氯化铵水溶液定向凝固实验的传热分析

选用类合金NH4Cl-H2O二元溶液进行垂直定向凝固实验研究,再现过共晶合金结晶过程,测量记录凝固过程中的温度场和固、液相界面位置;重点分析了两相区的传热特性,包括局部热流和释放潜热,并尝试用实验数据与数值计算相结合的方法确定两相区局部固相分数与温度的关系曲线。研究表明:在结晶过程中,各点温度呈线性下降,局部热流在进入两相状态后达到峰值;各相区内温度梯度恒定,但相界面附近温度梯度变化显著。两相区凝固过程中,先期潜热释放总量大,总凝固分数大,两相区厚度迅速增长;随后总凝固分数随相界面迅速上移而急剧下降,经历准稳态过程后再缓慢上升。溶液沿凝固方向分层,NH4Cl质量分数逐渐增大,相应结晶温度逐渐升高。     

Natural convection suppression and crystal growth during unidirectional solidification of a binary system

We studied experimentally the interaction between natural convection and dendritic growth in the mushy layer during unidirectional solidification of aqueous ammonium chloride solutions cooled from below. Small amounts of hydroxyethylcellulose were added to the solution to increase its viscosity, leading to the suppression of convection. Natural convection consists of salt fingers in the liquid phase and plumes in the mushy layer for a low‐viscosity solution, but the onset of plumes is suppressed for a high‐viscosity solution. The mushy layer becomes sparsely packed, and the primary and secondary arms of the dendrites grow to noticeable sizes with increasing its viscosity, which yields a low solid fraction, such as 1% on average in the mushy layer for a viscosity ratio of 25.5. This demonstrates that natural convection strongly affects the morphology of dendrites. © 2000 Scripta Technica, Heat Trans Asian Res, 29(2): 120–131, 2000     

Directional solidification of binary melts with a non-equilibrium mushy layer

When the melt or solution solidifies a constitutionally supercooled mushy layer is frequently formed ahead of the phase transition boundary. This leads to nucleation and growth mechanisms of newly born solid particles within a mush. The latter is responsible for the structures and properties appearing in the crystal. The process of solidification with a supercooled mushy layer is analytically described on the basis of two joint theories of directional and bulk crystallization. Such characteristics as the constitutional supercooling, the solid fraction and the radial density distribution function of solid particles in a mushy layer are found. The complex structure of the non-equilibrium mushy layer is completely recognized.     

Solidification in a water‐saturated porous medium when convection is present (response of solid‐liquid interface due to time‐varying cooling temperature)

A fundamental study on solidifying phenomenon in a rectangular space filled with water‐saturated porous medium has been carried out with a system, cooled from the upper boundary and heated from below, where vigorous convection develops in the un‐solidified liquid layer. The dynamic response of the solid‐liquid interface to the periodical cooling temperature with the bottom boundary kept at constant temperature T_H = 20°C, is investigated experimentally. In particular, the amplitude of the interface and the phase lag in respect to the oscillating cooling temperature have been monitored for various periods and average temperatures. A one‐dimensional numerical model, based on an assumption of constant heat flux from the vigorously convecting liquid regime has been also developed. The numerical model predicts quite well the time‐dependent behavior of the horizontally averaged ice‐layer thickness observed in the experiments. Our general findings are that the amplitude increases proportionally to the temperature fluctuation period and that both the thicker solid layer and the shorter period cause greater phase lags. © 2006 Wiley Periodicals, Inc. Heat Trans Asian Res, 35(4): 294–308, 2006; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20109     

Application of a hybrid model of mushy zone to macrosegregation in alloy solidification

Solidification of an aqueous ammonium chloride (NH₄Cl-H₂O) solution inside a two-dimensional cavity is numerically investigated using a continuum mixture mathematical model. The mushy region where solid and liquid phases co-exist is considered a non-Newtonian fluid below a critical solid fraction, and a porous medium thereafter. This critical solid fraction is chosen as that corresponding to the coherency point, where a solid skeleton begins to form. The numerical results show that the solidification of a hypereutectic NH₄Cl-H₂O solution is mainly characterized by the rejection of solute at the mushy region and double diffusive convection induced by the opposing solutal and thermal buoyancy forces. The mathematical model agrees satisfactorily with the available experimental and numerical data.     

