Conjugate heat transfer studies in closed cavities have many engineering applications, such as solar collectors, nuclear reactors, cooling of electronic systems, building design applications, etc. In particular, theoretical research in buil- ding thermal design provides the opportunity to quantify the heat transfer in complex systems in order to obtain thermal parameters required in commercial software or for making decisions at different building design stages. Also, it is well known that the interaction between indoor spaces and the en- vironment is highly influenced by the type of building mate- rials (thermophysical and optical properties): opaque and/or semitransparent walls. Thermal energy gains or losses throu- gh the envelope directly affect the thermal comfort of occu- pants and the final energy consumption inside rooms. On the other hand, building occupants are the main source of CO 2 emissions inside rooms, making mandatory the analysis of coupling heat and mass transfer in order to satisfy indoor air quality standards. Therefore, conjugate natural convection with surface radiation, mass transfer and conducting walls in closed cavities are worthy of research. A short literature review is presented next. For example, in 1976 Larson and Viskanta  reported a numerical study of conjugate heat transfer in a square cavity with opaque and diffusive walls. The authors found that thermal radiation is dominant. Weeb and Viskanta  included the heat condition through a semi- transparent wall, showing that 70% of the energy incoming to the cavity was provided by direct absorption of thermal radiation. Later, Behnia et al.  analysed a closed cavity with a semitransparent wall considering convective losses to the surroundings. They studied the effect of external con- vection and surface thermal radiation on heat transfer inside the cavity. Kwon et al.  reported the effect of considering a glazed surface in the middle of vertical conductive wall in the closed cavity. More recently, Álvarez and Estrada  considered a semitransparent wall with a solar film adhered to the inside surface. They found that total energy transfe- rred to the air through the glass wall with a control film is lower than the case of the simple clear glass. Zhao et al.  investigated the fluid flow and heat transfer in square enclo- sures representing building elements. They evaluated con- jugated heat conduction and natural convection in laminar flow regime. Results reveled that heat transfer rates across
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Thermocouples generate their signal in response to the temperature difference between the two ends of the loop. For accurate measurements, the temperature of the “reference junction” must be known. Laboratory users often use an ice bath made from a good-quality Dewar flask or vacuum-insulated bottle of at least 1 pt capacity, as shown in Figure 4.6.4. The flask should be filled with finely crushed ice and then flooded with water to fill the interstices between the ice particles. The reference thermocouple is inserted into a thin-walled glass tube containing a small amount of silicone oil and submerged six or eight diameters into the ice pack. The oil assures good thermal contact between the thermocouple junction and the ice/water mixture. The tube should be sealed at the top to prevent atmospheric moisture from condensing inside it, which would cause corrosion when using iron-constantan thermocouples. Figure 4.6.5 shows in iron-constantan thermocouple circuit with an ice bath. The individual thermocouple wires are connected to copper wires in the ice bath, and the two copper wires taken to the voltmeter. The lower portion of this figure shows the E–T diagram for this circuit, and proves that the output of this circuit is entirely due to the temperature difference from end to end of the iron-constantan loop: the two copper wires do not contribute to the output.
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Initially, this problem was attributed to very different causes. Kunii & Suzuki (1967) claimed that the reason was flow channeling in the bed, while Nelson & Galloway (1975) argued that it was because of the renewal of the fluid surrounding each particle, and Martin (1978) pointed out that the non-uniformity of the packing could be responsible for these discrepancies. Schlünder (1978) even showed under what assumptions the Nusselt number could decrease continuously with the Reynolds number. This issue is still being debated, with two clear different views being predominant. While some say that the Nusselt number decreases continuously as the Reynolds number does so, others say that it only decreases until it reaches a limiting Nusselt number at zero flow rate (Wakao & Kaguei, 1982). Values for the limiting Nusselt number varied from 3.8 to 18 (Gunn, 1978; Miyauchi, 1971; Pfeffer & Happel, 1964; Schlünder, 1975; Sørensen & Stewart, 1974) until Wakao et al. (1978) showed that the problem was in the fundamental equation used and proposed new parameters for the typical equation (Eq. 10) taking into account most of the experimental results up to date (Figure 3)
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In recent years, cities are using more land to accommodate the increasing population and migration from rural areas to the cities (Antrop 2004). This worldwide phenomenon is increasing the demand for new buildings as well as land, water, and energy. The demand may increase even more in the future because of the economic growth of undeveloped and developing regions (Valipour 2014, Valipour 2015). In particular, the building sector represents 32% of the global energy use in 2010 and causes one-third of the greenhouse gas emissions (Lucon et al. 2014, OECD/IEA 2013). In Chile, this sector is responsible for 28.8% of total energy consumption between 2000 and 2016 (MinEnergía 2013). Therefore, building energy efficiency plays a key role to limit the global warming and mitigate the impacts of climate change because the majority of these emissions are attributable to electricity consumption for heating, ventilation, air conditioning, lighting and equipment operation. This electricity consumption is generated mostly from fossil fuels such as gas, coal, and oil.
