Technical Note Transient behavior of vertical buoyancy layer in a stratified fluid

horizontal length scale of the vertical channelg acceleration of gravityRa Rayleigh number [ ≡ gβT_oD⁴ν]T temperaturew velocity component in the z-directionx horizontal coordinatez vertical coordinate.Greek symbols coefficient of thermometric expansionδ thermal perturbation thermal diffusivityν kinematic viscosityσ Prandtl number [ ≡ νχ].     

Entropy generation due to conjugate natural convection in enclosures bounded by vertical solid walls with different thicknesses

Entropy generation due to conjugate natural convection heat transfer and fluid flow has been studied inside an enclosure with bounded by two solid massive walls from vertical sides at different thicknesses. Enclosure is differentially heated from vertical walls and horizontal walls are adiabatic. Governing equations which are written in streamfunction-vorticity form solved by finite difference technique for the governing parameters as Rayleigh number, 10³ ≤ Ra ≤ 10⁶, length ratio of solid walls as ₁ (for left vertical wall) and ₂ (for right vertical wall) and thermal conductivity ratio of solid to fluid (k), 1 ≤ k ≤ 10. Entropy generation contours due to fluid friction and heat transfer irreversibility, isotherms, streamlines, Nusselt numbers and velocity profiles were obtained. It is found that entropy generation increases with increasing of thermal conductivity ratio and thicknesses of the walls. Entropy generation due to heat transfer is more significant than that of fluid flow irreversibility for all values of thickness of the solid vertical walls.     

Thermoelectric-generator with linear phenomenological heat-transfer law

The performance of multi-element thermoelectric-generators, assuming heat-transfer irreversibilities which obey the linear phenomenological heat-transfer law Q ∝ (ΔT⁻¹), is studied in this paper by combining finite-time thermodynamics with non-equilibrium thermodynamics. The performance characteristics of the output power, efficiency and working electrical-current are described by numerical examples.     

Reliable one dimensional 46-CPWTR model applied to two dimensional heat transfer problem of insulated triangular duct

In this study, the heat transfer characteristics of an insulated long triangular duct are analyzed by using the one dimensional plane wedge thermal resistance (PWTR) and plate thermal resistance (PTR) models. It is found that the errors produced by the PWTR model are all positive, but the errors produced by the PTR model are all negative. Thus, the combined plate wedge thermal resistance (CPWTR) model generated by paralleling PWTR and PTR models with the proportion factors of  = 0.4 vs. β = 0.6 (46-CPWTR model) is capable of neutralizing the positive and negative errors and returning very accurate results in comparison with the two dimensional numerical solutions analyzed by CFD software. The errors generated by the one dimensional 46-CPWTR model are within 1% for practical insulation thickness (t/R₂ < 0.5). In the rare situations of thicker insulation (0.5  t/R₂  2), most of the errors returned by the one dimensional 55-CPWTR model are within 2%. Thus, engineers can obtain very reliable heat transfer results by applying the one dimensional 46-CPWTR or 55-CPWTR models to an insulated triangular duct. Meanwhile, the PTR model can still be used to estimate the highest surface temperature for a hot fluid duct or the lowest surface temperature for a cool fluid duct.     

Turbulent natural convection in a porous square cavity computed with a macroscopic κ–ε model

Detailed numerical computations for laminar and turbulent natural convection within a square cavity filled with a fluid saturated porous medium are presented. Heated vertical walls are maintained at constant but different temperatures, while horizontal surfaces are kept insulated. The macroscopic κ–ε turbulence model with wall function is used to handle turbulent flows in porous media. In this work, the turbulence model is first switched off and the laminar branch of the solution is found when increasing the Rayleigh number, Ra_m. Computations covered the range 10 < Ra_m < 10⁶ and 10⁻⁷ < Da  < 10⁻¹⁰ and made use of the finite volume method. Subsequently, the turbulence model is included and calculations start at high Ra_m, merging to the laminar branch for a reducing Ra_m and for Ra_m less than a certain critical Rayleigh number, Ra_cr. This convergence of results as Ra_m decreases can be seen as a characterization of the laminarization phenomenon. For Ra_m values less than around 10⁴, both laminar and turbulent flow solutions merge, indicating that such critical value for Ra_m was reached. Results further indicate that when the parameters porosity, Pr, conductivity ratio between the fluid and the solid matrix and the Ra_m are kept fixed, the lower the Darcy number, the higher the average Nusselt number at the hot wall.     

