scholarly journals 3D Numerical Analysis of the Asymmetric Three-Phase Line of Floating Zone for Silicon Crystal Growth

Crystals ◽  
2020 ◽  
Vol 10 (2) ◽  
pp. 121 ◽  
Author(s):  
Xue-Feng Han ◽  
Xin Liu ◽  
Satoshi Nakano ◽  
Hirofumi Harada ◽  
Yoshiji Miyamura ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Silicon Crystal ◽  
Three Dimensional ◽  
Heat Transfer Fluid ◽  
Floating Zone ◽  
Phase Line ◽  
Three Phase ◽  
Em Field ◽  
Solid Liquid Interface ◽  
Solid Liquid

A numerical simulation has been carried out to study the asymmetric heat transfer, fluid flow, and three-phase line to explain the phenomenon of the spillage of the melt in floating zone (FZ) silicon growth. A three-dimensional high-frequency electromagnetic (EM) field is coupled with the heat transfer in the melt and crystal calculation domains. The current density along the three-phase line is investigated to demonstrate the inhomogeneous heating along the three-phase line. The asymmetric heating is found to affect the flow pattern and temperature distribution of the melt. The three-dimensional solid–liquid interface results show that, below the current supplies, the interface is deflected due to strong heating below the current supplies. The calculated asymmetric three-phase line shows a similar trend as the experimentally observed results. The results indicate that the re-melting and spillage phenomenon could occur below the current supplies.

Dependence of the Contact Angle on Adsorption at the Solid-Liquid Interface

2010 ◽  
Author(s):  
C. A. Ward
Keyword(s):  
Surface Tension ◽  
Contact Angle ◽  
Pressure Range ◽  
Line Tension ◽  
Liquid Interface ◽  
Fluid Interfaces ◽  
Phase Line ◽  
Three Phase ◽  
Solid Liquid Interface ◽  
Solid Liquid

A method for determining the surface tension of solid-fluid interfaces has been proposed. For a given temperature and fluid-solid combination, these surface tensions are expressed in terms of material properties that can be determined by measuring the amount of vapor adsorbed on the solid surface as a function of xV, the ratio of the vapor-phase pressure to the saturation-vapor pressure. The thermodynamic concept of pressure is shown to be in conflict with that of continuum mechanics, but is supported experimentally. This approach leads to the prediction that the contact angle, θ, can only exist in a narrow pressure range and that in this pressure range, the solid-vapor surface tension is constant and equal to the surface tension of the liquid-vapor interface, γLV. The surface tension of the solid-liquid interface, γSL, may be expressed in terms of measurable properties, γLV and θ: γSL = γLV(1 − cosθ). The value of θ is predicted to depend on both the pressure in the liquid at the three-phase, line x3L, and the three-phase line curvature, Ccl. We examine these predictions using sessile water droplets on a polished Cu surface, maintained in a closed, constant volume, isothermal container. The value of θ is found to depend on the adsorption at the solid-liquid interface, nSL = nSL(x3L,Ccl). The predicted value of θ is compared with that measured, and found to be in close agreement, but no effect of line tension is found.

Two-Dimensional Transient Heat Transfer Model for High-Temperature Laser-Scanning Confocal Microscopy

2021 ◽  
Author(s):  
Dasith Liyanage ◽  
Suk-Chun Moon ◽  
Ajith S. Jayasekare ◽  
Abheek Basu ◽  
Madeleine Du Toit ◽  
...  
Keyword(s):  
Heat Transfer ◽  
Phase Transformation ◽  
High Temperature ◽  
Laser Scanning ◽  
Laser Scanning Confocal Microscopy ◽  
Transfer Model ◽  
Two Dimensional ◽  
Scanning Confocal Microscopy ◽  
Solid Liquid Interface ◽  
Solid Liquid

Abstract High-temperature laser-scanning confocal microscopy (HT-LSCM) has proven to be an excellent experimental technique through in-situ observations of high temperature phase transformation to study kinetics and morphology using thin disk steel specimens. A 1.0 kW halogen lamp, within the elliptical cavity of the HT-LSCM furnace radiates heat and imposes a non-linear temperature profile across the radius of the steel sample. This local temperature profile when exposed at the solid/liquid interface determines the kinetics of solidification and phase transformation morphology. A two-dimensional numerical heat transfer model for both isothermal and transient conditions is developed for a concentrically solidifying sample. The model can accommodate solid/liquid interface velocity as an input parameter under concentric solidification with cooling rates up to 100 K/min. The model is validated against a commercial finite element analysis software package, Strand7, and optimized with experimental data obtained under near-to equilibrium conditions. The validated model can then be used to define the temperature landscape under transient heat transfer conditions.

