SOLIDIFICATION OF A PURE METAL WITH FINITE THERMAL CAPACITANCE ON A SINUSOIDAL MOLD SURFACE

Previous models of mold microgeometry-induced gap nucleation during pure metal solidification neglected the thermal capacitance of the solidifying shell: this is equivalent to the assumption that the shell has a small Stefan number. Although this assumption leads to steady heat conduction in the shell, and hence simplifies the solution for the thermal field, the corresponding assumption of a small Stefan number material is generally not appropriate for metals. In the present work, we remove the small Stefan number restriction used in a previous model for solidification of a pure metal on a rigid, perfectly conducting mold. The mold has a sinusoidal surface microgeometry for which the ratio of the amplitude to the wavelength is much less than one. This makes the aspect ratio a convenient perturbation parameter. Molten metal initially at its fusion temperature is assumed to wet the mold surface perfectly, which is held a constant temperature below the fusion temperature. The temperature field in the growing metal shell is numerically evaluated, and the instantaneous temperature field is incorporated into an analytical solution for the stress field in the shell. The evolving thermomechanical distortion of the shell is modeled assuming that the shell material follows a thermohypoelastic constitutive law that is a rate formulation of thermoelasticity. The contact pressure profile at the shell/asperity interface, which is indicative of shell distortion due to the asperity geometry, is obtained from the stress field. The effects of the mold wavelength and shell thermal capacitance on the contact pressure, temporal and spatial evolution of gap nucleation at the shell/mold interface, and mean shell thickness are examined for pure aluminum and iron shells.     

A THERMOMECHANICAL MODEL OF SOLIDIFICATION ON A MOLD MOVING WITH CONSTANT VELOCITY

A thermomechanical model of pure metal solidification on a moving mold plate is considered. The goal of the model is to obtain a formula for the contact pressure at the shell/mold interface as the mold moves into the molten liquid. From the contact pressure it is possible to infer the effects of the mold velocity and the mold microgeometry on the time and location of gap nucleation which results from irregular distortion of the shell as it grows from the melt. The mold, which moves at a constant velocity into the molten liquid, has a sinusoidal surface with a low aspect ratio: this means that its wavelength greatly exceeds its amplitude. The mold is of infinite area and is assumed to be perfectly conducting and thermomechanically rigid. We therefore neglect the complexities associated with the physics of edge constraints and/or free boundaries of the solidifying shell and the interacting distortions between deformable mold and shell materials along their interface. The ratio of the velocity of the solid/liquid interface to the mold velocity is identified as another dimensionless parameter in the analysis. In order to arrive at an analytical solution for the contact pressure along the shell/mold interface, we assume that this parameter is small. This makes the velocity ratio a convenient perturbation parameter for the analysis of thermomechanical distortion of the thin shell material as it grows from the melt. This necessarily limits the analysis to situations where the mold moves at faster rather than slower speeds. It is assumed that there is zero tangential shear stress between the fluid and the solidifying shell. As the molten liquid flows over the mold, it perfectly wets the surface. This precludes wetting effects due to surface tension. A hypoelastic constitutive law, which is a rate formulation of thermoelasticity, is assumed to govern deformation of the shell as it grows from the molten liquid. Latent heat liberated at the freezing front is extracted across a constant contact resistance at the shell/mold interface. Peculiar fluid motion at the tip is neglected. A solution for the contact pressure that is valid near the liquid surface (i.e., the meniscus) is derived from the main theoretical developments. Beyond the time of gap nucleation at the shell/mold interface, the model is no longer valid since it cannot account for gross distortion of the shell (i.e., distortions that greatly exceed the spatial perturbations considered in the model).     