Thermo-economics for endoreversible heat-engines

The thermoeconomics of endoreversible heat engines has been studied based on the linear phenomenological heat-transfer law [i.e., the heat flux Q ∝ Δ(1/T), where T is the absolute temperature]. Analytical formulae for profit, the maximum profit and the corresponding efficiency are derived.     

Thermodynamic evaluation of water splitting by a cation-excessive (Ni, Mn) ferrite

Water-splitting potential by cation-excessive (Ni, Mn) Ferrite, Ni_{0.5(1 + )}Fe_{1.99(1 + )}O₄ was evaluated using the standard Gibbs free energy change (ΔG°) for the cation-excessive ferrite formation in different O₂ partial pressures. The cation-excessive degree ranged from 0.026 to 0.16 in pO₂ values of 7.9 × 10⁻⁷ to 1.0 × 10⁻¹. From the relation between value of (Ni, Mn) ferrite and oxygen partial pressure, equilibrium constant K(th) was determined. Furthermore ΔH°s for O₂ releasing and water-splitting reactions with cation-excessive (Ni, Mn) ferrite were evaluated from the van't Hoff plot and compared with that for magnetite-wüstite system; where ΔH°s were assumed to be the same values for both (Ni, Mn) ferrite and magnetite-wüstite system: +300 kJ for O₂ releasing and −35 −63 kJ for water-splitting. ΔG°s evaluated for water-splitting with cation-excessive (Ni, Mn) ferrite and wüstite were −38 kJ and −35 kJ, respectively, at 298K. It suggests that water splitting with cation-excessive (Ni, Mn) ferrite proceed easily compared with that with wüstite. ΔS°s for water-splitting are −0.93 kJ K⁻¹ for the former and −0.83 kJ K⁻¹ for the latter. H₂ generation rates by reaction with H₂O for (Ni, Mn) ferrite were studied at temperatures of 573 K-1073 K. It reached the maximum at 1000 K while it proceeds preferentially below 830 K from thermodynamics.     

Triple vacuum glazing: Heat transfer and basic mechanical design constraints

Given the major role played by windows with regard to energy losses from buildings in cold climates, low thermal transmittance is an indispensable property of glazing in low-energy buildings. Evacuation offers the only means of achieving negligible gaseous conduction in glazing cavities. Application of low-emittance coatings to glass sheet surfaces inside the cavity reduces the radiative heat transfer. The feasibility of double vacuum glazing using arrays of support pillars between the glass sheets has been shown by other authors. This type of glazing is commercially manufactured today. Based on these achievements, our study set out to investigate heat transfer in triple vacuum glazing by means of (i) an analytical thermal network model and (ii) a numerical finite difference model. The study focused on the impact of the following parameters on thermal transmittance: emittances of glass sheet surfaces inside the cavity, support pillar radius, support pillar separation and thermal conductivity of support pillar material. The design procedure for triple vacuum glazing taking into account not only thermal but also mechanical stresses due to atmospheric pressure, i.e., to enable identification of favourable parameter sets, is presented. Our findings suggest that use of the triple vacuum glazing concept can significantly reduce the thermal transmittances achieved by the best insulation glazing units currently on the market. E.g., a centre-of-glazing thermal transmittance of less than 0.2 W m⁻² K⁻¹ is achievable using stainless steel support pillars, 6 mm/4 mm/6 mm sheets of untempered soda-lime glass and four low-emittance coatings (ε = 0.03).     

