Non-steady state heat conduction in composite walls

The problem of heat conduction in one-dimensional piecewise homogeneous composite materials is examined by providing an explicit solution of the one-dimensional heat equation in each domain. The location of the interfaces is known, but neither temperature nor heat flux are prescribed there. Instead, the physical assumptions of their continuity at the interfaces are the only conditions imposed. The problem of two semi-infinite domains and that of two finite-sized domains are examined in detail. We indicate also how to extend the solution method to the setting of one finite-sized domain surrounded on both sides by semi-infinite domains, and on that of three finite-sized domains.

Attribution of the spatial pattern of CO2-forced sea level change to ocean surface flux changes

Climate models taking part in the coupled model intercomparison project phase 5 (CMIP5) all predict a global mean sea level rise for the 21st century. Yet the sea level change is not spatially uniform and differs among models. Here we evaluate the role of air–sea fluxes of heat, water and momentum (windstress) to find the spatial pattern associated to each of them as well as the spread they can account for. Using one AOGCM to which we apply the surface flux changes from other AOGCMs, we show that the heat flux and windstress changes dominate both the pattern and the spread, but taking the freshwater flux into account as well yields a sea level change pattern in better agreement with the CMIP5 ensemble mean. Differences among the CMIP5 control ocean temperature fields have a smaller impact on the sea level change pattern.

Observations of urban boundary layer structure during a strong urban heat island event

It has long been known that the urban surface energy balance is different to that of a rural surface, and that heating of the urban surface after sunset gives rise to the Urban Heat Island (UHI). Less well known is how flow and turbulence structure above the urban surface are changed during different phases of the urban boundary layer (UBL). This paper presents new observations above both an urban and rural surface and investigates how much UBL structure deviates from classical behaviour. A 5-day, low wind, cloudless, high pressure period over London, UK, was chosen for analysis, during which there was a strong UHI. Boundary layer evolution for both sites was determined by the diurnal cycle in sensible heat flux, with an extended decay period of approximately 4 h for the convective UBL. This is referred to as the “Urban Convective Island” as the surrounding rural area was already stable at this time. Mixing height magnitude depended on the combination of regional temperature profiles and surface temperature. Given the daytime UHI intensity of 1.5∘C, combined with multiple inversions in the temperature profile, urban and rural mixing heights underwent opposite trends over the period, resulting in a factor of three height difference by the fifth day. Nocturnal jets undergoing inertial oscillations were observed aloft in the urban wind profile as soon as the rural boundary layer became stable: clear jet maxima over the urban surface only emerged once the UBL had become stable. This was due to mixing during the Urban Convective Island reducing shear. Analysis of turbulent moments (variance, skewness and kurtosis) showed “upside-down” boundary layer characteristics on some mornings during initial rapid growth of the convective UBL. During the “Urban Convective Island” phase, turbulence structure still resembled a classical convective boundary layer but with some influence from shear aloft, depending on jet strength. These results demonstrate that appropriate choice of Doppler lidar scan patterns can give detailed profiles of UBL flow. Insights drawn from the observations have implications for accuracy of boundary conditions when simulating urban flow and dispersion, as the UBL is clearly the result of processes driven not only by local surface conditions but also regional atmospheric structure.

Separating the influence of projected changes in air temperature and wind on patterns of sea level change and ocean heat content

We present ocean model sensitivity experiments aimed at separating the influence of the projected changes in the “thermal” (near-surface air temperature) and “wind” (near-surface winds) forcing on the patterns of sea level and ocean heat content. In the North Atlantic, the distribution of sea level change is more due to the “thermal” forcing, whereas it is more due to the “wind” forcing in the North Pacific; in the Southern Ocean, the “thermal” and “wind” forcing have a comparable influence. In the ocean adjacent to Antarctica the “thermal” forcing leads to an inflow of warmer waters on the continental shelves, which is somewhat attenuated by the “wind” forcing. The structure of the vertically integrated heat uptake is set by different processes at low and high latitudes: at low latitudes it is dominated by the heat transport convergence, whereas at high latitudes it represents a small residual of changes in the surface flux and advection of heat. The structure of the horizontally integrated heat content tendency is set by the increase of downward heat flux by the mean circulation and comparable decrease of upward heat flux by the subgrid-scale processes; the upward eddy heat flux decreases and increases by almost the same magnitude in response to, respectively, the “thermal” and “wind” forcing. Regionally, the surface heat loss and deep convection weaken in the Labrador Sea, but intensify in the Greenland Sea in the region of sea ice retreat. The enhanced heat flux anomaly in the subpolar Atlantic is mainly caused by the “thermal” forcing.

