Heat Transfer During Solidification Around a Horizontal Tube With Internal Convective Cooling

The solidification process of tin, inside a closed cavity, is numerically investigated by the finite volume method. A non-orthogonal system of coordinates is employed to adapt to the irregular geometry, with a moving mesh to account for the changing domain size. The momentum equations are solved for the contravariant velocity components. The SIMPLEC algorithm handles the coupling between velocity and pressure. A special treatment is given at the liquid-solid interface to obtain the momentum and energy balance. The phase change process is strongly influenced by natural convection in the melt. At the beginning of the process, the cavity is full of liquid, and the natural convection slightly influences the interface shape. But as the liquid region diminishes during the process, the influence of natural convection increases. Further, at the same time as the liquid size region is reduced, the intensity of the flow increases, and the flow can became turbulent, affecting the heat flux at the interface and consequently the size of the solid region. Therefore, the purpose of the paper is to analyze the influence of the turbulent regime on the kinetics of the solidification process. The turbulent flow is taken into account by a low Reynolds number model. The influence of the Rayleigh number on the velocity and temperature field is investigated.

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Permeability in the Mushy Zone

Materials Science Forum ◽

10.4028/www.scientific.net/msf.649.399 ◽

2010 ◽

Vol 649 ◽

pp. 399-408 ◽

Cited By ~ 4

Author(s):

R.G. Erdmann ◽

D.R. Poirier ◽

A.G. Hendrick

Keyword(s):

Mushy Zone ◽

Volume Fraction ◽

Primary Dendrite ◽

Fluid Velocity ◽

Interdendritic Liquid ◽

Creeping Flow ◽

Liquid Region ◽

Local Volume ◽

Local Volume Fraction ◽

Deterministic Function

When modeled at macroscopic length scales, the complex dendritic network in the solid-plus-liquid region of a solidifying alloy (the “mushy zone”) has been modeled as a continuum based on the theory of porous media. The most important property of a porous medium is its permeability, which relates the macroscopic pressure gradient to the throughput of ﬂuid ﬂow. Knowledge of the permeability of the mushy zone as a function of the local volume-fraction of liquid and other morphological parameters is thus essential to successfully modeling the ﬂow of interdendritic liquid during alloy solidiﬁcation. In current continuum models, the permeability of the mushy zone is given as a deterministic function of (1) the local volume fraction of liquid and (2) a characteristic length scale such as the primary dendrite arm spacing or the reciprocal of the speciﬁc surface area of the solid-liquid interface. Here we ﬁrst provide a broad overview of the experimental data, mesoscale numerical ﬂow simulations, and resulting correlations for the deterministic permeability of both equiaxed and columnar mushy zones. A extended view of permeability in mushy zones which includes the stochastic nature of permeability is discussed. This viewpoint is the result of performing extensive numerical simulations of creeping ﬂow through random microstructures. The permeabilities obtained from these simulations are random functions with spatial autocorrelation structures, and variations in the local permeability are shown to have dramatic eﬀects on the ﬂow patterns observed in such microstructures. Speciﬁcally, it is found that “lightning-like” patterns emerge in the ﬂuid velocity and that the ﬂows in such geometries are strongly sensitive to small variations in the solid structure. We conclude with a comparison of deterministic and stochastic permeabilities which suggests the importance of incorporating stochastic descriptions of the permeability of the mushy zone in solidiﬁcation modeling.

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Figure of Merit-Based Optimization Approach of Phase Change Material-based Composites for Portable Electronics Using Simplified Model

Journal of Electronic Packaging ◽

10.1115/1.4052074 ◽

2021 ◽

Author(s):

Ayushman Singh ◽

Srikanth Rangarajan ◽

Leila Choobineh ◽

Bahgat Sammakia

Keyword(s):