GROWTH INSTABILITY DURING PLANAR SOLIDIFICATION WITH A MOLD OF FINITE THERMAL CAPACITY

The temperature and the stress fields in the solidified layer and in the mold of finite thickness for a unidirectional casting process are investigated. Earlier solutions are extended to include the effect of the thermal capacity of the mold on the freezing front growth instability. A numerical solution is obtained for both the heat conduction and the residual stress problem. The results show that the perturbation in contact pressure tends asymptotically to a maximum value at larger times for the lower values of the thermal capacities of the mold materials. The magnitude of the contact pressure perturbation is decreased by the inclusion of the thermal capacity of the mold material, and this effect is enhanced for less distortive and thicker molds. The present article assumes that the thermal and mechanical problems are uncoupled along the casting mold interface. Despite this limitation, the results presented in this article indicate that a mold with a higher thermal capacity (or lower thermal diffusivity) might be less susceptible to thermoelastic instabilities associated with the contact pressure and its dependence on the thermal contact resistance at the casting mold interface.     

Perturbation solution for solidification of pure metals on a sinusoidal mold surface

A linear perturbation method is used to solve two-dimensional heat conduction problem in which a liquid, becomes solidified by heat transfer to a sinusoidal mold of finite thickness. The finite difference method is used to discretize the governing equations. The molten metal perfectly wets the mold surface prior to the beginning of solidification, and this leads to a corresponding undulation of the metal shell thickness. The influence of physical parameters such as the thermal capacities of shell and mold materials, and mold surface wavelength on the growth of solidified shell thickness is investigated. Analytical results are obtained for the limiting case in which diffusivities of the solidified shell and the mold materials are infinitely large, and compared with the numerical predictions to establish the validity of the model and the numerical approach.     

Spatial variation of heat flux at the metal–mold interface due to mold filling effects in gravity die-casting

Most of the research work pertaining to metal–mold heat transfer in casting solidification either assumes no spatial variation in the air gap formation or limits the study to only those experimental systems in which air gap formation is uniform. However, in gravity die-casting, filling effects induce variation in thermal field in the mold and casting regions. In this paper, we show that this thermal field variation greatly influences the time of air gap initiation along a vertical mold wall, which subsequently leads to the spatial variation of air gap and in turn, the heat flux at the metal–mold interface.In order to study the spatial variation of heat flux at the metal–mold interface, an experimental setup that involved mold filling was devised. A Serial-IHCP (inverse heat conduction problem) algorithm was used to estimate the multiple heat flux transients along the metal–mold interface. The analysis indicates that the fluxes at different mold segments (bottom, middle, and top) of the metal–mold interface reaches the peak value at different time steps, which shows that the initiation of air gap differs along the mold wall. The experimental and numerical results show that the heat transfer in the mold is two-dimensional during the entire period of phase change, which is initially caused by the filling effects and further enhanced by the spatial variation of the air gap at the metal–mold interface.     

Bubble generation in micro-volumes of “nanofluids”

We report experimental investigation of a transparent flat mini evaporator heated by laser beam. The influence of non-absorbing and absorbing nanoparticles immersed in pure water, and heat absorbing fluid on the heat transfer intensification was analyzed. Nanoparticles may initiate vaporization and boiling of fluid at low heat input. Providing specific task and conditions the nanoparticles may be used in passive or active modes. Passive mode assumes that nanoparticles do not generate thermal energy and improve bubble nucleation conditions due to additional nucleation of the fluid, thus decreasing boiling/vaporization temperature thresholds. Active mode assumes that nanoparticles act as converters of optical energy into thermal one.     

Fluid flow and heat transfer behavior of liquid steel in slab mold with different corner structures. Part 1: Mathematical model and verification

A three-dimensional model considering the fluid and temperature field of the liquid steel and cooling water, along with the copper plate temperature was established to study the fluid flow and heat transfer behavior of liquid steel in slab mold with different corner structures. Then, a two-dimensional stress–strain model was established to calculate the strand shrinkage. The two-dimensional stress and three-dimensional temperature were connected through the thermal resistance. The model was validated by the measured solidification shell, copper plate temperature, and cooling water temperature rise. Results show that this model is suitable to study the complex transmission behavior in slab mold.     

