Recovering boundary data in planar heat conduction using boundary integral equation method

We consider a Cauchy problem for the heat equation, where the temperature field is to be reconstructed from the temperature and heat flux given on a part of the boundary of the solution domain. We employ a Landweber type method proposed in [2], where a sequence of mixed well-posed problems are solved at each iteration step to obtain a stable approximation to the original Cauchy problem. We develop an efficient boundary integral equation method for the numerical solution of these mixed problems, based on the method of Rothe. Numerical examples are presented both with exact and noisy data, showing the efficiency and stability of the proposed procedure and approximations.

Numerical investigation on the heat transfer enhancement using micro/nano phase-change particulate flow

The introduction of phase change material fluid and nanofluid in micro-channel heat sink design can significantly increase the cooling capacity of the heat sink because of the unique features of these two kinds of fluids. To better assist the design of a high performance micro-channel heat sink using phase change fluid and nanofluid, the heat transfer enhancement mechanism behind the flow with such fluids must be completely understood. ^ A detailed parametric study is conducted to further investigate the heat transfer enhancement of the phase change material particle suspension flow, by using the two-phase non-thermal-equilibrium model developed by Hao and Tao (2004). The parametric study is conducted under normal conditions with Reynolds numbers of Re = 90–600 and phase change material particle concentrations of ϵp ≤ 0.25, as well as extreme conditions of very low Reynolds numbers (Re < 50) and high phase change material particle concentration (ϵp = 50%–70%) slurry flow. By using the two newly-defined parameters, named effectiveness factor ϵeff and performance index PI, respectively, it is found that there exists an optimal relation between the channel design parameters L and D, particle volume fraction ϵp, Reynolds number Re, and the wall heat flux qw. The influence of the particle volume fraction ϵp, particle size dp, and the particle viscosity μ p, to the phase change material suspension flow, are investigated and discussed. The model was validated by available experimental data. The conclusions will assist designers in making their decisions that relate to the design or selection of a micro-pump suitable for micro or mini scale heat transfer devices. ^ To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and its many numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed, through incorporating the different forces acting on the nanoparticles to the two-component lattice Boltzmann model. It is found that the nanofluid has better heat transfer enhancement at low Reynolds numbers, and the Brownian motion effect of the nanoparticles will be weakened by the increase of flow speed. ^

Design construction and testing of a heat loop for study of fouling and its interrelationship to corrosion in heat exchanger tubes

A heat loop suitable for the study of thermal fouling and its relationship to corrosion processes was designed, constructed and tested. The design adopted was an improvement over those used by such investigators as Hopkins and the Heat Transfer Research Institute in that very low levels of fouling could be detected accurately, the heat transfer surface could be readily removed for examination and the chemistry of the environment could be carefully monitored and controlled. In addition, an indirect method of electrical heating of the heat transfer surface was employed to eliminate magnetic and electric effects which result when direct resistance heating is employed to a test section. The testing of the loop was done using a 316 stainless steel test section and a suspension of ferric oxide and water in an attempt to duplicate the results obtained by Hopkins. Two types of thermal ·fouling resistance versus time curves were obtained . (i) Asymptotic type fouling curve, similar to the fouling behaviour described by Kern and Seaton and other investigators, was the most frequent type of fouling curve obtained. Thermal fouling occurred at a steadily decreasing rate before reaching a final asymptotic value. (ii) If an asymptotically fouled tube was cooled with rapid cir- ·culation for periods up to eight hours at zero heat flux, and heating restarted, fouling recommenced at a high linear rate. The fouling results obtained were observed to be similar and 1n agreement with the fouling behaviour reported previously by Hopkins and it was possible to duplicate quite closely the previous results . This supports the contention of Hopkins that the fouling results obtained were due to a crevice corrosion process and not an artifact of that heat loop which might have caused electrical and magnetic effects influencing the fouling. The effects of Reynolds number and heat flux on the asymptotic fouling resistance have been determined. A single experiment to study the effect of oxygen concentration has been carried out. The ferric oxide concentration for most of the fouling trials was standardized at 2400 ppM and the range of Reynolds number and heat flux for the study was 11000-29500 and 89-121 KW/M², respectively.

