Significance of thermal radiation and thermo-physical properties on the modeling of sodium droplet explosion with different reaction rates

The temperature of explosive substances (i.e., coolants) in the nuclear industries are necessary to ensure safety. The present study is focused on the analysis of the significance of thermal radiation and variable thermo-physical properties on thermal stability characteristics of sodium droplet use as a coolant in the design of nuclear facilities. It is pertinent to note that the inclusion of heat loss by convection and heat generated by the reaction is based on Newton's law of cooling and Arrhenius kinetic equation, respectively, with the P-1 approximation radiative heat loss model. The emerging mathematical model is a highly nonlinear ordinary differential equation. The model is solved using the classical fourth-order Runge-Kutta scheme. Consequently, the analysis of the results of the present study reveals the quantitative impacts of the thermal radiative model and variable thermo-physical properties on the temperature of the sodium droplet. The results reveal that the combined inclusion of variable thermophysical properties and thermal radiation significantly reduces the droplet temperature. The temperature of the coolant increases with an increase in the reactants' numerical exponent and thermal radiation reduces the temperature of the sodium droplet at the initial temperature with the reverse effect at free stream temperature.     

Recursive formulation on thermal analysis of an annular fin with variable thermal properties

This study introduces a discrete model which is pertinent for calculating thermal performance of singular annular fin with variable thermal properties. The singular annular fin can be divided into several circular sections, and each section can take its variable thermal properties, such as heat transfer coefficient and thermal conductivity, into account. The result from each section can be combined and calculated together by a recursive formula. Then, the solutions of temperature distribution and heat transfer rate on singular annular fin can be quickly obtained. For this model, the recursive formulae for both conditions with and without heat transfer on fin tip are demonstrated. Finally, some examples including composite materials for an annular fin have been successfully simulated through the present approach.     

Convective heat transfer and second law analysis of non-Newtonian fluid flows with variable thermophysical properties in circular channels

This study presents an analytical solution, for fully developed non-Newtonian fluid flows in circular channels under isoflux thermal boundary conditions based on perturbation techniques. Since the physical properties are generally a function of temperature and may not be assumed constant under certain circumstances, the change in viscosity and thermal conductivity with temperature was taken into account. Viscous dissipation term was also included in the performed analysis. In this study, first closed form expressions for velocity, temperature distributions, and Nusselt numbers corresponding to constant thermophysical properties were given in terms of governing parameters. Then, numerical calculation was performed to obtain the values of Nusselt number and global entropy generation for variable thermophysical properties. The results revealed that neglecting the property variation significantly affects heat transfer characteristics and entropy generation, in which the deviation from the constant physical property assumption may reach up to about 32.6%.     

Combustion behavior of a falling sodium droplet: Burning rate‐constant and drag coefficient

The combustion behavior of a single sodium droplet has been studied experimentally, by use of a falling droplet. It was found that D²‐law can hold for the sodium droplet combustion after the ignition, which can be observed to occur through an increase in the droplet temperature under a condition without a gaseous flame, suggesting that a surface reaction plays an important role in the ignition of sodium. It was also found that the burning rate‐constant without forced convection has nearly the same value as those for conventional hydrocarbon droplets, although it is considered that the sodium combustion proceeds in an oxidizer‐rich environment even in the air. This can be judged by comparing a temporal variation of the flame/droplet diameter ratio for the sodium droplet with that for the hydrocarbon droplet. A micro‐explosion of the burning droplet is also observed when oxygen concentration in the ambience exceeds 0.33 in mass fraction. As for the falling velocity and/or distance of the burning droplet, it turned out that the use of the drag coefficient for solid sphere under isothermal condition is inappropriate in obtaining accurate values. It was also found in another experiment that when Re > 500, the drag coefficient of the falling droplet undergoing combustion is as high as 2 depending on combustion situation and/or droplet temperature, while that of the solid sphere under an isothermal condition is 0.44. © 2005 Wiley Periodicals, Inc. Heat Trans Asian Res, 34(7): 481–495, 2005; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20084     

Thermal analysis of a longitudinal fin with variable thermal properties by recursive formulation

The present study supplies a new approach to calculate thermal performance of a singular fin with variable thermal properties. With discrete model, the singular fin can be divided into many sections. Then, each section can be combined together to obtain the whole solution of the fin by recursive numerical formulation. The recursive formulas for both conditions with and without heat transfer on fin tip are derived in the present study. Finally, several examples including composite and boiling mode of a fin have been successfully simulated to demonstrate the validity of the present approach.     

