erilaisten muuttujien, kuten kaasun tilavuusvirran, nesteen viskositeetin, suutinkoon ja nesteen jakoputken rakenteen, vaikutusta kaasun tilavuusosuuteen ja nesteen nopeuteen nousuputkissa. Nesteen nopeudet mitataan merkkiainemenetelmällä ja kaasun tilavuusosuudet manometrimenetelmällä. Lämmönsiirtoa tutkitaan mittaamalla lämpötilaeroja nousuputkissa NiCr-Ni –termoelementeillä. Mittaustulosten perusteella muokataan korrelaatiot kaasun tilavuusosuudelle ja nesteen tyhjäputkinopeudelle. Korrelaatioista lasketut tulokset sopivat kohtuullisen hyvin yhteen mitattujen tulosten kanssa. "Slug flown" ei todettu muodostuvan ongelmaksi 2.5 mPa s pienemmillä viskositeetin arvoilla 2 metriä pitkissä ja 19 mm halkaisijaltaan olevissa putkissa. Lisäksi todettiin, että kaasu- ja nestefaasien jakautumisongelmat voidaan ratkaista rakenteellisesti.

Radiative Heat Transfer in Boiler Furnaces

Better models are needed for radiative heat transfer in boiler furnaces. If the process is known better, combustion in the furnace can be optimized to produce low emissions. It makes the process to be environmental friendly. Furthermore, if there is a better model of the furnace it can more fully explain what is happening inside the furnace. Using of the model one can quickly and easily analyze how it operates with bio fuels, moist fuels or difficult fuels and improve the operation. Models helps with better estimation of furnace dimensions and result in more accurate understanding of operation. Key component lacking in these models is radiative heat transfer in particle laden gases. If there are no particles than radiative heat transfer can be calculated approximately. There are two problems with current models when used with flow modeling. The first one is a need to account for a particle laden gas and the second one is an absence of a fast algorithm. Fast calculation is needed if radiative heat transfer calculation is done for a large CDF model. Computations slow down if time is required for calculating radiative properties over and over again. This thesis presents a band model for radiative heat transfer in boiler furnaces. Advantage is a quickness of calculation and account of particles in the process.

Coolant Flow and Heat Transfer in Pebble-Bed Reactor Core

This thesis gathers knowledge about ongoing high-temperature reactor projects around the world. Methods for calculating coolant flow and heat transfer inside a pebble-bed reactor core are also developed. The thesis begins with the introduction of high-temperature reactors including the current state of the technology. Process heat applications that could use the heat from a high-temperature reactor are also introduced. A suitable reactor design with data available in literature is selected for the calculation part of the thesis. Commercial computational fluid dynamics software Fluent is used for the calculations. The pebble-bed is approximated as a packed-bed, which causes sink terms to the momentum equations of the gas flowing through it. A position dependent value is used for the packing fraction. Two different models are used to calculate heat transfer. First a local thermal equilibrium is assumed between the gas and solid phases and a single energy equation is used. In the second approach, separate energy equations are used for the phases. Information about steady state flow behavior, pressure loss, and temperature distribution in the core is obtained as results of the calculations. The effect of inlet mass flow rate to pressure loss is also investigated. Data found in literature and the results correspond each other quite well, considered the amount of simplifications in the calculations. The models developed in this thesis can be used to solve coolant flow and heat transfer in a pebble-bed reactor, although additional development and model validation is needed for better accuracy and reliability.

Heat Transfer in Plate Heat Exchangers

This study illustrates the different types of plate heat exchangers that are commonly used in various domestic and industrial applications. The main purpose of this paper was to devise a methodology that is capable of calculating optimum number of plates in the design of a plate heat exchanger. To obtain the appropriate number of plates, typically several iterations must be made before a final acceptable design is completed, since plate amount depends on many factors such as, flow velocities, physical properties of the streams, flow channel geometry, allowable pressure drop, plate dimensions, and the gap between the plates. The methodology presented here can be used as a general guide for designing a plate heat exchanger. To investigate the effects of relevant parameters on the thermal-hydraulic design of a plate heat exchanger, several experiments were carried out for single-phase and counter flow arrangement with two brazed plate heat exchangers by varying the flow rates and the inlet temperatures of the fluid streams. The actual heat transfer coefficients obtained based on the experiment were nearly close to the calculated values and to improve the design, a correction factor was introduced. Besides, the effect of flow channel velocity on the pressure drop inside the unit is presented.

Heat transfer in superheaters of the bubbling fluidized bed boiler conversions

It is often reasonable to convert old boiler to bubbling fluidized bed boiler instead of building a new one. Converted boiler consists of old and new heat surfaces which must be fitted to operate together. Prediction of heat transfer in not so ideal conditions sets challenges for designers. Two converted boilers situated in Poland were studied on the grounds of acceptance tests and further studies. Calculation of boiler process was performed with boiler design program. Main interest was heat transfer in superheaters and factors affecting it. Theory for heat transfer is presented according to information found from literature. Results obtained from experimental studies and calculations have been compared. With correct definitions calculated parameters corresponded well to measured data at boiler maximum design load. However overload situations revealed to be difficult to model at least without considering changes in the combustion process which requires readjustments to the design program input values.

A three dimensional study of heat transfer in a supercritical circulating fluidized bed combustor

From the boiler design point of view, it is imperative to know and understand the operation of the boiler. Since comprehensive measurement of a large furnace is impossible, the furnace can be modeled in order to study its behavior and phenomena. This requires the used model to be validated to correspond with the physical furnace behavior. In this thesis, a three dimensional furnace model is validated to match a bituminous coal utilizing, supercritical once-through circulating fluidized bed combustor based on measurement data. The validated model is used for analyzing the furnace heat transfer. Other heat transfer analysis methods are energy balance method based on tube surface temperature measurements and a method based on measured temperature difference between the tube crest and the fin. The latter method was developed in the thesis using Fluent-software. In the theory part, literature is reviewed and the fundamental aspects of circulating fluidized bed are discussed. These aspects are solid particle behavior in fluidization known as hydrodynamics, behavior of fuel and combustion and heat transfer. Fundamental aspects of modeling are also presented.