Numerical Investigation on the Heat Transfer Enhancement Using Micro/Nano Phase-Change Particulate Flow

The introduction of phase change material fluid and nanofluid in micro-channel heat sink design can significantly increase the cooling capacity of the heat sink because of the unique features of these two kinds of fluids. To better assist the design of a high performance micro-channel heat sink using phase change fluid and nanofluid, the heat transfer enhancement mechanism behind the flow with such fluids must be completely understood. A detailed parametric study is conducted to further investigate the heat transfer enhancement of the phase change material particle suspension flow, by using the two-phase non-thermal-equilibrium model developed by Hao and Tao (2004). The parametric study is conducted under normal conditions with Reynolds numbers of Re=600-900 and phase change material particle concentrations ¡Ü0.25 , as well as extreme conditions of very low Reynolds numbers (Re < 50) and high phase change material particle concentration (0.5-0.7) slurry flow. By using the two newly-defined parameters, named effectiveness factor and performance index, respectively, it is found that there exists an optimal relation between the channel design parameters, particle volume fraction, Reynolds number, and the wall heat flux. The influence of the particle volume fraction, particle size, and the particle viscosity, to the phase change material suspension flow, are investigated and discussed. The model was validated by available experimental data. The conclusions will assist designers in making their decisions that relate to the design or selection of a micro-pump suitable for micro or mini scale heat transfer devices. To understand the heat transfer enhancement mechanism of the nanofluid flow from the particle level, the lattice Boltzmann method is used because of its mesoscopic feature and its many numerical advantages. By using a two-component lattice Boltzmann model, the heat transfer enhancement of the nanofluid is analyzed, through incorporating the different forces acting on the nanoparticles to the two-component lattice Boltzmann model. It is found that the nanofluid has better heat transfer enhancement at low Reynolds numbers, and the Brownian motion effect of the nanoparticles will be weakened by the increase of flow speed.

Monitoring of active layer dynamics at two transects on Svalbard using multi-channel ground-penetrating radar

Multi-channel ground-penetrating radar is used to investigate the late-summer evolution of the thaw depth and the average soil water content of the thawed active layer at a high-arctic continuous permafrost site on Svalbard, Norway. Between mid of August and mid of September 2008, five surveys have been conducted over transect lengths of 130 and 175 m each. The maximum thaw depths range from 1.6 m to 2.0 m, so that they are among the deepest thaw depths recorded for Svalbard so far. The thaw depths increase by approximately 0.2 m between mid of August and beginning of September and subsequently remain constant until mid of September. The thaw rates are approximately constant over the entire length of the transects within the measurement accuracy of about 5 to 10 cm. The average volumetric soil water content of the thawed soil varies between 0.18 and 0.27 along the investigated transects. While the measurements do not show significant changes in soil water content over the first four weeks of the study, strong precipitation causes an increase in average soil water content of up to 0.04 during the last week. These values are in good agreement with evapotranspiration and precipitation rates measured in the vicinity of the the study site. While we cannot provide conclusive reasons for the detected spatial variability of the thaw depth at the study site, our measurements show that thaw depth and average soil water content are not directly correlated. The study demonstrates the potential of multi-channel ground-penetrating radar for mapping thaw depth in permafrost areas. The novel non-invasive technique is particularly useful when the thaw depth exceeds 1.5 m, so that it is hardly accessible by manual probing. In addition, multi-channel ground-penetrating radar holds potential for mapping the latent heat content of the active layer and for estimating weekly to monthly averages of the ground heat flux during the thaw period.

Combined Conduction-Convection-Radiation Heat Transfer of Slip Flow inside a Micro-channel Filled with a Cellular Porous Material