The phase change thermoelastic analysis of biological tissue with variable thermal properties during cryosurgery

Abstract

In this work, the coupling phase change heat transfer process and thermal stress behavior of biological tissue during cryosurgery are studied in the context of a generalized thermoelastic theory. The nonlinear governing equations are constructed while considering the variable thermal properties and solved by a time-domain finite element method based on the effective heat capacity formulation. A 2-D tumor and normal tissue model is adopted for simulating the freezing process in cryosurgery. The effects of temperature-dependent thermal properties and relaxation time on the responses of biological tissue are discussed and illustrated graphically.     

石墨烯泡沫热物性与界面热导温度相关性研究

石墨烯泡沫是将石墨烯立体化形成的复合材料,在锂离子电池等领域有较好的应用前景,而其导热性质成为限制工业应用的重要因素。基于瞬态电热技术,研究了石墨烯泡沫的导热性质及其随温度的变化。结果表明,不同于Umklapp声子散射机理,石墨烯泡沫的热导率随温度呈正相关性:由室温至373 K时,热导率由0.71升高至1.10 W/(m·K)。分析发现,泡沫内部的大量界面是其低导热性质的主要因素。利用分子动力学模拟验证了石墨烯与基体材料间的界面传热随温度成正相关,与宏观材料测量结果相符。     

Analytical approaches for thermal analysis of radiative fin with a step change in thickness and variable thermal conductivity

In this paper, heat transfer in a straight fin with a step change in thickness and variable thermal conductivity which is losing heat by radiation to its surroundings is analyzed. The calculations are carried out by using the differential transformation method (DTM) and variational iteration method (VIM) that can be applied to various types of differential equations. The results obtained employing the DTM and VIM are compared with a finite difference technique with Richardson extrapolation which is an accurate numerical solution to verify the accuracy of the proposed methods. As an important result, it is depicted that the DTM results are more accurate in comparison with those obtained by VIM. After these verifications the effects of parameters such as thickness parameter α, dimensionless fin semi‐thickness δ, length ratio λ, thermal conductivity parameter β, and radiation–conduction parameter N_r, on the temperature distribution and fin efficiency are illustrated and explained. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj) . DOI 10.1002/htj.21000     

Numerical simulation study and dimensional analysis of hydrogen explosion characteristics in a closed rectangular duct with obstacles

The influence of obstacles on hydrogen explosion is studied by numerical simulation and dimensional analysis. The numerical simulation is conducted based on the premixed model in a closed rectangular duct with rectangular obstacles, and ten variables that affect the flame propagation velocity are analyzed by dimensional analysis. Continuous acceleration of flame and collision annihilation of flame were successfully realized through triangular obstacles in simulation. The result shows that with the number of obstacles changes, the flame invariably converts to hemispherical flame, finger flame, tongue flame, quasi-plane flame, and mouth flame in turn. But the flame front is more twisted in two obstacles due to hydrodynamic instability and vortices. Through the comparative analysis of the flame and flow field in the duct during hydrogen explosion. It is found that the flame-obstacles-flow field coupling and its hydrodynamic phenomena determine the flame deformation and changes in propagation velocity. The result of the dimensional analysis shows that the drag coefficient can well depict the effects of the shape of the obstacles, and the dimensionless qualitative and quantitative model of flame propagation speed is given and verified.     

Experimental and numerical analysis of the temperature transition of a suspended freezing water droplet

The objective of this study was to develop a simple experimental and numerical method to study the temperature transition of freezing droplets. One experimental approach and several numerical methods were explored. For the experimental method, a droplet was suspended in a cold air stream from the junction of a thermocouple. The droplet’s temperature transition was able to be accurately measured and the freezing of the droplet observed. The numerical models developed were able to predict the temperature transition and the freezing time of the droplet. Of the numerical methods, a simple heat balance model was determined to be an accurate means of predicting the freezing time of the droplet.     

Closing the hydrogen cycle with the couple sodium borohydride-methanol,via the formation of sodium tetramethoxyborate and sodium metaborate

Methanolysis of sodium borohydride (NaBH₄) is one of the methods efficient enough to release, on demand, the hydrogen stored in the hydride as well as in 4 equiv of methanol (CH₃OH). It is generally reported that, in methanolysis, sodium tetramethoxyborate (NaB(OCH₃)₄) forms as single component of the spent fuel. It is, however, necessary to clearly investigate some critical aspects related to it. We first focused on the methanolysis reaction where NaBH₄ was reacted with 2, 4, 8, 16, or 32 equiv of CH₃OH. With 2 equiv of CH₃OH, the conversion of NaBH₄ is not complete. With 4 to 32 equiv of CH₃OH, NaBH₄ is totally methanolized (conversion of 100%). The best conditions are those involving 4 equiv of CH₃OH as they offer the highest effective gravimetric hydrogen storage capacity with 4.8 wt%, an attractive H₂ generation rate with 331 mL(H₂) min⁻¹—a performance achieved without any catalyst—and the formation of NaB(OCH₃)₄ as single product as identified by X-ray diffraction, Fourier transform infrared spectroscopy, and nuclear magnetic resonance. We then focused on the transformation of this product NaB(OCH₃)₄ into sodium metaborate (NaBO₂), via the formation of sodium tetrahydroxyborate (NaB(OH)₄). NaB(OCH₃)₄ is easily transformed in water, by hydrolysis, at 80°C and for 90 minutes, into NaB(OH)₄ and 4 equiv of CH₃OH. In doing so, the cycle with CH₃OH is closed. Subsequently, NaB(OH)₄ is recovered and converted into NaBO₂ under heating at 500°C. This reaction liberates 4 equiv of H₂O, which allows to close the cycle with water. Based on these achievements, we have finally proposed a triangular recycling scheme aiming at closing the cycle with the protic reactants of the aforementioned reactions. This scheme may be used as base for implementing a closed cycle with the couple NaBH₄-CH₃OH.     