Molecular Dynamics Simulations of Interfacial Heat and Mass Transfer at Nanostructured Surface

2007 ◽  
Author(s):  
Gyoko Nagayama ◽  
Masako Kawagoe ◽  
Takaharu Tsuruta
Keyword(s):  
Heat Transfer ◽  
Molecular Dynamics ◽  
Boundary Condition ◽  
Thermal Resistance ◽  
Hydrodynamic Resistance ◽  
Hydrophilic Surface ◽  
Dynamics Simulations ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
The Continuum

The nanoscale heat and mass transport phenomena play important roles on the applications of nanotechnologies with great attention to its differences from the continuum mechanics. In this paper, the breakdown of the continuum assumption for nanoscale flows has been verified based on the molecular dynamics simulations and the heat transfer mechanism at the nanostructured solid-liquid interface in the nanochannels is studied from the microscopic point of view. Simple Lennard-Jones (LJ) fluids are simulated for thermal energy transfer in a nanochannel using nonequilibrium molecular dynamics techniques. Multi-layers of platinum atoms are utilized to simulate the solid walls with arranged nanostructures and argon atoms are employed as the LJ fluid. The results show that the interface structure (i.e. the solid-like structure formed by the adsorption layers of liquid molecules) between solid and liquid are affected by the nanostructures. It is found that the hydrodynamic resistance and thermal resistance dependents on the surface wettability and for the nanoscale heat and fluid flows, the interface resistance cannot be neglected but can be reduced by the nanostructures. For the hydrodynamic boundary condition at the solid-liquid interface, the no-slip boundary condition holds good at the super-hydrophilic surface with large hydrodynamic resistance. However, apparent slip is observed at the low hydrodynamic resistance surface when the driving force overcomes the interfacial resistance. For the thermal boundary condition, it is found that the thermal resistance at the interface depends on the interface wettability and the hydrophilic surface has lower thermal resistance than that of the hydrophobic surfaces. The interface thermal resistance decreases at the nanostructed surface and significant heat transfer enhancement has been achieved at the hydrophilic nanostructured surfaces. Although the surface with nanostrutures has larger surface area than the flat surface, the rate of heat flux increase caused by the nanostructures is remarkable.

Numerical Modeling of Microporosity Formation in Aluminum-Rich Aluminum-Copper Alloys in Microgravity Conditions

2000 ◽  
Author(s):  
M. Xiong ◽  
A. V. Kuznetsov
Keyword(s):  
Copper Alloys ◽  
Heat Transfer Fluid ◽  
Gas Phases ◽  
Alloy Casting ◽  
Cu Alloy ◽  
Aluminum Copper Alloys ◽  
Three Phase ◽  
Microgravity Conditions ◽  
Parametric Analyses ◽  
Solid Liquid

Abstract The microporosity formation in a vertical unidirectionally solidifying Al-4.1%Cu alloy casting is modeled in both microgravity and standard gravity as well as in the conditions of decreased (Moon, Mars) and increased (Jupiter) gravity. Due to the unique opportunities offered by a low-gravity environment (absence of metallostatic pressure and of natural convection in the solidifying alloy) future microgravity experiments will significantly contribute to attaining a better physical understanding of the mechanisms of microporosity formation. One of the aims of the present theoretical investigation is to predict what microporosity patterns will look like in microgravity in order to help plan a future microgravity experiment. To perform these simulations, the authors suggest a novel three-phase model of solidification that accounts for the solid, liquid, and gas phases in the mushy zone. This model accounts for heat transfer, fluid flow, macrosegregation, and microporosity formation in the solidifying alloy. Special attention is given to the investigation of the influence of microporosity formation on the inverse segregation. Parametric analyses for different initial hydrogen concentrations and different gravity conditions are carried out.

scholarly journals The numerical simulation of enhanced heat transfer on a Linear Fresnel molten salt-type receiver tube filled with porous media