Combined conduction–convection–radiation heat transfer is investigated numerically in a micro-channel filled with a saturated cellular porous medium, with the channel walls held at a constant heat flux. Invoking the velocity slip and temperature jump, the thermal behaviour of the porous–fluid system are studied by considering hydrodynamically fully developed flow and applying the Darcy–Brinkman flow model. One energy equation model based on the local thermal equilibrium condition is adopted to evaluate the temperature field within the porous medium. Combined conduction and radiation heat transfer is treated as an effective conduction process with a temperature-dependent effective thermal conductivity. Results are reported in terms of the average Nusselt number and dimensionless temperature distribution, as a function of velocity slip coefficient, temperature jump coefficient, porous medium shape parameter and radiation parameters. Results show that increasing the radiation parameter (Tr)(Tr) and the temperature jump coefficient flattens the dimensionless temperature profile. The Nusselt numbers are more sensitive to the variation in the temperature jump coefficient rather than to the velocity slip coefficient. Such that for high porous medium shape parameter, the Nusselt number is found to be independent of velocity slip. Furthermore, it is found that as the temperature jump coefficient increases, the Nusselt number decrease. In addition, for high temperature jump coefficients, the Nusselt number is found to be insensitive to the radiation parameters and porous medium shape parameter. It is also concluded that compared with the conventional macro-channels, wherein using a porous material enhances the rate of heat transfer (up to about 40 % compared to the clear channel), insertion of a porous material inside a micro-channel in slip regime does not effectively enhance the rate of heat transfer that is about 2 %.

Modeling long-term variability and change of soil moisture and groundwater level - from catchment to global scale

The water stored in and flowing through the subsurface is fundamental for sustaining human activities and needs, feeding water and its constituents to surface water bodies and supporting the functioning of their ecosystems. Quantifying the changes that affect the subsurface water is crucial for our understanding of its dynamics and changes driven by climate change and other changes in the landscape, such as in land-use and water-use. It is inherently difficult to directly measure soil moisture and groundwater levels over large spatial scales and long times. Models are therefore needed to capture the soil moisture and groundwater level dynamics over such large spatiotemporal scales. This thesis develops a modeling framework that allows for long-term catchment-scale screening of soil moisture and groundwater level changes. The novelty in this development resides in an explicit link drawn between catchment-scale hydroclimatic and soil hydraulics conditions, using observed runoff data as an approximation of soil water flux and accounting for the effects of snow storage-melting dynamics on that flux. Both past and future relative changes can be assessed by use of this modeling framework, with future change projections based on common climate model outputs. By direct model-observation comparison, the thesis shows that the developed modeling framework can reproduce the temporal variability of large-scale changes in soil water storage, as obtained from the GRACE satellite product, for most of 25 large study catchments around the world. Also compared with locally measured soil water content and groundwater level in 10 U.S. catchments, the modeling approach can reasonably well reproduce relative seasonal fluctuations around long-term average values. The developed modeling framework is further used to project soil moisture changes due to expected future climate change for 81 catchments around the world. The future soil moisture changes depend on the considered radiative forcing scenario (RCP) but are overall large for the occurrence frequency of dry and wet events and the inter-annual variability of seasonal soil moisture. These changes tend to be higher for the dry events and the dry season, respectively, than for the corresponding wet quantities, indicating increased drought risk for some parts of the world.

Heat flow from the Southeast Indian Ridge flanks between 80°E and 140°E: Data review and analysis - art. no. B01101

We analyze available heat flow data from the flanks of the Southeast Indian Ridge adjacent to or within the Australian-Antarctic Discordance (AAD), an area with patchy sediment cover and highly fractured seafloor as dissected by ridge- and fracture-parallel faults. The data set includes 23 new data points collected along a 14-Ma old isochron and 19 existing measurements from the 20- to 24-Ma old crust. Most sites of measurements exhibit low heat flux (from 2 to 50 mW m(-2)) with near-linear temperature-depth profiles except at a few sites, where recent bottom water temperature change may have caused nonlinearity toward the sediment surface. Because the igneous basement is expected to outcrop a short distance away from any measurement site, we hypothesize that horizontally channelized water circulation within the uppermost crust is the primary process for the widespread low heat flow values. The process may be further influenced by vertical fluid flow along numerous fault zones that crisscross the AAD seafloor. Systematic measurements along and across the fault zones of interest as well as seismic profiling for sediment distribution are required to confirm this possible, suspected effect.