Dust explosion of oil shale and olive cake solid fuels: a comparison study

This paper investigates the inhibition of oil shale and olive cake dust explosions when they are used as an alternative source of fuel. Special emphasis was given to the effect of particle size of the same material on the maximum permissible oxygen concentration to prevent dust explosion for different concentrations using nitrogen as the diluent gas. It was found that olive cake is ignited more easily than oil shale all over the range of particle sizes and dust concentration. Tests on different particle sizes were carried out, and it was found that the maximum permissible oxygen concentration for a given dust concentration increases with increasing the particle size for both oil shale and olive cake. Copyright © 2005 John Wiley & Sons, Ltd.     

悬垂水滴与悬浮气泡表面气体水合物形成特性对比

基于悬垂水滴和悬浮气泡表面形成气体水合物的可视化耐高压实验装置,分析探讨了反应压力、温度、水质等因素对水滴和气泡表面气体水合物成核和生长规律的影响.对已有的关于研究单个静止悬垂水滴和悬浮气泡表面气体水合物生长特性的实验现象及结果进行了对比分析,得出结论:温度和压力是影响表面水合物结晶与生长的重要因素;温度的降低或压力的升高均使水合反应速度加快.研究为发展喷雾法和鼓泡法这两种强化制备水合物的方式提供了有效的实验支撑.     

Study on the sodium oxidation properties of low-iron vanadium-titanium magnetite with high vanadium and titanium

In this work, the oxidation properties of low-iron vanadium-titanium magnetite with high vanadium and titanium in a laboratory muffle furnace was investigated. XRD, SEM, and TG-DSC method are employed to identify the main phases and chemical composition of the samples. The roasting time of 4h and Na₂CO₃/vanadium titanium magnetite mass ratio of 7.5:100 were determined. The results showed that the blank oxidation roasting temperature ranged from 593°C to 1035°C, the mixed oxidation roasting temperature of vanadium-titanium magnetite and Na₂CO₃ at the range of 204°C to 825°C, and the forming temperature of soluble vanadate at the range of 700°C to 825°C. When roasting temperature reached 1000°C, consolidation was started. When roasting temperature was 850°C, the roasting conversion efficiency, acid leaching efficiency and water leaching efficiency were 92.4%, 87%, and 85%, respectively.     

Tuning of thermal properties of sodium acetate trihydrate by blending with polymer and silver nanoparticles

The use of phase change materials (PCMs) is one of the pathways for the storage of temporarily excessive energy from natural sources (solar) and industry for use at a more suitable later time. One of the materials with a high energy storage density is sodium acetate trihydrate (SAT), on which several studies were conducted in order to solve phase segregation and supercooling problems, e.g. by adding polymers and nucleating agents. Here we investigate the effectiveness of adding a polymer blend of carboxymethyl cellulose (CMC) and silica gel to avoid phase segregation, and silver nanoparticles (AgNPs) as nucleating agent. The synthesis of silver nanoparticles was carried out by a green method in CMC as a way to ensure compatibility with SAT. The addition of AgNPs in higher concentrations to 0.5% reduces supercooling, and mixing silica gel with CMC to avoid segregation phase, yields an increment in the stability of the phase change behavior, during heating and cooling cycles. The latent heat release upon crystallization of the PCM was optimum for the mixture with 0.5% AgNPs, and for the highest amounts of CMC with respect to silica gel, with nearly 95% of latent heat recovery compared to pure SAT.     