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BCRs are considered to be a potential alternative to the conventional STBs, in which mixing of gaseous substrates is achieved by gas sparging without mechanical agitation, and are considered to be economically viable in terms of saving energy costs. Some advantages of bubble columns include low capital and operational costs, lack of moving parts, and satisfactory high heat and mass transfer rates. Increasing the flow rate for enhancing mixing will cause a heterogeneous flow to occur. Such a condition will eventually lead to back mixing of the gaseous components. Less research has been done using BCRs for ethanol production compared to STBs. Ethanol production by E. limosum KIST612 using CO was carried out in a 200- mL bubble column reactor in batch and continuous mode by Chang et al. In that study, a membrane module of pore size 0.2 μm was connected to the reactor for cell recycling. High ethanol yields were easily obtained from CO in a 4.5 L BCR, and these values were, respectively 6 and 2 times higher than for acetic acid and butanol for C. carboxidivorans P7 T .
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the free convection along a vertical, isothermal plate under the effect of a con- stant, horizontal, magnetic field. Takhar and Soundalgekar  have studied the dissipation effects on MHD free convection flow past a semi-infinite vertical plate. Sparrow and Cess  presented their research work on the effect of a magnetic field on free convection heat transfer.
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One of the challenges in thermal applications is to ﬁ nd a nano ﬂ uid providing the best thermal conductivity to viscosity ratio thus increas- ing the ef ﬁ ciency of heat transfer processes. Recently, thanks to its struc- ture and properties, halloysite (Hal) nanotubes have increased their interest for the nanotechnology of advanced materials in areas such as catalysis, drug delivery, biomedical implants, corrosion protection of metals, biosensors, organic synthesis, ﬂ ame retardant coatings, speci ﬁ c ion adsorbents, materials for sustained release of herbicides and anti- microbials and energy storage devices (Deen et al., 2012). Hal is a clay mineral of the kaolin group, having a hollow tubular-like structure with particle sizes within the nanometrical size range and large aspect ratio. The outer diameter of typical Hal nanotubes is within the range of 15–100 nm, and length is between 500 and 1500 nm (Alhuthali and Low, 2013; Cavallaro et al., 2012; Lvov et al., 2008; Pasbakhsh et al., 2013; Vergaro et al., 2010). The size and shape of Hal nanotubes togeth- er with its chemical composition and structure make this material a good candidate to be dispersed in water, thus obtaining an interesting nano ﬂ uid for heat transfer applications. Other interesting applications of Hal nanotubes are as carriers for drug delivery, adsorbents and ﬁ llers in clay polymer nanocomposites (Tan et al., in press)
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17. Kell, G. S. Density, thermal expansivity, and compressibility of liquid water from 0.deg. to 150.deg.. Correlations and tables for atmospheric pressure and saturation reviewed and expressed on 1968 temperature scale. J. Chem. Eng. Data 20, 97–105 (1975). DOI: 10.1021/je60064a005 18. Riddick, J. & Bunger, W. Organic Solvents (Techniques of
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In equations (57) and (58) one can observe that the eigenvalues are negative because α and β are negative; then, the system is stable for every value of C and τ. That is, every small perturbation around the steady-state values of temperature x ¯ and y ¯ decays exponentially with time. Eigenvectors given by equations (59) and (60) represent the directions along which relaxation times can be defined by equations (61) and (62). In figures 7(a) and 7(b) we plot the relaxation times against τ for several values of the ratio β/α, for a fixed value of α. For a given value of the ratio β/α, we observe that both relaxation times decrease as τ increases; that is, the stability improves as τ → 1. In the region β/α 1, as the ratio β/α decreases (figure 7(a)), the relaxation time t 1 (k=−1) increases. In the limit β/α → 0, t 1 (k=−1) → ∞ and the stability is lost. If β/α > 1, both relaxation times decrease (see figure 7(b)).