Heat Transfer ◽

Thermal Conductivity ◽

Phase Change ◽

Effective Thermal Conductivity ◽

Phase Change Material ◽

Figure Of Merit ◽

Volume Fraction ◽

Simplified Model ◽

Transient Temperature ◽

Change Material

Abstract This work presents an approach to optimally designing a composite with thermal conductivity enhancers (TCEs) infiltrated with phase change material (PCM) based on figure of merit (FOM) for thermal management of portable electronic devices. The FOM defines the balance between effective thermal conductivity and energy storage capacity. In present study, TCEs are in the form of a honeycomb structure. TCEs are often used in conjunction with PCM to enhance the conductivity of the composite medium. Under constrained composite volume, the higher volume fraction of TCEs improves the effective thermal conductivity of the composite, while it reduces the amount of latent heat storage simultaneously. The present work arrives at the optimal design of composite for electronic cooling by maximizing the FOM to resolve the stated trade-off. In this study, the total volume of the composite and the interfacial heat transfer area between the PCM and TCE are constrained for all design points. A benchmarked two-dimensional direct CFD model was employed to investigate the thermal performance of the PCM and TCE composite. Furthermore, assuming conduction-dominated heat transfer in the composite, a simplified effective numerical model that solves the single energy equation with the effective properties of the PCM and TCE has been developed. The effective thermal conductivity of the composite is obtained by minimizing the error between the transient temperature gradient of direct and simplified model by iteratively varying the effective thermal conductivity. The FOM is maximized to find the optimal volume fraction for the present design.

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Solidification Process and Volume Fraction in Sn-Ag-Cu Alloy

Journal of The Japan Institute of Electronics Packaging ◽

10.5104/jiep.13.521 ◽

2010 ◽

Vol 13 (7) ◽

pp. 521-530 ◽

Cited By ~ 6

Author(s):

Yoshiko Takamatsu ◽

Hisao Esaka ◽

Kei Shinozuka

Keyword(s):

Volume Fraction ◽

Solidification Process ◽

Cu Alloy

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A Volume-of-Fluid Based Numerical Simulation of Solidification in Binary Alloys on Fixed Non-Uniform Co-Located Grids

ASME 2009 International Manufacturing Science and Engineering Conference, Volume 1 ◽

10.1115/msec2009-84239 ◽

2009 ◽

Author(s):

Mehdi Farrokhnejad ◽

Anthony G. Straatman ◽

Jeffrey T. Wood

Keyword(s):

Volume Fraction ◽

Binary Alloys ◽

Solidification Process ◽

Casting Process ◽

Reconstruction Algorithm ◽

Volume Of Fluid ◽

Mold Filling ◽

Mg Alloys ◽

Uniform Grid ◽

Spurious Currents

In this paper, the authors present a platform for the modeling of mold filling and solidification of binary alloys with properties similar to Mg alloys. A volume-of-fluid (VOF) based method is used to capture the interface between solid and liquid in binary alloys solidification process on a fixed non-uniform grid, developed for implementation in a colocated finite volume framework. Contrary to other works, to update the volume fraction (of fluid) in the field, a link between source-based type of energy equation and VOF reconstruction algorithm is described and implemented. A new approximation to the pressure gradient is presented to remove all ‘Spurious Currents’ [1] resulting from pressure jumps in the vicinity of the interface. Based upon the work presented, it is concluded that the present combination of the equations are not only computationally straightforward to implement and upgrade to a 3D problem, but also provides an excellent platform to capture the interface between constituents in a die-casting process including solidification and mold filling process. The current framework will be used in future works to characterize the local mechanical properties of Mg alloys by using information from simulation at the dendritic level.

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Microstructure and Fabrication of Cu-Pb-Sn/Q235 Laminated Composite by Semi-Solid Rolling

Metals ◽

10.3390/met8090722 ◽

2018 ◽

Vol 8 (9) ◽

pp. 722 ◽

Cited By ~ 1

Author(s):

Yubo Zhang ◽

Jiaming Liu ◽

Ying Fu ◽

Jinchuan Jie ◽

Yiping Lu ◽

...