An assessment of air-sea heat fluxes from ocean and coupled reanalyses

Sixteen monthly air–sea heat flux products from global ocean/coupled reanalyses are compared over 1993–2009 as part of the Ocean Reanalysis Intercomparison Project (ORA-IP). Objectives include assessing the global heat closure, the consistency of temporal variability, comparison with other flux products, and documenting errors against in situ flux measurements at a number of OceanSITES moorings. The ensemble of 16 ORA-IP flux estimates has a global positive bias over 1993–2009 of 4.2 ± 1.1 W m−2. Residual heat gain (i.e., surface flux + assimilation increments) is reduced to a small positive imbalance (typically, +1–2 W m−2). This compensation between surface fluxes and assimilation increments is concentrated in the upper 100 m. Implied steady meridional heat transports also improve by including assimilation sources, except near the equator. The ensemble spread in surface heat fluxes is dominated by turbulent fluxes (>40 W m−2 over the western boundary currents). The mean seasonal cycle is highly consistent, with variability between products mostly <10 W m−2. The interannual variability has consistent signal-to-noise ratio (~2) throughout the equatorial Pacific, reflecting ENSO variability. Comparisons at tropical buoy sites (10°S–15°N) over 2007–2009 showed too little ocean heat gain (i.e., flux into the ocean) in ORA-IP (up to 1/3 smaller than buoy measurements) primarily due to latent heat flux errors in ORA-IP. Comparisons with the Stratus buoy (20°S, 85°W) over a longer period, 2001–2009, also show the ORA-IP ensemble has 16 W m−2 smaller net heat gain, nearly all of which is due to too much latent cooling caused by differences in surface winds imposed in ORA-IP.

Proper evaluation of the external convective heat transfer for the thermal analysis of cool roofs

Cool materials are characterized by high solar reflectance and high thermal emittance; when applied to the external surface of a roof, they make it possible to limit the amount of solar irradiance absorbed by the roof, and to increase the rate of heat flux emitted by irradiation to the environment, especially during nighttime. However, a roof also releases heat by convection on its external surface; this mechanism is not negligible, and an incorrect evaluation of its entity might introduce significant inaccuracy in the assessment of the thermal performance of a cool roof, in terms of surface temperature and rate of heat flux transferred to the indoors. This issue is particularly relevant in numerical simulations, which are essential in the design stage, therefore it deserves adequate attention. In the present paper, a review of the most common algorithms used for the calculation of the convective heat transfer coefficient due to wind on horizontal building surfaces is presented. Then, with reference to a case study in Italy, the simulated results are compared to the outcomes of a measurement campaign. Hence, the most appropriate algorithms for the convective coefficient are identified, and the errors deriving by an incorrect selection of this coefficient are discussed.

How do green roofs mitigate urban thermal stress under heat waves?

As the climate warms, heat waves (HW) are projected to be more intense and to last longer, with serious implications for public health. Urban residents face higher health risks because urban heat islands (UHIs) exacerbate HW conditions. One strategy to mitigate negative impacts of urban thermal stress is the installation of green roofs (GRs) given their evaporative cooling effect. However, the effectiveness of GRs and the mechanisms by which they have an effect at the scale of entire cities are still largely unknown. The Greater Beijing Region (GBR) is modeled for a HW scenario with the Weather Research and Forecasting (WRF) model coupled with a state-of-the-art urban canopy model (PUCM) to examine the effectiveness of GRs. The results suggest GR would decrease near-surface air temperature (ΔT2max = 2.5 K) and wind speed (ΔUV10max = 1.0 m s-1) but increase atmospheric humidity (ΔQ2max = 1.3 g kg-1). GRs are simulated to lessen the overall thermal stress as indicated by apparent temperature (ΔAT2max = 1.7 °C). The modifications by GRs scale almost linearly with the fraction of the surface they cover. Investigation of the surface-atmosphere interactions indicate that GRs with plentiful soil moisture dissipate more of the surface energy as latent heat flux and subsequently inhibit the development of the daytime planetary boundary layer (PBL). This causes the atmospheric heating through entrainment at the PBL top to be decreased. Additionally, urban GRs modify regional circulation regimes leading to decreased advective heating under HW.