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Juan Manuel Olivares-Ramírez. He obtained his bachelor´s degree in mechanical engineering from the Morelia Technological Institute (in Mexico), and his master´s degree in materials science from the same institution. His doctoral degree is from the National Polytechnic Institute, conferred by the Graduate Program in Advanced Technologies, CICATA-IPN, Querétaro Section. At present he is an associate professor at the Technological University in San Juan del Río, in the state of Querétaro. He has published four articles in strictly refereed journals. His research work has centered on methods of hydrogen produc- tion, refrigeration systems, CFD element finite, mechanic flow and heat transfer.
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These models focus on different aspects of a FPR: particle velocity, curtain opacity, solar irradiation... but they often do not simulate the particles themselves, but consider that the rays bounce randomly in the particle-laden area. Many models neglect the time it takes for heat transfer to happen inside the particles, considering that because of their small size, the heating process can be assumed to be instantaneous. That is only a realistic consideration when the size of the particles is similar or smaller than the wavelength of sunlight - from 0.5 µm to 2.5 µm approximately - which occurs, for example, in the Small Particle Receivers (SPR) that work with nanoparticles. Since the average diameter of the particles in the FPR is close to 500 µm, the time it takes for a particle to reach the desired temperatures can be an important factor and should not be disregarded. Figure 1.3 shows a schematic comparison of the sizes of a SPR and a FPR.
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by Valdés and Rapún . The simulation model used there, and developed by Rapún , includes continuous variables and non-linear equations. It demands to take in advance fixed values for the gas turbine parameters (i.e. the gas inlet temperature, the compression ratio, the air mass flow rate), according to manufacturer data. On the other hand, in the present NLP optimization model, those parameters are treated as operative variables which values are bounded by inequality constraints in order to consider the whole range of commercially available options. In addition, the Pinch Point, the Approach Point, the temperature difference between gas and steam at the superheater entry, and the boiler and the condenser operative pressures need to be fixed in Rapún’s model ; while here they can vary freely within feasible ranges (see Appendix I) to obtain an optimal HRSG design.
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However, in this case, the use of a cubic spline in approaching global optimization problems with random search techniques can produce superior results over discrete step-wise functions , mainly because the cubic spline approximation allows for significantly reducing the number of decision variables and therefore the necessary number of objective function computations to reach the global solution. Therefore, the cubic spline approximation coupled with adaptive random search algorithm  are utilized in this study in order to find optimal variable retort temperature (VRT) profiles.
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In this paper, the entransy dissipation theory is used for a multi-objective optimization, instead of the principle of minimum entropy generation. A set of solutions was obtained, the solutions found matches with the design principles found in the consulted literature, in all cases increasing effectiveness decreases the number of entransy dissipation. Finally, for the designs obtained is selected the equipment with maximum heat transfer speed and minimum cost, this equipment ensures a fuel outlet temperature in the range of operating conditions.