Keyword(s):

Laminated Composite ◽

Solidification Process ◽

Extrusion Process ◽

Interfacial Structure ◽

Elemental Distribution ◽

Casting Defects ◽

Pouring Temperature ◽

Element Simulation ◽

Solid Region ◽

Semi Solid

In the present work, Cu-Pb-Sn and Q235 laminated composite were fabricated by a horizontal semisolid rolling procedure. The interfacial structure, elemental distribution, and properties of the composite were investigated. Finite-element simulation was conducted to analyze the temperature field and solidification process during the semisolid rolling. An appropriate semi-solid region was observed at a pouring temperature of 1598 K in the simulation, which would effectively kept fluidity and avoided casting defects. The experimental results showed that good interface between Cu-Pb-Sn alloy and Q235 steel was achieved by the proposed process at 1598 K, without casting defects or excessive deformation. The Cu and Fe alloys were bonded mainly by the diffusion of Fe into Cu matrix, and a handful of microscopic Pb-rich layer. Fine Pb-rich precipitates were uniformly distributed in the Cu-Pb-Sn alloy, and were considered to be advantageous to the self-lubrication property. The average tensile-shear strength of the interface was higher than 57.68 MPa at a pouring temperature of 1598 K, which fulfilled the requirements for a further extrusion process.

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Course of Solidification Process of AlMMC – Comparison of Computer Simulations and Experimental Casting

Solid State Phenomena ◽

10.4028/www.scientific.net/ssp.191.89 ◽

2012 ◽

Vol 191 ◽

pp. 89-98

Author(s):

Roman Zagórski ◽

Anna J. Dolata ◽

Maciej Dyzia

Keyword(s):

Experimental Data ◽

Temperature Distribution ◽

Volume Fraction ◽

Aluminum Matrix ◽

Solidification Process ◽

Sand Mold ◽

Phase System ◽

Discrete Phase Model ◽

Composite Matrix ◽

Solidification Temperature

The aim of the paper is to present the possibilities of computational simulations for the casting of aluminum matrix composite (AlMMC) reinforced with ceramics based on experimental data. The comparison of simulation and experimental results concerned the solidification process i.e. the course of solidification, temperature distribution and final arrangement of reinforcement particles. First, we have performed the experimental gravity casting of the aluminum matrix alloy AK12 (AlSi12CuNiMg2) and the composites AK12/SiC and AK12/Cg reinforced with silicon carbide SiC and glass carbon Cg, respectively, into the sand mold. During the experiment we have recorded the temperature using the ThermaCAM photometer system as well as in the selected point inside the sand mold. Using experimental data we have carried out the numerical calculations according to the methods and procedures contained in the program ANSYS Fluent 13. We have based the simulations on the two-dimensional model in which the Volume of Fluid (VOF) and enthalpy methods have been applied. The former is to describe two-phase system (air-composite matrix free surface, volume fraction of particular continuous phase) and the latter shows modeling of the solidification process of the alloy and composite matrix. We have used the Discrete Phase Model (DPM) to depict the presence of reinforcement particles. The assumption of the appropriate values of simulation parameters has shown that the simulation results are convergent with experimental ones. We have observed a similar course of the composite solidification (temperature change at the designated point), the temperature distribution and the arrangement of reinforcement particles for the simulation and experiment.

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Structural Investigations of Solidification and Heat Treatments Influence on High Alloyed Cast Irons Grades with Nb-V-Ti Additions

Defect and Diffusion Forum ◽

10.4028/www.scientific.net/ddf.289-292.77 ◽

2009 ◽

Vol 289-292 ◽

pp. 77-86 ◽

Cited By ~ 4

Author(s):

Jacqueline Lecomte-Beckers ◽

Jérôme Tchoufang Tchuindjang

Keyword(s):

Phase Transformations ◽

Volume Fraction ◽

Raw Materials ◽

Solidification Process ◽

Heat Treatments ◽

Hot Strip Mill ◽

Cast Irons ◽

Structural Investigations ◽

Alloyed Cast ◽

The Matrix

Two High Alloyed Cast Irons (HACI) were studied, both belonging to the Fe-C-Cr-Si-X system where X represented a strong carbide forming element. One of these alloys was obtained after adding Nb, V and Ti to the chemical composition of the other alloy. Raw materials originated from spun cast rolls for hot strip mill were submitted to different heat treatments routes, in order to study the influence of alloying elements on the microstructure. Both HACI grades contained a mixture of martensite and retained austenite matrix in the as-cast conditions and after quenching. Differential Thermal Analysis was carried out on the heat treated samples in order to determine the phase transformations occurring during re-melting and subsequent solidification sequence. Diffusionless transformations leading to various types of martensite were found in the matrix. Bulky NbC carbides precipitating at the beginning of the solidification process strongly influence the nature and the rate of the subsequent diffusional phase transformations, particularly for HACI grade with Nb, V and Ti additions. Quantitative metallography was done to determine graphite, NbC carbides, cementite and matrix volume fraction in HACI studied grades.