Heat transfer in inclined rectangular receivers for concentrated solar radiation

We study heat transfer in inclined rectangular cavities, which may be used as receivers of concentrated solar radiation. One of the active walls is subject to concentrated solar radiation and the other is kept at constant temperature. Continuity, momentum and energy equations are solved by finite difference — control volume numerical method. The relevant governing parameters are: the Rayleigh numbers from 10³ to10¹², the cavity aspect ratio, A = L/H from 0.5 to 2, the inclination angle, from 30 to 90°.We found that the Nusselt number is an increasing function of the Rayleigh number, the aspect ratio and the inclination angle. Based on the computed data a correlation is derived in the form of Nu = f(Ra, A, ).     

Frequency-dependent performance of an endoreversible Carnot engine with a linear phenomenological heat-transfer law

On the basis of an endoreversible Carnot heat-engine model, the frequency-dependent performance of the engine is analyzed when the heat transfers between the working fluid and the heat reservoirs obey a linear phenomenological heat-transfer law, i.e., Q ∝ (ΔT⁻¹). The relations among average power-output, efficiency, available temperature-drop, cycle frequency and ratio of the heat-transfer times are derived. They are different from those obtained with Newton’s law. The results can provide guidance for selecting the appropriate working points of heat engines.     

Studies on membrane viscosity stabilized solar pond

In this nonsalt type of solar pond, the nonconvecting layer is composed of a viscous polymer solution partitioned by a number of transparent films. An advantage of partitioning is that a thinner polymer solution can be used and that the light transmittance increases. Results of experimental and theoretical investigations on the performance of this solar pond are summarized as follows:

1. 1. Ionized polyacrylamide solution was chosen as the thickener based on tests about solubility, viscosity, light transmittance and stability.

2. 2. The critical temperature difference for the onset of convection in the polymer layer (ΔT/L)_cr [°C/m] was given by the following formula based on the measurements in various thicknesses of the polymer layers (L) [m] and various concentrations (ζ) [%],

(ΔT/l)_cr=(55−185lnL)exp(4.66L^0.505lnζ

3. 3. An outdoor model pond, 200 × 150 cm surface and 100 cm depth, was constructed in Osaka. Four types of model ponds were tested, and the availability of membrane type with partition films was confirmed.

4. 4. The theoretical temperature rise of the pond using a one-dimensional model was calculated by solving the equations of the heat balance in the pond. As a result, the optimum values of thickness of polymer layer and number of films was determined

     

PMMA-assisted synthesis of Li1−xNi0.5Mn1.5O4−δ for high-voltage lithium batteries with expanded rate capability at high cycling temperatures

In this work, poly(methyl methacrylate) (PMMA), a non-surfactant polymer was used to synthesize nonstoichiometric Li_0.82Ni_0.52Mn_1.52O_4−δ (0 ≤ δ ≤ 0.25) spinels. The presence of the polymer was found to be beneficial with a view to facilitating the use of the spinel in electrodes for lithium batteries. Thus, PMMA allowed spinel particles of a high crystallinity and uniform size and shape to be obtained, and particle size to be tailored by using an appropriate calcining temperature and time. By controlling these variables, spinels in nanometric, submicrometric and micrometric particle sizes were prepared and characterized by chemical analysis, X-ray diffraction, electron microscopy, thermogravimetry and nitrogen adsorptions measurements. The spinels were obtained as highly crystalline phases with lithium and oxygen deficiency and some cation disorder as revealed by chemical analysis, thermogravimetric and XRD data. Their electrochemical performance in two-electrode cells was tested at room temperature and 50 °C over a wide range of charge/discharge rates (from C/4 to 4C). Cell performance was found to depend on particle size rather than on structural properties. Thus, the spinel best performing at 50 °C was that consisting of submicrometric particles, which delivered a high capacity and exhibited the best capacity retention and rate capability. Particles of submicronic size share the advantages of nanometric particles (viz. the ability to withstand high charge/discharge rates) and micrometric particles (a high capacity and stability at low rates).     