Mathematical model for turbulent flow,heat transfer,and solidification

A steady‐state, two‐dimensional numerical model has been used to describe coupled liquid steel's turbulent flow and heat transfer with solidification for Fe‐C binary alloy in a crystallizer of inverse casting. The solid‐liquid phase change phenomena have been modeled by using continuum formulations and considering the mushy zone as porous media. The turbulence flow in the crystallizer has been accounted for using a modified version of the low‐Reynolds‐number κ?ε turbulence model. The flow pattern in the liquid zone and the temperature distribution in the solid, mushy, and liquid regions have been predicted. The numerical analysis indicates that the residence time of the mother sheet in the crystallizer is one of the key parameters. The effects of some other main parameters on the solidification behavior have also been studied, such as the thickness and the initial temperature of the mother sheet, and the superheat degree of liquid steel. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(7): 582–592, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10112     

Phase change characteristics of ethylene glycol solution‐based nanofluids for subzero thermal energy storage

Nanofluids, particularly water‐based nanofluids, have been extensively studied as liquid–solid phase change materials (PCMs) for thermal energy storage (TES). In this study, nanofluids with aqueous ethylene glycol (EG) solution as the base fluid are proposed as a novel PCM for cold thermal energy storage. Nanofluids were prepared by dispersing 0.1–0.4 wt% TiO₂ nanoparticles into 12, 22, and 34 vol.% EG solutions. The dispersion stability of the nanofluids was evaluated by Turbiscan Lab. The liquid–solid phase change characteristics of the nanofluids were also investigated. Phase change temperature (PCT), nucleation temperature, and half freezing time (HFT) were investigated in freezing experiments. Subcooling degree and HFT reduction were then calculated. Latent heat of solidification was measured using differential scanning calorimetry. Thermal conductivity was determined using the hot disk thermal constant analyzer. Experimental results show that the nanoparticles decreased the PCT of 34 vol.% EG solution but minimally influenced the PCT of 12 and 22 vol.% EG solutions. For all nanofluids, the nanoparticles decreased the subcooling degree, HFT, and latent heat but increased the thermal conductivity of the EG solutions. The mechanism of the improvement of the phase change characteristics and decrease in latent heat by the nanoparticles was discussed. The nanoparticles simultaneously served as nucleating agent that induced crystal nucleation and as impurities that disturbed the growth of water crystals in EG solution‐based nanofluids. Copyright © 2016 John Wiley & Sons, Ltd.     

A Semi-Exact Solution for Solidification of a Binary Solution on a Cold Isothermal Surface below Eutectic Temperature

The solidification of a binary solution on a cold horizontal surface below eutectic temperature is solved using a semi-exact method. The temperature distributions in the solid and liquid zones are obtained by exact solutions, while heat transfer in the mushy zone is obtained by an integral approximate method. The locations of the interface between solid and mushy zones and interface between mushy and liquid zones are obtained by coupling the temperature distributions in the three regions. The effects of initial temperatures, wall temperatures, and initial concentrations on the solidification of the binary solution are investigated.     

Analytical modelling of transient phase‐change problems

In this paper, an analytical solution for the temporal location of moving solid–liquid interface of a phase‐change process, occurring in parallel plate channels, is presented. The motion of the solid–liquid interface is governed by the convection from the surface of one of the plates, while constant heat supply is assumed to occur on the surface of the other plate. The steady location of the solid–liquid interface is also determined. The variation of the Biot number versus the Fourier number is investigated. The results of this study indicate that simple analytical solutions for transient phase‐change problems with heat flux and convective boundary conditions that are of practical importance to the people working in the field can be obtained. Copyright © 2000 John Wiley & Sons, Ltd.     

To the theory of underwater ice evolution,or nonlinear dynamics of “false bottoms”

We present a mathematical model describing evolution of false bottoms often met between an under-ice melt pond and the underlying ocean during summer. The model treats a false bottom as the region of mixed phase (mushy layer) whose coordinates depend on time and determine the phase transition area. As the heat and the salt fluxes in the ocean are strongly influenced by turbulence and the ice meltwater accumulating underneath the ice cover is practically fresh, we use modified boundary conditions for heat and mass fluxes at the interfaces of phase transition. Explicit analytical solutions (thickness of false bottom and growth rates of its boundaries, temperature and salinity distributions, solid phase fraction and ocean-to-ice heat flux) of the nonlinear model under consideration are found. Model predictions are in good agreement with existing experimental data and physical concepts of phenomena under study.     

Nonlinear dynamics of directional solidification with a mushy layer. Analytic solutions of the problem

We present new analytic results relating to the nonstationary Stefan-type problems for the unidirectional solidification of binary solutions or melts with a mushy layer. Our detailed analysis of the field data is based on the classical model of a mushy layer, which is modified in order to obtain explicit solutions (solid phase thickness and growth rate, temperature distributions, conductive and latent heat fluxes are determined). Predictions for the growth rate and temperature profiles of the mixed-phase and solid regions agree well with existing observations on young sea ice dynamics.     