Modeling and simulation of heat transfer phenomena during investment casting

Determining the heat transfer phenomena during casting processes is an important parameter for measuring the overall performance of process. It gives information about the properties of the metal being casted and its possible behavior in the mold during casting process. Improper determination of heat transfer phenomena and use of improper molding materials and casting conditions leads to defects such as misruns, cold shuts, shrinkage, pin holes, air holes and porosity in final product. A mathematical model was developed using standard transport equations incorporating all heat transfer coefficients to calculate the time for solidification of metal in casting and computer simulation of the model was carried out in C++ to validate the model. The metal used was pure iron casted in investment molds of silica sand with zircon coating. It was shown that airflow near the mold surfaces was partially restricted due to geometry of the molds and arrangement of the pieces around a tree. So, the changes in heat transfer coefficient also contribute towards time of solidification. The time calculated was found to be in good agreement with experimental values.     

THERMOMECHANICAL BEHAVIOR OF THE SOLIDIFYING SHELL WITHIN CONTINUOUS-CASTING BILLET MOLDS-A NUMERICAL APPROACH

A two-dimensional numerical model is given for the analysis of the coupled thermal and mechanical behavior of the solidifying shell within the mold during continuous casting of steel. The influence of different mold wall profiles on gap formation and heat flow during casting of billets is investigated. The calculated temperatures, stresses, and strains in the shell are used to estimate the risk for formation of longitudinal cracks. The effect of an initiated and growing macroscopic subsurface crack on the shell behavior is studied. The genesis of surface cracks is discussed. The calculated results are shown to be in reasonable agreement with experimental observations reported in the literature.     

Thermomagnetoelastic Stability of Ferromagnetic Cylindrical Shell Carrying Constant Electric Current

The modeling and study of the instability behavior of a magnetically active ferromagnetic cylindrical shell exposed to thermal and magnetic fields with a constant electric current is considered in this paper. It is assumed that the internal surface area of the shell is covered by the thin conductive cylindrical strip. The thickness of this metallic strip is small as compared to the total thickness of the shell and therefore its contribution to the elastic properties of the overall cylindrical shell can be considered negligible. The thermal and magnetic fields of the undisturbed state of the shell are determined assuming that the edges of the shell are thermo-isolated. Undisturbed state coincides with the equilibrium which was generated under the action of thermal field (in equilibrium the forces of magnetic origin are equal to zero). It is also assumed that the thermal exchanges shell-to-strip and shell-to-external media follow Newton-Rickman's law. Using the theory of thermo-magneto-elasticity of undisturbed state in conjunction with the predetermined thermal and magnetic fields the stresses of the undisturbed state are determined under the assumption that the deflection along the generators of the shell equals to zero. The solutions of the homogeneous boundary value problems are carried out and the buckling analysis of the shell is investigated. In particular, a close-form solution for the critical value of electric current for which the shell becomes statically unstable is presented.     

结晶器用铜板强化技术的研究进展

铜及铜合金具有优良的导电导热性能,其在钢铁冶炼过程中的连铸结晶器上起着举足轻重的关键作用.然而结晶器所在的恶劣服役条件却限制了其性能的发挥,较常见的损耗形式为结晶器铜板内表面弯月面处的热裂纹及结晶器铜板下部的摩擦磨损,这些损耗形式在一定程度上大大缩短了结晶器的使用寿命,针对此现象综述了国内外不同表面改性强化技术在结晶器铜板上的应用,通过不同表面改性强化处理,可提高结晶器铜板耐磨性、耐热冲击及耐腐蚀性能,从而提高铸坯质量、延长结晶器使用寿命及降低生产成本的目的.     