Effects of cold fronts on MODIS-derived sensible and latent heat fluxes in Itumbiara reservoir (Central Brazil)

In this work we investigate the cold front passage effects on sensible and latent heat flux in a tropical hydroelectric reservoir. The study area, Itumbiara reservoir (Goiás State/Brazil) at the beginning of the austral winter, is characterized by the presence of a weak thermal stratification and the passage of several cold fronts from higher latitudes of South America. Sensible and latent heat fluxes were estimated considering the atmospheric boundary layer stability. In situ and MODIS water surface temperature data were used to adjust the coefficients for momentum and heat exchanges between water and atmosphere and spatialize the sensible and latent heat fluxes. The results showed that during a cold front event the sensible heat flux can be up to five times greater than the flux observed before. The latent heat flux tends to decrease during the cold front but increase again after the passage. The highest values of heat loss were observed at littoral zone and some Reservoir's embayment. The heat loss intensification can be separated in two moments: first, during the cold front passage, when the wind speed increases and the air temperature decreases; second, after the cold front passage, with air humidity decreasing. This can be considered a key process to understanding the heat loss in the Itumbiara reservoir. © 2013 COSPAR. Published by Elsevier Ltd. All rights reserved.

Regimes térmico e hídrico em solos sob ecossistemas naturais e área agrícola no Leste da Amazônia

A temperatura e umidade do solo são variáveis cujo conhecimento é fundamental para determinar os balanços de energia e água na biosfera. Os regimes térmico e hídrico dos solos sob cada ecossistema apresentam variações consideráveis, de acordo com sua mineralogia, o clima local e a vegetação. Nesse contexto, as temperaturas e umidades do solo foram medidas sob três ecossistemas existentes na região leste da Amazônia, a saber: floresta nativa (FLONA Caxiuanã, 01° 42' 30" S e 51° 31' 45" W), pastagem nativa (Soure, 00° 43' 25" S e 48° 30' 29" W) e área agrícola (!garapé-Açu, 01° 07' 59" S e 47° 36' 55" W). Os dados de campo na floresta e na pastagem foram coletados entre dezembro de 2001 e fevereiro de 2005; enquanto que na área agrícola, o monitoramento foi limitado de agosto de 2003 a fevereiro de 2005. Estas observações das variáveis físicas do solo foram analisadas levando em consideração as variáveis meteorológicas medidas simultaneamente tais como o fluxo de radiação solar incidente e a precipitação pluviométrica, que interferem diretamente nas variáveis do solo em cada sitio escolhido para estudo. As temperaturas do solo foram monitoradas por meio de sondas térmicas em profundidades de 0,05; 0,20 e 0,50 m. Fluxímetros de calor mediram esta variável em níveis de profundidade em 0,05 e 0,20 m. A umidade volumétrica do solo na camada superior de 0,30 m foi medida por sensor de sonda dupla por Reflectometria no Domínio do Tempo (TDR) em cada sitio. Foram feitas analises considerando as respostas do solo durante o período seco e chuvoso local, nestes três ecossistemas representativos do leste da Amazônia. Estimativas de difusividade térmica aparente do solo foram feitas pelos métodos da amplitude e da fase usando os dados de propagação do pulso diário de calor nesses solos. Os resultados mostraram valores bem diferentes, porém,no primeiro método pareceu mais confiável e adequado para o modelamento numérico. Como esperado, considerando a sua pouca cobertura vegetal, as temperaturas dos solos nos níveis superficiais, apresentaram grandes variações na pastagem e na área agrícola. Inesperadamente, as temperaturas na profundidade de 0,5 m abaixo da floresta mostraram maiores variações de amplitude que as profundidades de 0,20 e 0,05 m. O modelamento numérico das variações temporais da temperatura, em função da profundidade, para cada solo foi feito através do método harmônico Os resultados mostraram que o primeiro harmônico representou mais de 90% da variação total observada do pulso diário da temperatura da pastagem e área agrícola em 0,2 e 0,05 m de profundidade. Performance similar do modelamento foi observada na floresta nos níveis de 0,05 e 0,20 m. A magnitude dos fluxos de calor abaixo da pastagem e área agrícola atingiram valores seis vezes maiores que aqueles observados sob a floresta. Os resultados mostraram que, para a camada do solo superior de 0,30 m, a umidade volumétrica do solo sob a floresta é maior que sob os outros ecossistemas estudados neste trabalho. Este resultado é devido aparentemente; à proteção da floresta contra a evaporação da superfície do solo. Uma análise do comportamento sazonal e diário das temperaturas e umidade solos em resposta à radiação solar e precipitação é apresentada. Estudos de caso da taxa de perda da umidade do solo depois de significativa recarga de água por eventos de precipitação, também foram analisados. Algumas estimativas diárias de diminuição de água e recarga durante a noite e madrugada por subida de água de camadas subjacentes para a camada de 0.30 m foram feitas. Este trabalho analisou a maior serie temporal dos dados de temperatura e umidade dos solos coletados com alta freqüência de amostragem disponível até o momento, para o leste da Amazônia. Foi possível caracterizar as diferenças dos regimes destas variáveis físicas, abaixo de três ecossistemas importantes desta região. Estudos futuros dos minerais e materiais orgânicos nestes solos, bem como dos índices de área foliar e da biomassa das coberturas vegetais desses ecossistemas, melhoraria a compreensão dos regimes descritos neste trabalho.