MICROSOLIDIFICATION PROCESS IN MULTICOMPONENT SYSTEM

In conventional solidification of multicomponent mixtures, a mushy zone appears between the pure solid and liquid regions and promotes stable solidification by accepting the rejected solute regionally. From the standpoint that the fineness of inhomogeneity influences the mechanical properties in material processing, the linking of macro heat transfer and microsolidification in the mushy zone was studied. First, the crystal growth and its accompanying concentration field near the advancing front of the mushy zone were observed precisely by using the light absorption method. It was clarified that the mushy zone consisted of the leading front in which the frame structure formed with an accompanying concentration boundary layer and a growing region where the solidification proceeds by fattening of the crystals. Second, the mechanism of side-branch evolution was studied in conjunction with interfacial instability due to constitutional supercooling and curvature supercooling around the primary arm surface. Summarizing these results, the microsolidification process is discussed quantitatively in relation to macro heat transfer.     

Adhesion and detachment characteristics of a TBAB hydrate solid on a heat transfer surface (Effect of concentration of TBAB solutions)

In air‐conditioning systems, it is desirable that the liquid–solid phase change temperature of a cool energy storage material be approximately 10^°C, with respect to improving the coefficient of performance (COP). Moreover, a thermal storage material that forms slurry can realize a large heat capacity of the working fluids. A solid that adheres to the heat transfer surface forms a thermal resistance layer and significantly reduces the rate of cold storage; therefore, it is important to avoid the adhesion of a thick solid layer on the surface so as to realize efficient energy storage. Considering a harvest type cooling unit, the force required for removal of the solid phase from the heat transfer surface was investigated. Tetra‐n‐butylammonium bromide (TBAB) clathrate hydrate was used as a cold storage material and the effect of the TBAB solution concentration on the scraping force required to detach the adhered TBAB hydrate solid from the heat transfer surface was experimentally examined. The TBAB hydrate solids were broadly categorized into two types, and the scraping force required for removal of these two types of TBAB hydrate solid was different. The scraping force required for removal of the solid increased due to the effect of increasing the concentration of the TBAB solution. © 2009 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20254     

The steady-state solidification scenario of ternary systems: Exact analytical solution of nonlinear model

A mathematical model describing the steady-state solidification of ternary systems with mushy layers (primary and cotectic) is formulated: solidification along a liquidus surface is characterized by a primary mushy layer, and solidification along a cotectic line is characterized by a secondary (cotectic) mushy layer. Exact analytical solutions of the model under consideration are found in a parametric form (thicknesses of mushy layers, growth rate of their boundaries, temperature and composition fields, solid fractions are determined in an explicit form). The velocity of solidification is completely determined by temperature gradients in the solid and liquid phases. This velocity coincides with similar expressions describing binary melt solidification with a planar front or a mushy layer. It is shown that the liquid composition of the main component decreases in the cotectic and primary layers, whereas the second (cotectic) composition increases in the cotectic layer, attains a maximum point and decreases in the primary layer.     

Analysis of solidification in a finite PCM storage with internal fins by employing heat balance integral method

Here, a simplified analytical model has been proposed to predict solid fraction, solid–liquid interface, solidification time, and temperature distribution during solidification of phase change material (PCM) in a two‐dimensional latent heat thermal energy storage system (LHTES) with horizontal internal plate fins. Host of boundary conditions such as imposed constant heat flux, end‐wall temperature, and convective air environment on the vertical walls are considered for the analysis. Heat balance integral method was used to obtain the solution. Present model yields closed‐form solution for temperature variation and solid fraction as a function of various modeling parameters. Also, solidification time of PCM, which is useful in optimum design of PCM‐based thermal energy storages, has been evaluated during the analysis. The solidification time was found to be reduced by 93% by reducing the aspect ratio from 8 to 0.125 for constant heat flux boundary condition. While, for constant wall temperature boundary condition, the solidification time reduces by 99% by changing the aspect ratio from 5 to 0.05. In case of convective air boundary surrounding, the solidification time is found to reduce by 88% by reducing the aspect ratio from 8 to 0.125. Based on the analytical solution, correlations have been proposed to predict solidification time in terms of aspect ratio and end‐wall boundary condition.     