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We expect the remaining unknown constants, U and C, to be of order unity, as they are for a line source of heat. They must be obtained from the requirement that the inner expansion should match the outer expansion in the intermediate region ε r 1. However, for a pure line source of heat the outer field does not include the dipole source of vorticity, represented by the last term in (5.4), that we must include in the inner region, together with the last term of (5.3), to satisfy the boundary conditions on the wire. Hence, matching of the flow field near the wire and the outer field due to a pure line source of heat is not possible unless we include the effect on the outer flow field of the vorticity input from the wire, represented by the last term in (5.4), of order δ. Then, in order to account for this effect (or, equivalently, for the effect of the drag force on the wire due to the flow induced by the buoyancy forces) we must include in the small-r description (3.3), used for the line source of heat, the dipole term − 2E 1 sin ϕ/r ln ε, and in (3.4) the corresponding term in the ψ
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On the one hand, the higher latent heat of R152a than that of R134a will imply that its mass flow rate will be smaller to obtain the same cooling duty, which will have a bearing on lesser compressor power consumption. On the other hand, the higher specific volume of R152a with respect to R134a will mean that less refrigerant mass will need to be charged in the facility in order to reach the same saturation temperatures. The result of dividing the latent heat between the specific volume, named volumetric refrigerating effect (q v ), yields values that are 10%y greater for R134a than for R152a, which means that
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In TTR technique a femtosecond pulse is split into an intense heating pulse and a weaker probe pulse (Fig. 1). The heating pulse is used to generate the transient event to be observed. Control of the optical path length of the probe pulse produces a variable time delay between the pump and probe pulses. The probe then takes a snapshot of the reflectance at a specific experimental time delay relative to the pump, with a temporal resolution on the order of the probe pulse duration. In our case the delay line is capable of producing time steps of 3 fs. Pulses
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The volume of precipitation received by the lake does not only correspond to the rain amount that falls above its surface, but also incorporates the runoff waters. However, the total catchment area (the full crater) cannot be consid- ered since an unknown fraction of the runoff water may infiltrate or evaporate before reaching the lake. Therefore, a correction factor, also called catchment coefficient must be applied to the total volume falling directly on the lake surface. Lake depth and precipitation data from Figure 7 are considered to estimate this parameter. The events ‘a’ and ‘b’ were selected to be important rain events (72 and 189 mm, respectively; Figure 7), because they occurred on a short time interval (less than a day) and the lake depth showed a simultaneous increase. Furthermore, these events occurred after a few days without rain, unlike other rain events from Figure 7, allowing a clear relationship between the amount of rain and the water level increase. Therefore, it is reason- able to believe that the lake depth variation is mainly due to the rain event and that the impact of lake evaporation and infiltration is limited. Considering the lake depth and surface increase after those two events, a catchment coef- ficient of 1.2 was calculated. Taran and Rouwet (2008) estimated a higher factor of 1.9 by the heat-isotopic-mass balance method. However, their value is an average value calculated with data collected over a period of more than 10 years, and this correction factor probably varies with the lake surface, being less important when the lake surface is higher than when the surface is smaller. Furthemore, the Taran and Rouwet (2008) estimation corresponds to a lake with an average surface that is smaller than the average surface area of the lake during this study.
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In addition, it was concluded in section 4 that this program can be used to adjust the SFE of caffeine and oil. However, it could be used with any other solid or solvent since it was based on a general model for a solid extraction processes. This last statement would be true as long as the bed porosity can be assumed as a constant and the equilibrium follows a Henry’s relation. Regarding this last limitation, it can be overcome by the addition of Excel programing. So, if the user would be interested in analysing a SFE with a thermodynamic solubility calculation, they only have to include these calculations in the Excel sheet and given the solution in the Cell of the solubility. In the same way, the parameters of the thermodynamic expression can be defined as fitting parameters. 6. Conclusions
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Figure 33 shows the velocity and temperature contours for case 1-2. This case represents a natural convection scenario due the “no ventilation” strategy used. The length of the vectors indicates the high air velocity in both upper and lower room and through the opening. The air velocity in case 1-2 is much higher than case 2-3 (Figure 34) and cases 4-1(Figure 35) which represent mixed convection scenarios. The flow pattern is dominated by vortices in all studied cases. In case 1-2 the major vortex is identified in the upper room in the left side of the upward flow while a smaller vortex is formed in the right side. At the lower room, another vortex can be identified at the left side of the downward airflow. The air exchange between the zones takes place at the horizontal opening, where the upward and downward flow seems to take place in the same part of the opening but in opposite directions. The warmer air from the lower room comes from the baseboard heater and flows along the ceiling, and then it flows upward through the right half of the opening into the upper room causing the temperature rise. The downwards cold air takes place at the same right half of the opening. Also, it is possible to see a stratified fluid inside the room, with the main flow of warm air coming from the baseboard heater and heat source flowing upward through the opening and the temperature increases from bottom to the top level of the test-hut.
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