3-D numerical and experimental models for flat and embedded heat pipes applied in high-end VGA card cooling system

The present study utilizes the three-dimension numerical and experimental methods to investigate the optimum thermal performance of a flat heat pipe-thermal module application in high-end VGA card cooling system, and compares that with a traditional copper metal based plate embedded three 6 mm diameter heat pipe-thermal module under three dissimilar inclination angles of 0°, 90° and 180°. The optimization for the thermal modules researches into various fin material, thickness and gap. Results show that the flat heat pipe-thermal module has the best thermal performance at high power GPU of 180 W and inclination angle of 180°. Simulation results show in good agreement with experimental results within 5%. Therefore, the thermal performance of a flat heat pipe-thermal module can be accurately simulated and analyzed by employed the manner introduced in this paper and is able to cope with the higher heat flux GPU over 62.5 W/cm² in the future.     

Thermal gap conductance at low contact pressures (<1 MPa): Effect of gold plating and plating thickness

Thermal contact conductance (TCC) measurements are made on bare and gold plated (?0.5 μm) oxygen free high conductivity (OFHC) Cu and brass contacts in vacuum, nitrogen, and argon environments. It is observed that the TCC in gaseous environment is significantly higher than that in vacuum due to the enhanced thermal gap conductance. It is found that for a given contact load and gas pressure, the thermal gap conductance for bare OFHC Cu contacts is higher than that for gold plated contacts. It is due to the difference in the molecular weights of copper and gold, which influences the exchange of kinetic energy between the gas molecules and contact surfaces. Furthermore, the gap conductance is found to increase with increasing thickness of gold plating. Topography measurements and scanning electron microscopy (SEM) analysis of contact surfaces revealed that surfaces become smoother with increasing gold plating thickness, thus resulting in smaller gaps and consequently higher gap conductance.     

The effects of TiO2 pigmented coatings characteristics on temperature and brightness of a coated black substrate

The high visible reflectivity of the cool coatings made by typical white pigment particles produces high glare, which is unpleasant to the human eye and possibly distorts the view of coated objects. A new approach to optimizing pigmented coatings considering both thermal and esthetic effects was proposed in previous works. For an accurate thermal analysis, a full spectral evaluation of radiative properties of pigmented coatings from UV to far IR wavelengths is required. We made a full spectral analysis of TiO₂ pigment particles in polyethylene resin as the host medium in the wavelength range of 0.3–36 μm. To find the spectral transmittance and reflectance of the pigmented layer, we conducted a radiation analysis using the radiation element method by ray emission model (REM²). The effects of characteristics of the coating layer, including size and volume concentration of pigment particles and coating thickness on esthetic and thermal behaviors were studied. The results show that by using the proposed optimum particle size, i.e., 0.8 μm, it is possible to design a coating with reasonable temperature and moderate brightness.     

Fluid flow and heat transfer behavior of liquid steel in slab mold with different corner structures. Part 2: Fluid flow,heat transfer,and solidification characteristics

In this article, the complex transmission behavior was discussed in the slab mold with different corner structures. Results show that the up backflow is stronger than the down backflow. The cooling water temperature rise and heat flux through the wide face in the right-angle mold are the largest, while those through the narrow face in the multichamfered mold are larger than those in the big-chamfered mold. The corner temperature at mold exit of the right-angle, big-chamfered, and multichamfered strand increases. The shell thickness at the narrow face center in the chamfered mold is thinner than that in the right-angle mold.     

Influence of cooling medium characteristics on embedded tube fusion condition in the process of embedded tube sand mold casting

Embedded copper tube sand mold casting is the main manufacturing method of iron‐making blast furnace copper cooling stave, comparing embedded copper tube outer wall temperature with copper melting point is used to judge the fusion between liquid copper and embedded copper tube. On the basis that the computational model is reliable though experimental proof, the paper studies the influence of cooling medium characteristics on the embedded copper tube outer wall temperature. The calculated results show that the cooling medium thermal physical properties play a vital role on heat transfer between the liquid and embedded copper tube in the process of casting and determine the embedded copper tube outer wall temperature and the fusion. Through the numerical research, the cooling medium with suitable physical properties is found, adjusting the cooling media Reynolds number is an effective way to regulate the embedded tube outer wall temperature to the temperature required for fusion; in addition, modifying the cooling medium temperature entering the embedded tube is also a means adjusting the embedded tube outer wall temperature and improving the fusion between the embedded tube and liquid copper, but the method is not easy to operate in practice.     