Effect of viscosity variation on natural convection flow of water–alumina nanofluid in an annulus with internal heat generation

Heat transfer enhancement in a horizontal annulus using the variable viscosity property of an Al₂O₃–water nanofluid is investigated. Two different viscosity models are used to evaluate heat transfer enhancement in the annulus. The base case uses the Pak and Cho model and the Brinkman model for viscosity which take into account the dependence of this property on temperature and nanoparticle volume fraction. The inner surface of the annulus is heated uniformly by a constant heat flux q_w and the outer boundary is kept at a constant temperature T_c. The nanofluid generates heat internally. The governing equations are solved numerically subject to appropriate boundary conditions by a penalty finite‐element method. It is observed that for a fixed Prandtl number Pr = 6.2, Rayleigh number Ra = 10⁴ and solid volume fraction ? = 10%, the average Nusselt number is enhanced by diminishing the heat generation parameter, mean diameter of nanoparticles, and diameter of the inner circle. The mean temperature for the fluids (nanofluid and base fluid) corresponding to the above mentioned parameters is plotted as well. © 2012 Wiley Periodicals, Inc. Heat Trans Asian Res; Published online in Wiley Online Library ( wileyonlinelibrary.com/journal/htj ). DOI 10.1002/htj.21016     

Effect of macro scale phenomena on microsegregation

A metal solidification system consists of solid, mushy and liquid regions. In many systems the two phase mushy region has a fine scaled columnar dendritic morphology. Microscopic models of metal solidification systems focus on the mass diffusion (microsegregation) and movement of the solid/liquid interface in the dendrite arm spaces. In this paper the effects of macroscopic variables on the microsegregation predictions are studied. In particular, the effect of cooling and macrosegregation histories on the solid solute profile, the eutectic fraction formed and solid/liquid interface movement in the arm spacing will be investigated.     

A theoretical study of evaporative heat transfer in high‐velocity two‐phase flow of air–water in a small vertical tube

A theoretical study was performed to investigate the evaporative heat transfer of high‐velocity two‐phase flow of air–water in a small vertical tube under both heating conditions of constant wall temperature and constant heat flux. A simplified two‐phase flow boundary layer model was used to evaluate the evaporative heat transfer characteristics of the annular two‐phase flow. The analytical results show that the gravitational force, the gas–liquid surface tension force, and the inertial force are much smaller than the frictional force and hence can be neglected for a small tube. The evaporative heat transfer characteristics of the small tube with constant wall temperature are quite close to those of the small tube with constant heat flux. The mechanism of the heat transfer enhancement is the forced convective evaporation on the surface of the thin liquid film. © 2003 Wiley Periodicals, Inc. Heat Trans Asian Res, 32(5): 430–444, 2003; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10110     

Boiling heat transfer in a narrow space controlled by punched interference plate

An experiment on pool boiling in methanol was performed for a case in which the boiling space was controlled by an interference plate with many holes. The narrow space, 0.12 mm in thickness, between the heat transfer surface and the interference plate was hermetically sealed at the perimeter. Therefore, the vapor and liquid were only exchanged through the holes in the interference plate. The degree of superheat at the onset of boiling was 0.7 K without overshoot at 10‐mm plate thickness, 1‐mm hole diameter, and 3.85‐mm hole pitch. The critical heat flux obtained was the same value without the interference plate mentioned above. The interference plate disturbed free convection and a superheat layer was provided under small heat flux on the heat transfer surface. The critical bubble diameter for the onset of boiling was decreased as the temperature of the superheat layer was increased. Thus, the degree of superheat at the onset of boiling was decreased. © 2004 Wiley Periodicals, Inc. Heat Trans Asian Res, 33(7): 462–471, 2004; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.20028     

Slip and micro flow characteristics near a wall of evaporating thin films in a micro channel

The microscopic liquid flow and heat transfer characteristics near the solid–liquid interface in the evaporating thin film region of a mini channel were investigated based on the augmented Young–Laplace equation and kinetic theory. A physical model using the boundary layer approximation and a constant slip length was developed to obtain the solid–liquid interfacial thermal resistances and interfacial temperatures. The results show that the ordered micro layer and micro flow near the wall reduce the effective liquid superheat and the liquid pressure difference mainly due to the reduced capillary pressure gradient. The solid–liquid interfacial thermal resistances and U‐shaped temperature drops tend to reduce the thin film spreading and heat transfer. The effects of the solid–liquid interfacial thermal resistances on the thin film evaporation outweigh the effects of the thermal conductivity enhancement due to the liquid ordering. The concepts of the micro flow and ordered adsorbed flowing micro layer are clarified to express the Kapitza resistance analytically in terms of the slip length and micro layer thickness. © 2010 Wiley Periodicals, Inc. Heat Trans Asian Res; 39(7): 460–474, 2010; Published online 3 June 2010 in Wiley Online Library ( wileyonlinelibrary.com ). DOI 10.1002/htj.20310