Avaliação da dinâmica temporal da evaporação no reservatório de Itumbiara, GO, utilizando dados obtidos por sensoriamento remoto

The object of this work was to study the dynamics of evaporation in the Itumbiara reservoir, located in Central Brazil, using MODIS-derived water surface temperature (product MOD11A1) and meteorological data acquired over the water surface. The evaporation rates were derived from latent heat flux, estimated through a mass transfer model. The estimates were carried out for the period between 1/1/2010 and 31/12/2010. The results showed that evaporation rate tends to increase from January to September and then decrease from September to December. The evaporation rate reached values near 20 mm day-1 in Itumbiara reservoir during the dry season in 2010. The mean evaporation rate for the wet season was 3.66 mm day-1 and 8.25 mm day-1 for the dry season. The total water volume evaporated from Itumbiara reservoir during 2010 was estimated at about 1.7 billion m³ (2,300 mm) which represents 10% of total reservoir volume. The results suggest that advection is the main transport mechanism which drives the evaporation in Itumbiara. The convective processes contribute secondarily to evaporation in Itumbiara reservoir.

Modeling heat transfer in die milling

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Two-Phase Frictional Pressure Drop and Flow Boiling Heat Transfer for R245fa in a 2.32-mm Tube

Experimental two-phase frictional pressure drop and flow boiling heat transfer results are presented for a horizontal 2.32-mm ID stainless-steel tube using R245fa as working fluid. The frictional pressure drop data was obtained under adiabatic and diabatic conditions. Experiments were performed for mass velocities ranging from 100 to 700 kg m−2 s−1 , heat flux from 0 to 55 kW m−2 , exit saturation temperatures of 31 and 41◦C, and vapor qualities from 0.10 to 0.99. Pressures drop gradients and heat transfer coefficients ranging from 1 to 70 kPa m−1 and from 1 to 7 kW m−2 K−1 were measured. It was found that the heat transfer coefficient is a strong function of the heat flux, mass velocity, and vapor quality. Five frictional pressure drop predictive methods were compared against the experimental database. The Cioncolini et al. (2009) method was found to work the best. Six flow boiling heat transfer predictive methods were also compared against the present database. Liu and Winterton (1991), Zhang et al. (2004), and Saitoh et al. (2007) were ranked as the best methods. They predicted the experimental flow boiling heat transfer data with an average error around 19%.

What drives the seasonality of photosynthesis across the Amazon basin? A cross-site analysis of eddy flux tower measurements from the Brasil flux network

We investigated the seasonal patterns of Amazonian forest photosynthetic activity, and the effects thereon of variations in climate and land-use, by integrating data from a network of ground-based eddy flux towers in Brazil established as part of the ‘Large-Scale Biosphere Atmosphere Experiment in Amazonia’ project. We found that degree of water limitation, as indicated by the seasonality of the ratio of sensible to latent heat flux (Bowen ratio) predicts seasonal patterns of photosynthesis. In equatorial Amazonian forests (5◦ N–5◦ S), water limitation is absent, and photosynthetic fluxes (or gross ecosystem productivity, GEP) exhibit high or increasing levels of photosynthetic activity as the dry season progresses, likely a consequence of allocation to growth of new leaves. In contrast, forests along the southern flank of the Amazon, pastures converted from forest, and mixed forest-grass savanna, exhibit dry-season declines in GEP, consistent with increasing degrees of water limitation. Although previous work showed tropical ecosystem evapotranspiration (ET) is driven by incoming radiation, GEP observations reported here surprisingly show no or negative relationships with photosynthetically active radiation (PAR). Instead, GEP fluxes largely followed the phenology of canopy photosynthetic capacity (Pc), with only deviations from this primary pattern driven by variations in PAR. Estimates of leaf flush at three