变齿距电磁作动器集中参数热模型的构建与分析

根据变齿距电磁作动器的几何结构和传热特点,建立其集中参数热模型。对加工好的样机温度进行了试验测量,并将集中参数热模型的计算结果与试验数据进行了对比,结果表明,在不同线圈电压下,作动器线圈和外壳温度的最大相对误差仅为8.40%和9.22%,证明了所建立模型的有效性。利用所建立的集中参数热模型,研究了作动器温升对各个热阻的敏感性,结果表明,作动器温升对外壳与环境之间的散热热阻最为敏感,当其增加20%时,线圈温度和外壳温度将分别增加6.10%和8.40%,而其他热阻对作动器的线圈和外壳温度的影响都非常小。最后,对变齿距电磁作动器的冷却方式进行了探讨,高电密的情况下,在外壳设计散热肋片是提高冷却效果的实用方式。     

The influence of binary mixture thermophysical properties in the analysis of heat and mass transfer processes in solar distillation systems

Although a substantial amount of research work has already been devoted to various aspects of modeling the convective and mass transport processes in solar distillation systems, it appears that the role of thermophysical and transport properties of the working medium and their effect on the thermal behavior and performance analysis of such systems has been left almost completely unnoticed. The working medium in these systems, which is a binary mixture of water vapor and dry air in equilibrium, appears to exhibit a completely different set of properties than dry air, especially at saturation conditions and at the higher region of the solar still operational temperature range. An analysis is presented aiming to signify the effect of binary mixture thermophysical properties on the transport processes and the associated quantities and evaluate the thermophysical properties of the working medium in these systems, based on contemporary data for dry air and water vapor. The derived results, in the form of convenient algebraic correlations, are employed to investigate the effect of using the appropriate thermophysical properties on the calculation of the convective heat and mass transfer, as well as the distillate mass flow rates. According to the results from the present investigation, although the use of improper dry air data leads to a significant overestimation of the convective heat transfer coefficient, the errors associated with the use of improper dry air properties is a moderate overestimation of distillate output which is estimated to be up to 10% for maximum average still temperatures of 100 °C.     

含相变材料双层玻璃窗光热分析模型

建立了含相变材料双层玻璃窗的光热传输模型,考虑相变材料和玻璃半透明特性,采用有限差分求解方程。在通过实验数据验证模型准确的基础上,分析了相变材料的融化温度对含相变材料双层玻璃窗光热性能的影响。结果显示:建立的模型可模拟相变材料双层玻璃窗的光热传输过程;随融化温度升高,含相变材料双层玻璃窗温度衰减因子则逐渐增大,相变材料融化时间延后,相变材料呈液态的时间变短,但温度滞后值、热流密度和太阳透射能则呈不规则变化。     

A theoretical analysis of the capture of greenhouse gases by single water droplet at atmospheric and elevated pressures

Gas absorption by droplets is an important route to reduce greenhouse gas emissions, especially for carbon dioxide. To recognize the fundamental absorption processes of greenhouse gases by single droplets, the mass transport phenomena of greenhouse gas uptake by a quiescent water droplet at atmospheric and elevated pressures are analyzed theoretically and four common greenhouse gases of CO₂, N₂O, CH₄ and O₃ are taken into consideration. On account of piecewise function encountered at the droplet surface, it is impossible to obtain a fully analytical solution for describing the mass transfer process. Instead, a semi-analytical method is developed to predict the mass diffusion between the gas phase and the liquid phase. The obtained results indicate that, by virtue of the four greenhouse gases characterized by low mass diffusion number, the entire mass transfer is controlled by the liquid phase. A unified formula has been successfully established to aid in estimating the dimensionless solute uptake process and the dimensionless aqueous diffusion time of 0.45 is sufficiently long the implement the absorption process. For the ambient temperature and pressure in the ranges of 280–350 K and 1–20 atm, respectively, it is found that increasing the two parameters will intensify the solute absorption amount significantly and the absorption process can be accelerated by increasing temperature.     

Thermal performance of straight porous fin with variable thermal conductivity under magnetic field and radiation effects

The present numerical study reports the thermal performance of the straight porous fin with temperature-dependent thermal conductivity, radiation, and magnetic field effects. The heat transfer model comprising the Darcy's law for simulating flow with solid-fluid interactions in porous medium, Rosseland approximation for heat transfer through radiation, Maxwell equations for magnetic field effect and linearly varying temperature dependent thermal conductivity, results into highly nonlinear ordinary differential equation. The governing equation is solved using a finite difference scheme with suitable boundary conditions. The obtained solutions are physically interpreted by considering the impact of different nondimensional parameters on thermal performance, efficiency, and effectiveness of the system through plotted graphs. A detailed result with regard to the Nusselt number at the fin base is calculated. The results obtained are observed to be in excellent agreement with previous studies. From the study, it is observed that there is a significant effect on the thermal performance of the fin in the presence of porous constraints; also, results reveal that the nonlinear thermal conductivity parameter strengthens the thermal performance, efficiency, and effectiveness of the fin. Furthermore, the results of the study reveal that the rate of heat transfer of the fin increases with the increase in the magnetic parameter and radiation parameter.