High temperature rate coefficient for the reaction of O(P) with H2 obtained by the resonance absorption of O and H atoms

The reaction of O(³P) with H₂ has been studied behind reflected shock waves in the temperature range of 1713–3532K at total pressures of about 1.4–2.0 bar by Atomic Resonance Absorption Spectroscopy using mixtures of N₂O and H₂ highly diluted in Ar. The O atoms were generated by the fast thermal decomposition of N₂O and the reaction with H₂ was followed by monitoring the time dependent O and H atom concentrations in the postshock reaction zone. For the experimental conditions chosen, the measured O and H atom concentrations were primarily sensitive to the well-known N₂O dissociation and to the studied reaction and hence its rate coefficient could be deduced. The measured rate coefficient data are fitted by the least-squares method to obtain the following three parameter expression: K₄=3.72×10⁶(T/K)^2.17exp(−4080K/T)cm³ mol⁻¹8⁻, which is in excellent agreement with the recent ab initio calculations for the rate coefficient of this reaction in the overlapping temperature range. The present result is also compared to the experimental results reported by earlier investigators.     

Electrochemical performance of Nd0.6Sr0.4Co0.5Fe0.5O3−δ–Ag composite cathodes in intermediate temperature solid oxide fuel cells

The electrochemical performances of Nd_0.6Sr_0.4Co_0.5Fe_0.5O_3−δ–Ag composite cathodes have been investigated in intermediate temperature solid oxide fuel cells. The Nd_0.6Sr_0.4Co_0.5Fe_0.5O_3−δ–Ag cathodes prepared by ball milling followed by firing at 920 °C show the maximum performance (power density: 0.15 W cm⁻² at 800 °C) at 3 wt.% Ag. On the other hand, the Nd_0.6Sr_0.4Co_0.5Fe_0.5O_3−δ–Ag composite cathodes with 0.1 mg cm⁻² (0.5 wt.%) Ag that were prepared by an impregnation of Ag into Nd_0.6Sr_0.4Co_0.5Fe_0.5O_3−δ followed by firing at 700 °C (but the electrolyte–Nd_0.6Sr_0.4Co_0.5Fe_0.5O_3−δ assembly was prepared first by firing at 1100 °C) exhibit much better performance (power density: 0.27 W cm⁻² at 800 °C) than the composite cathodes prepared by ball milling, despite a much smaller amount of Ag due to a better dispersion and an enhanced adhesion. AC impedance analysis indicates that the Ag catalysts dispersed in the porous Nd_0.6Sr_0.4Co_0.5Fe_0.5O_3−δ cathode reduce the ohmic and the polarization resistances due to an increased electronic conductivity and enhanced electrocatalytic activity.     

Phase transitions and phase decomposition of La1−xSrxCoO3−δ in low oxygen partial pressures

High-temperature X-ray diffraction has been used to investigate the phase stability of lanthanum strontium cobalt oxide (LSC) for a range of materials with the formula La_1−xSr_xCoO_3−δ (x = 0.7, 0.4, and 0.2). The stability of LSC increases with La content in low oxygen partial pressures at high temperature. Oxygen vacancy ordering has been observed for all three compositions in either low oxygen pressure or under reducing gas, as evidenced by the formation of the brownmillerite phase. The crystal structure of the vacancy-ordered phase was determined using Rietveld analysis of synchrotron X-ray diffraction data. The decomposition products under low oxygen pressure and in reducing conditions have been identified and characterized, including the phase transition and thermal expansion of the primary decomposition products, LaSrCoO₄ and LaSrCoO_3.5.     

CFD investigation of the flow and heat transfer characteristics in a tangential inlet cyclone

This work presents a computational fluid dynamics (CFD) calculation to investigate the flow field and the heat transfer characteristics in a tangential inlet cyclone which is mainly used for the separation of the dens phase of a two phase flow. Governing equations for the steady turbulent 3D flow were solved numerically under certain boundary conditions covering an inlet velocity range of 3 to 30 m/s. Finite volume based Fluent software was used and the RNG k −  turbulence model was adopted for the modeling highly swirling turbulent flow. Good agreement was found between computed pressure drop and experimental data available in the literature. The structure of the vortices and variation of local heat transfer were studied under the effects of inlet velocity.     