Thermal interaction effect on nucleation site distribution in subcooled boiling

An experimental work on subcooled boiling of refrigerant, R134a, to examine nucleation site distributions on both copper and stainless steel heating surfaces was performed. In order to obtain high fidelity active nucleation site density and distribution data, a high-speed digital camera was utilized to record bubble emission images from a view normal to heating surfaces. Statistical analyses on nucleation site data were done and their statistical distributions were obtained. Those experimentally observed nucleation site distributions were compared to the random spatial Poisson distribution. The comparisons showed that, rather than purely random, active nucleation site distributions on boiling surfaces are relatively more uniform. Experimental results also showed that on the copper heating surface, nucleation site distributions are slightly more uniform than on the stainless steel surface. This was concluded as the results of thermal interactions between nucleation sites with different solid thermal conductivities. A two dimensional thermal interaction model was then developed to quantitatively examine the thermal interactions between nucleation sites. The results give a reasonable explanation to the experimental observation on nucleation site distributions.     

泡沫铜内石蜡凝固的孔隙尺度实验研究

对泡沫铜内石蜡凝固相变进行孔隙尺度实验研究。采用高分辨率相机与红外热像仪对凝固过程相场与温度场进行可视化,并通过热电偶测量石蜡与泡沫铜骨架局部温度以获得相变过程热响应及热非平衡特性。揭示了泡沫铜孔隙内凝固相变中包括固液相界面移动、液态石蜡流动及石蜡体积收缩等多个物理过程。研究表明:在多物理过程交互影响下,泡沫铜可高效扩展凝固相界面、提升样品热响应速率,采用孔隙率为0.974的泡沫铜可将石蜡凝固相变速率提升至2.8倍;泡沫铜能有效避免石蜡凝固过程由体积收缩引起的裂缝问题,消除由其引起的热阻;石蜡与泡沫铜骨架间存在局部热非平衡性,且在相变阶段尤为明显。     

Thermal buckling analysis of FGM sandwich truncated conical shells reinforced by FGM stiffeners resting on elastic foundations using FSDT

This work presents an analytical approach to investigate the mechanical and thermal buckling of functionally graded materials sandwich truncated conical shells resting on Pasternak elastic foundations, subjected to thermal load and axial compressive load. Shells are reinforced by closely spaced stringers and rings, in which the material properties of shells and stiffeners are graded in the thickness direction following a general sigmoid law distribution and a general power law distribution. Four models of coated shell-stiffener arrangements are investigated. The change of spacing between stringers in the meridional direction also is taken into account. Two cases on uniform temperature rise and linear temperature distribution through the thickness of shell are considered. Using the first-order shear deformation theory, Lekhnitskii smeared stiffener technique and the adjacent equilibrium criterion, the linearization stability equations have been established. Approximate solution satisfies simply supported boundary conditions and Galerkin method is applied to obtain closed-form expression for determining the critical compression buckling load and thermal buckling load in cases uniform temperature rise and linear temperature distribution across the shell thickness. The effects of temperature, foundation, core layer, coating layer, stiffeners, material properties, dimensional parameters and semi-vertex angle on buckling behaviors of shell are shown.     

精铸工艺对重型燃机叶片质量的影响研究

采用数值模拟的方法,研究精铸工艺参数对某重型燃机叶片铸件质量的影响规律,优化工艺参数,指导生产实际。研究结果表明：在文章研究范围内,随着浇注温度的升高,叶根缺陷大幅度减少,叶身缺陷变化不大;随着模壳温度的升高,叶身的缺陷大幅度增多,叶根缺陷略有下降,叶顶缺陷变化不明显;随着模壳厚度的增加,叶根和叶身的缺陷急剧减少,叶顶的缺陷变化不明显。