TWO-PHASE HEAT TRANSFER MECHANISMS WITHIN PLATE HEAT EXCHANGERS: EXPERIMENTS AND MODELING

Two-phase flow heat exchangers have been shown to have very high efficiencies, but the lack of a dependable model and data precludes them from use in many cases. Herein a new method for the measurement of local convective heat transfer coefficients from the outside of a heat transferring wall has been developed, which results in accurate local measurements of heat flux during two-phase flow. This novel technique uses a chevron-pattern corrugated plate heat exchanger consisting of a specially machined Calcium Fluoride plate and the refrigerant HFE7100, with heat flux values up to 1 W cm-2 and flow rates up to 300 kg m-2s-1. As Calcium Fluoride is largely transparent to infra-red radiation, the measurement of the surface temperature of PHE that is in direct contact with the liquid is accomplished through use of a mid-range (3.0-5.1 µm) infra-red camera. The objective of this study is to develop, validate, and use a unique infrared thermometry method to quantify the heat transfer characteristics of flow boiling within different Plate Heat Exchanger geometries. This new method allows high spatial and temporal resolution measurements. Furthermore quasi-local pressure measurements enable us to characterize the performance of each geometry. Validation of this technique will be demonstrated by comparison to accepted single and two-phase data. The results can be used to come up with new heat transfer correlations and optimization tools for heat exchanger designers. The scientific contribution of this thesis is, to give PHE developers further tools to allow them to identify the heat transfer and pressure drop performance of any corrugated plate pattern directly without the need to account for typical error sources due to inlet and outlet distribution systems. Furthermore, the designers will now gain information on the local heat transfer distribution within one plate heat exchanger cell which will help to choose the correct corrugation geometry for a given task.

Heat transfer performance investigation of nanofluids flow in pipe

Different types of base fluids, such as water, engine oil, kerosene, ethanol, methanol, ethylene glycol etc. are usually used to increase the heat transfer performance in many engineering applications. But these conventional heat transfer fluids have often several limitations. One of those major limitations is that the thermal conductivity of each of these base fluids is very low and this results a lower heat transfer rate in thermal engineering systems. Such limitation also affects the performance of different equipments used in different heat transfer process industries. To overcome such an important drawback, researchers over the years have considered a new generation heat transfer fluid, simply known as nanofluid with higher thermal conductivity. This new generation heat transfer fluid is a mixture of nanometre-size particles and different base fluids. Different researchers suggest that adding spherical or cylindrical shape of uniform/non-uniform nanoparticles into a base fluid can remarkably increase the thermal conductivity of nanofluid. Such augmentation of thermal conductivity could play a more significant role in enhancing the heat transfer rate than that of the base fluid. Nanoparticles diameters used in nanofluid are usually considered to be less than or equal to 100 nm and the nanoparticles concentration usually varies from 5% to 10%. Different researchers mentioned that the smaller nanoparticles concentration with size diameter of 100 nm could enhance the heat transfer rate more significantly compared to that of base fluids. But it is not obvious what effect it will have on the heat transfer performance when nanofluids contain small size nanoparticles of less than 100 nm with different concentrations. Besides, the effect of static and moving nanoparticles on the heat transfer of nanofluid is not known too. The idea of moving nanoparticles brings the effect of Brownian motion of nanoparticles on the heat transfer. The aim of this work is, therefore, to investigate the heat transfer performance of nanofluid using a combination of smaller size of nanoparticles with different concentrations considering the Brownian motion of nanoparticles. A horizontal pipe has been considered as a physical system within which the above mentioned nanofluid performances are investigated under transition to turbulent flow conditions. Three different types of numerical models, such as single phase model, Eulerian-Eulerian multi-phase mixture model and Eulerian-Lagrangian discrete phase model have been used while investigating the performance of nanofluids. The most commonly used model is single phase model which is based on the assumption that nanofluids behave like a conventional fluid. The other two models are used when the interaction between solid and fluid particles is considered. However, two different phases, such as fluid and solid phases is also considered in the Eulerian-Eulerian multi-phase mixture model. Thus, these phases create a fluid-solid mixture. But, two phases in the Eulerian-Lagrangian discrete phase model are independent. One of them is a solid phase and the other one is a fluid phase. In addition, RANS (Reynolds Average Navier Stokes) based Standard κ-ω and SST κ-ω transitional models have been used for the simulation of transitional flow. While the RANS based Standard κ-ϵ, Realizable κ-ϵ and RNG κ-ϵ turbulent models are used for the simulation of turbulent flow. Hydrodynamic as well as temperature behaviour of transition to turbulent flows of nanofluids through the horizontal pipe is studied under a uniform heat flux boundary condition applied to the wall with temperature dependent thermo-physical properties for both water and nanofluids. Numerical results characterising the performances of velocity and temperature fields are presented in terms of velocity and temperature contours, turbulent kinetic energy contours, surface temperature, local and average Nusselt numbers, Darcy friction factor, thermal performance factor and total entropy generation. New correlations are also proposed for the calculation of average Nusselt number for both the single and multi-phase models. Result reveals that the combination of small size of nanoparticles and higher nanoparticles concentrations with the Brownian motion of nanoparticles shows higher heat transfer enhancement and thermal performance factor than those of water. Literature suggests that the use of nanofluids flow in an inclined pipe at transition to turbulent regimes has been ignored despite its significance in real-life applications. Therefore, a particular investigation has been carried out in this thesis with a view to understand the heat transfer behaviour and performance of an inclined pipe under transition flow condition. It is found that the heat transfer rate decreases with the increase of a pipe inclination angle. Also, a higher heat transfer rate is found for a horizontal pipe under forced convection than that of an inclined pipe under mixed convection.