2019 ◽  
Vol 118 ◽  
pp. 01041
Author(s):  
Chenggang Yang ◽  
Yuning Zhang ◽  
Fenghe Yan ◽  
Wenguang Zhang ◽  
Wei Li
Keyword(s):  
Heat Transfer ◽  
Thermal Conductivity ◽  
Numerical Simulation ◽  
Porous Media ◽  
Molten Salt ◽  
Temperature Difference ◽  
Wall Temperature ◽  
Three Dimensional ◽  
Heat Transfer Fluid ◽  
Filling Rate

In this paper, three-dimensional numerical simulation was taken on a Linear Fresnel solar receiver tube using molten salt as heat transfer fluid (HTF), in which the porous media was filled to enhance the heat transfer efficiency. The simulation was to analyze the influence of the different conditions (filling rate, porosity and thermal conductivity) on heat transfer effect and wall temperature difference. The results revealed that the Nu (Nusselt number) increased firstly and then decreased with the increasing filling rate in both center filling and annular filling types. The optimal thermal performance were obtained when filling rate were 0.8 and 0.2 in center filling and annular filling, respectively. The Nu were about 1.7 and 1.5 times as the clear receiver. The circumferential temperature difference decreased firstly and then increased with filling rate increasing in both center filling and annular filling types. The lowest circumferential temperature differences were achieved at the filling rate 0.8 and 0.4 in center filling and annular filling types, and temperature difference decreased 15.88°C and 22°C compared with clear receiver, respectively. The Nu and PEC both decreased with porosity increasing. However, the thermal conductivity of porous media had little influence to the Nu and circumferential wall temperature.

Experimental and Numerical Analysis of Droplet Cooling

2010 ◽  
Author(s):  
Paolo Tartarini ◽  
Mauro A. Corticelli ◽  
Paolo E. Santangelo
Keyword(s):  
Three Dimensional ◽  
Numerical Approach ◽  
Solid Substrate ◽  
Liquid Interface ◽  
Temperature Trend ◽  
Numerical Code ◽  
Uniform Mesh ◽  
Thermal Transient ◽  
Solid Liquid Interface ◽  
Solid Liquid

Dropwise cooling represents a major subject of interest for both academic and industrial researches. The present work is focused on investigating the thermal transient occurring as two water droplets are gently released (We < 30) onto a heated solid surface. This latter has been kept at initial temperature lower than 373.15 K to analyze the single-phase-evaporation regime. To the purpose, both an experimental and a numerical approach have conveniently been employed. Infrared thermography has been used to evaluate the temperature trend at the solid-liquid interface: an experimental facility has been built to carry out measurements from below, thus realizing a fully non-intrusive approach. A transparent-crystal disk has been inserted to serve as the solid substrate; its upper surface has been painted by a black coating, thus providing a black-body surface as the solid-liquid interface. The infrared thermocamera has been placed below and perpendicular to that surface; temperature has been thereby measured, being emissivity a known parameter. A numerical code has been developed to predict the involved physical phenomena: temperature trend, evaporation time and evaporated flux result from discretizing the three-dimensional energy-diffusion equation by the finite-volume method. Moreover, the model is based on structured non-uniform mesh to adapt to the occurring temperature gradients. Very good agreement is shown between experimental and numerical outcomes in terms of thermal transient and recovery.

Analysis of Melting in a Mixed Metal Powder Bed With Finite Thickness Subjected to Constant Heat Flux Heating

2003 ◽  
Author(s):  
Tiebing Chen ◽  
Yuwen Zhang
Keyword(s):  
Selective Laser Sintering ◽  
Finite Thickness ◽  
Three Dimensional ◽  
Constant Heat Flux ◽  
Metal Powders ◽  
Powder Bed ◽  
Solid Foundation ◽  
Solid Liquid Interface ◽  
Solid Liquid ◽  
Liquid And Solid Phases

Melting of a subcooled powder bed with the finite thickness that contains a mixture of two metal powders with significantly different melting points is investigated analytically. Shrinkage induced by melting is taken into account in the physical model. The temperature distributions in the liquid and solid phases were obtained using an exact solution and an integral approximate solution, respectively. The effects of porosity, Stefan number, and subcooling on the surface temperature and solid-liquid interface are also investigated. The present work built solid foundation to investigate the complex three-dimensional selective laser sintering (SLS) process.

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