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Heat transfer across sheared suspensions: role of the shear-induced diffusion

Journal of Fluid Mechanics ◽

10.1017/jfm.2013.173 ◽

2013 ◽

Vol 724 ◽

pp. 527-552 ◽

Cited By ~ 28

Author(s):

Bloen Metzger ◽

Ouamar Rahli ◽

Xiaolong Yin

Keyword(s):

Thermal Diffusivity ◽

Volume Fraction ◽

Spherical Particles ◽

Transient Temperature ◽

Particle Diffusion ◽

Driving Mechanism ◽

Average Particle ◽

Particle Rotation ◽

Effective Thermal Diffusivity ◽

Couette Cell

AbstractSuspensions of non-Brownian spherical particles undergoing shear provide a unique system where mixing occurs spontaneously at low Reynolds numbers. Through a combination of experiments and simulations, we investigate the effect of shear-induced particle diffusion on the transfer of heat across suspensions. The influence of particle size, particle volume fraction and applied shear are examined. By applying a heat pulse to the inner copper wall of a Couette cell and analysing its transient temperature decay, the effective thermal diffusivity of the suspension, $\alpha $, is obtained. Using index matching and laser-induced fluorescence imaging, we measured individual particle trajectories and calculated their diffusion coefficients. Simulations that combined a lattice Boltzmann technique to solve for the flow and a passive Brownian tracer algorithm to solve for the transfer of heat are in very good agreement with experiments. Fluctuations induced by the presence of particles within the fluid cause a significant enhancement (${\gt }200\hspace{0.167em} \% $) of the suspension transport properties. The effective thermal diffusivity was found to be linear with respect to both the Péclet number ($\mathit{Pe}= \dot {\gamma } {d}^{2} / {\alpha }_{0} \leq 100$) and the solid volume fraction ($\phi \leq 40\hspace{0.167em} \% $), leading to a simple correlation $\alpha / {\alpha }_{0} = 1+ \beta \phi \mathit{Pe}$ where $\beta = 0. 046$ and ${\alpha }_{0} $ is the thermal diffusivity of the suspension at rest. In our Couette cell, the enhancement was found to be optimum for a volume fraction, $\phi \approx 40\hspace{0.167em} \% $, above which, due to steric effects, both the particle diffusion motion and of the effective thermal diffusion dramatically decrease. No such correlation was found between the average particle rotation and the thermal diffusivity of the suspension, suggesting that the driving mechanism for enhanced transport is the translational particle diffusivity. Movies are available with the online version of the paper.

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Phase Field Simulations of Dendritic Crystal Growth with Focus on the Computational Efficiency

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.1025-1026.745 ◽

2014 ◽

Vol 1025-1026 ◽

pp. 745-748 ◽

Cited By ~ 1

Author(s):

Alexandre Furtado Ferreira ◽

José Adilson de Castro

Keyword(s):

Crystal Growth ◽

Microstructural Evolution ◽

Computational Efficiency ◽

Numerical Technique ◽

Computation Time ◽

Solidification Process ◽

Liquid Region ◽

Computational Domain ◽

Grid Spacing ◽

Dendritic Crystal

In this study, we present a numerical technique for the improvement of computational efficiency for computation of microstructural evolution in alloy during solidification process. The goal of this technique is for the computational domain to grow around the microstructure and fixed the grid spacing, while solidification advances into the liquid region. The growth around the microstructure is controlled according with the solute diffusivity for binary alloy in the liquid region. The computation showed that the microstructure with well-developed secondary arms can be obtained with low computation time and moderate memory demand.

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