Experimental investigation of regular fluids and nanofluids during flow boiling in a single microchannel at different heat fluxes and mass fluxes

The dissipation of high heat flux from integrated circuit chips and the maintenance of acceptable junction temperatures in high powered electronics require advanced cooling technologies. One such technology is two-phase cooling in microchannels under confined flow boiling conditions. In macroscale flow boiling bubbles will nucleate on the channel walls, grow, and depart from the surface. In microscale flow boiling bubbles can fill the channel diameter before the liquid drag force has a chance to sweep them off the channel wall. As a confined bubble elongates in a microchannel, it traps thin liquid films between the heated wall and the vapor core that are subject to large temperature gradients. The thin films evaporate rapidly, sometimes faster than the incoming mass flux can replenish bulk fluid in the microchannel. When the local vapor pressure spike exceeds the inlet pressure, it forces the upstream interface to travel back into the inlet plenum and create flow boiling instabilities. Flow boiling instabilities reduce the temperature at which critical heat flux occurs and create channel dryout. Dryout causes high surface temperatures that can destroy the electronic circuits that use two-phase micro heat exchangers for cooling. Flow boiling instability is characterized by periodic oscillation of flow regimes which induce oscillations in fluid temperature, wall temperatures, pressure drop, and mass flux. When nanofluids are used in flow boiling, the nanoparticles become deposited on the heated surface and change its thermal conductivity, roughness, capillarity, wettability, and nucleation site density. It also affects heat transfer by changing bubble departure diameter, bubble departure frequency, and the evaporation of the micro and macrolayer beneath the growing bubbles. Flow boiling was investigated in this study using degassed, deionized water, and 0.001 vol% aluminum oxide nanofluids in a single rectangular brass microchannel with a hydraulic diameter of 229 µm for one inlet fluid temperature of 63°C and two constant flow rates of 0.41 ml/min and 0.82 ml/min. The power input was adjusted for two average surface temperatures of 103°C and 119°C at each flow rate. High speed images were taken periodically for water and nanofluid flow boiling after durations of 25, 75, and 125 minutes from the start of flow. The change in regime timing revealed the effect of nanoparticle suspension and deposition on the Onset of Nucelate Boiling (ONB) and the Onset of Bubble Elongation (OBE). Cycle duration and bubble frequencies are reported for different nanofluid flow boiling durations. The addition of nanoparticles was found to stabilize bubble nucleation and growth and limit the recession rate of the upstream and downstream interfaces, mitigating the spreading of dry spots and elongating the thin film regions to increase thin film evaporation.

EXPERIMENTAL INVESTIGATION OF CERTAIN INTERNAL CONDENSING AND BOILING FLOWS: THEIR SENSITIVITY TO PRESSURE FLUCTUATIONS AND HEAT TRANSFER ENHANCEMENTS

Space-based (satellite, scientific probe, space station, etc.) and millimeter – to – microscale (such as are used in high power electronics cooling, weapons cooling in aircraft, etc.) condensers and boilers are shear/pressure driven. They are of increasing interest to system engineers for thermal management because flow boilers and flow condensers offer both high fluid flow-rate-specific heat transfer capacity and very low thermal resistance between the fluid and the heat exchange surface, so large amounts of heat may be removed using reasonably-sized devices without the need for excessive temperature differences. However, flow stability issues and degradation of performance of shear/pressure driven condensers and boilers due to non-desirable flow morphology over large portions of their lengths have mostly prevented their use in these applications. This research is part of an ongoing investigation seeking to close the gap between science and engineering by analyzing two key innovations which could help address these problems. First, it is recommended that the condenser and boiler be operated in an innovative flow configuration which provides a non-participating core vapor stream to stabilize the annular flow regime throughout the device length, accomplished in an energy-efficient manner by means of ducted vapor re-circulation. This is demonstrated experimentally. Second, suitable pulsations applied to the vapor entering the condenser or boiler (from the re-circulating vapor stream) greatly reduce the thermal resistance of the already effective annular flow regime. For experiments reported here, application of pulsations increased time-averaged heat-flux up to 900 % at a location within the flow condenser and up to 200 % at a location within the flow boiler, measured at the heat-exchange surface. Traditional fully condensing flows, reported here for comparison purposes, show similar heat-flux enhancements due to imposed pulsations over a range of frequencies. Shear/pressure driven condensing and boiling flow experiments are carried out in horizontal mm-scale channels with heat exchange through the bottom surface. The sides and top of the flow channel are insulated. The fluid is FC-72 from 3M Corporation.