Heat Transfer Measurements in a Supersonic Film Flow

This thesis presents measurements of wall heat flux and flow structure in a canonical film cooling configuration with Mach 2.3 core flow in which the coolant is injected parallel to the wall through a two-dimensional louver. Four operating conditions are investigated: no film (i.e. flow over a rearward-facing step), subsonic film, pressure-matched film, and supersonic film. The overall objective is to provide a set of experimental data with well characterized boundary conditions that can be used for code validation. The results are compared to RANS and LES simulations which overpredict heat transfer in the subsonic film cases and underpredict heat transfer in supersonic cases after film breakdown. The thesis also describes a number of improvements that were made to the experimental facility including new Schlieren optics, a better film heater, more data at more locations, and a verification of the heat flux measurement hardware and data reduction methods.

Canopy-scale biophysical controls of transpiration and evaporation in the Amazon Basin.

Canopy and aerodynamic conductances (gC and gA) are two of the key land surface biophysical variables that control the land surface response of land surface schemes in climate models. Their representation is crucial for predicting transpiration (λET) and evaporation (λEE) flux components of the terrestrial latent heat flux (λE), which has important implications for global climate change and water resource management. By physical integration of radiometric surface temperature (TR) into an integrated framework of the Penman?Monteith and Shuttleworth?Wallace models, we present a novel approach to directly quantify the canopy-scale biophysical controls on λET and λEE over multiple plant functional types (PFTs) in the Amazon Basin. Combining data from six LBA (Large-scale Biosphere-Atmosphere Experiment in Amazonia) eddy covariance tower sites and a TR-driven physically based modeling approach, we identified the canopy-scale feedback-response mechanism between gC, λET, and atmospheric vapor pressure deficit (DA), without using any leaf-scale empirical parameterizations for the modeling. The TR-based model shows minor biophysical control on λET during the wet (rainy) seasons where λET becomes predominantly radiation driven and net radiation (RN) determines 75 to 80 % of the variances of λET. However, biophysical control on λET is dramatically increased during the dry seasons, and particularly the 2005 drought year, explaining 50 to 65 % of the variances of λET, and indicates λET to be substantially soil moisture driven during the rainfall deficit phase. Despite substantial differences in gA between forests and pastures, very similar canopy?atmosphere "coupling" was found in these two biomes due to soil moisture-induced decrease in gC in the pasture. This revealed the pragmatic aspect of the TR-driven model behavior that exhibits a high sensitivity of gC to per unit change in wetness as opposed to gA that is marginally sensitive to surface wetness variability. Our results reveal the occurrence of a significant hysteresis between λET and gC during the dry season for the pasture sites, which is attributed to relatively low soil water availability as compared to the rainforests, likely due to differences in rooting depth between the two systems. Evaporation was significantly influenced by gA for all the PFTs and across all wetness conditions. Our analytical framework logically captures the responses of gC and gA to changes in atmospheric radiation, DA, and surface radiometric temperature, and thus appears to be promising for the improvement of existing land?surface?atmosphere exchange parameterizations across a range of spatial scales.

Canopy-scale biophysical controls of transpiration and evaporation in the Amazon Basin.