The optimal spacing of parallel plates cooled by forced convection

This paper reports the optimal board-to-board spacing and maximum total heat transfer rate from a stack of parallel boards cooled by laminar forced convection. The optimal spacing is proportional to the board length raised to the power 1/2, the property group (μ)^1/4, and (ΔP)^−1/4, where ΔP is the pressure head maintained across the stack. The maximum total heat transfer rate is proportional to (ΔP)^1/2, the total thickness of the stack (H), and the maximum allowable temperature difference between the board and the coolant inlet. Board surfaces with uniform temperature and uniform heat flux are considered. It is shown that the surface thermal condition (uniform temperature vs uniform heat flux) has a minor effect on the optimal spacing and the maximum total heat transfer rate.     

Intensification of turbulent free heat transport in various configurations with adequate binary gas mixtures

The present paper investigates a promising avenue for the intensification of turbulent free convection in various configurations using adequate binary gas mixtures in which helium (He) is the primary gas component and carbon dioxide (CO₂), methane (CH₄), nitrogen (N₂), oxygen (O₂) and xenon (Xe) are the secondary gas components. In the context of binary gas mixtures, the thermo-physical properties: viscosity, thermal conductivity, density and isobaric heat capacity depend on three quantities: temperature, pressure and molar gas composition. Within the platform of turbulent free convection using the five binary gas mixtures for Ra > 10⁹, results are presented for the allied convective coefficient h_mix/B varying with the molar gas composition w in the w-domain [0, 1]. Values of the maximum allied convective coefficients h_mix,max/B attained at the correlative optimal molar gas compositions w_opt are easily extracted from suitable design charts.     

Optimal performance of a generalized irreversible Carnot-engine

This paper presents a generalized irreversible Carnot-engine model that incorporates several internal and external irreversibilities, such as heat-resistance, bypass heat-leak, friction and turbulence. The added irreversibilities besides heat-resistance are characterized by a constant parameter and a constant coefficient. The relation between optimal power-output and efficiency is derived based on a generalized heat-transfer law q ∝ (ΔT)ⁿ. Detailed numerical examples show the effect of bypass heat-leakage, internal irreversibility and heat-transfer law on the optimal performance of the generalized irreversible heat-engine.     

Importance of the band gap energy and flat band potential for application of modified TiO2 photoanodes in water photolysis

The influence on water photolysis of two important parameters of the electronic structure of photocatalytic semiconductors: the forbidden band gap, E_g, that decides about the absorption spectrum and the flat band potential, V_Fb, that affects the recombination probability, was studied. The photoelectrochemical experiments were performed in a three-electrode cell PEC with a TiO₂ thin film photoanode immersed in liquid electrolyte of variable pH. Titanium dioxide photoanodes doped with chromium (up to 16 at.%) and tin (up to 50 at.%) were prepared by rf reactive sputtering. Different methods of flat band potential determination: Mott–Schottky plots and photocurrent versus voltage characteristics were used. The energy band gap was derived from the spectrophotometric measurements of optical transmittance and reflectance coefficients of thin films. For TiO₂ + 7.6 at.% Cr high and negative flat band potential V_Fb = −0.72 eV (at pH 4) has been found but the recombination time τ = 8 s was the shortest of all TiO₂ modifications. Despite additional absorption feature at about 2.8 eV, i.e., at wavelength corresponding to visible range of the light spectrum, the photoconversion efficiency of TiO₂ + 7.6 at.% Cr was found to be much smaller (η_c = 0.1%) than that of undoped TiO₂ (η_c = 1.8%) and TiO₂ doped with 8 at.% of Sn (η_c = 1.0%).