Canopy and aerodynamic conductances (gC and gA) are two of the key land surface biophysical variables that control the land surface response of land surface schemes in climate models. Their representation is crucial for predicting transpiration (?ET) and evaporation (?EE) flux components of the terrestrial latent heat flux (?E), which has important implications for global climate change and water resource management. By physical integration of radiometric surface temperature (TR) into an integrated framework of the Penman?Monteith and Shuttleworth?Wallace models, we present a novel approach to directly quantify the canopy-scale biophysical controls on ?ET and ?EE over multiple plant functional types (PFTs) in the Amazon Basin. Combining data from six LBA (Large-scale Biosphere-Atmosphere Experiment in Amazonia) eddy covariance tower sites and a TR-driven physically based modeling approach, we identified the canopy-scale feedback-response mechanism between gC, ?ET, and atmospheric vapor pressure deficit (DA), without using any leaf-scale empirical parameterizations for the modeling. The TR-based model shows minor biophysical control on ?ET during the wet (rainy) seasons where ?ET becomes predominantly radiation driven and net radiation (RN) determines 75 to 80?% of the variances of ?ET. However, biophysical control on ?ET is dramatically increased during the dry seasons, and particularly the 2005 drought year, explaining 50 to 65?% of the variances of ?ET, and indicates ?ET to be substantially soil moisture driven during the rainfall deficit phase. Despite substantial differences in gA between forests and pastures, very similar canopy?atmosphere "coupling" was found in these two biomes due to soil moisture-induced decrease in gC in the pasture. This revealed the pragmatic aspect of the TR-driven model behavior that exhibits a high sensitivity of gC to per unit change in wetness as opposed to gA that is marginally sensitive to surface wetness variability. Our results reveal the occurrence of a significant hysteresis between ?ET and gC during the dry season for the pasture sites, which is attributed to relatively low soil water availability as compared to the rainforests, likely due to differences in rooting depth between the two systems. Evaporation was significantly influenced by gA for all the PFTs and across all wetness conditions. Our analytical framework logically captures the responses of gC and gA to changes in atmospheric radiation, DA, and surface radiometric temperature, and thus appears to be promising for the improvement of existing land?surface?atmosphere exchange parameterizations across a range of spatial scales.

Quantificação de fluxos de mercúrio gasoso na interface solo/atmosfera utilizando câmara de fluxo dinâmica: aplicação na bacia do Rio Negro

Gaseous mercury sampling conditions were optimized and a dynamic flux chamber was used to measure the air/surface exchange of mercury in some areas of the Negro river basin with different vegetal coverings. At the two forest sites (flooding and non-flooding), low mercury fluxes were observed: maximum of 3 pmol m-2 h-1 - day and minimum of -1 pmol m-2 h-1 - night. At the deforested site, the mercury fluxes were higher and always positive: maximum of 26 pmol m-2 h-1 - day and 17 pmol m-2 h-1 - night. Our results showed that deforestation could be responsible for significantly increasing soil Hg emissions, mainly because of the high soil temperatures reached at deforested sites.

Modeling and experimental study of nucleate boiling on a vertical array of horizontal plain tubes

An investigation of nucleate boiling on a vertical array of horizontal plain tubes is presented in this paper. Experiments were performed with refrigerant RI 23 at reduced pressures varying from 0.022 to 0.64, tube pitch to diameter ratios of 1.32, 1.53 and 2.00, and heat fluxes from 0.5 to 40 kW/m(2). Brass tubes with external diameters of 19.05 mm and average roughness of 0.12 mu m were used in the experiments. The effect of the tube spacing on the local heat transfer coefficient along the tube array was negligible within the present range of experimental conditions. For partial nucleate boiling, characterized by low heat fluxes, and low reduced pressures, the tube positioning shows a remarkable effect on the heat transfer coefficient. Based on these data, a general correlation for the prediction of the nucleate boiling heat transfer coefficient on a vertical array of horizontal tubes under flooded conditions was proposed. According to this correlation, the ratio between the heat transfer coefficients of a given tube and the lowest tube in the array depends only on the tube row number, the reduced pressure and the heat flux. By using the proposed correlation, most of the experimental heat transfer coefficients obtained in the present study were predicted within +/- 15%. The new correlation compares reasonably well with independent data from the literature. (C) 2008 Elsevier Inc. All rights reserved.