Dynamic simulation of the vertical zone-melting crystal growth

Lan, C.W.; Yang, Da

doi:10.1016/s0017-9310(98)00119-7

Cited by 21 publications

(17 citation statements)

References 21 publications

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“…Lan and Yang [7] extended their previous work to the study of bifurcating and oscillatory flows in a horizontal Bridgman furnace, from which a supercritical Hopf bifurcation was observed to appear at an intermediate Rayleigh number. Within the time periodic flow regime, they showed that the interface, which was shown to temporally oscillate, could lead to crystal striations.…”

Section: Introductionmentioning

confidence: 89%

Three-dimensional bifurcations in a cubic cavity due to buoyancy-driven natural convection

Sheu

Lin

2011

International Journal of Heat and Mass Transfer

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Section: Introductionmentioning

confidence: 89%

Three-dimensional bifurcations in a cubic cavity due to buoyancy-driven natural convection

Sheu

Lin

2011

International Journal of Heat and Mass Transfer

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“…Constants L and M are shown in equation (9), constant C need to be evaluated from boundary conditionequation (4). As follows from equations (7), (8) and (11), a final form of mathematical description of impurity distribution after second pass of zone refining can be written as Last four members on left side of equation 14cancel each other and remaining members on left and right side are equalmaterial balance equation 7is satisfied.…”

Section: Resultsmentioning

confidence: 99%

Mathematical Equation for Impurity Distribution After Second Pass of Zone Refining

Škrobian

Pernis

2021

Acta Metall Slovaca

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A mathematical equation has been derived that describes impurity distribution in ingot after second pass of zone refining. While an exponential impurity distribution is calculated by a simplified model after first pass, second pass is described by mixed linear - exponential model. Relationship of transformed impurity concentration is constant over whole length of semi-infinite ingot for first pass. However, it has linear trend for second pass. Last part of molten zone at infinity solidifies differently and can be described mathematically as directional crystallization. A mathematical tool devised for second pass of zone refining can be tried to be used for derivation of functions of more complex models that would describe impurity distribution in more realistic way compared to simplified approach. Such models could include non-constant distribution coefficient and/or shrinking or widening molten zone over a length of ingot.

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“…The melting temperature of the PCM, T m = 306.8°C, and all other thermophysical properties (e.g. Pr = 9.2) were acquired from a study by Lan and Yang [10]. Using this system, three melting processes were studied to compare the impact of convection and turbulence on the thermal behaviour of PCM.…”

Section: Pcm Systemmentioning

confidence: 99%

Numerical study of melting process of a high-temperature phase change material including natural convection and turbulence

Riahi¹,

Saman²,

Bruno³

et al. 2017

Int. J. CMEM

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The design and optimisation of a latent heat thermal storage system require knowledge of flow, heat and mass transfer during the melting (charging) and solidification (discharging) processes of hightemperature phase change materials (PCMs). Using fluent, numerical modeling was performed to study the impact of natural convection and turbulence in the melting process of a high-temperature PCM in a latent heat storage system with Ra = 10 12. Numerical calculation was conducted, considering a two dimensional symmetric grid of a dual-tube element in a parallel flow shell and tube configuration where the heat transfer fluid passes through the tube and PCM fills the shell. Three melting processes of PCM were considered; pure conduction, conduction and natural convection, and finally the latter with turbulence. The first study showed a one dimensional melt front, evolving parallel to the tube, which results in lower peak temperatures and temperature gradients, higher heat transfer area for a longer period of time, however lower heat transfer rate due to natural convection being ignored. The second study presented a two dimensional melt front which evolves mainly perpendicular to the tube, shrinking downward, resulting in the loss of heat transfer area and higher peak temperatures and temperature gradient, however, the higher rate of heat transfer rate due to the creation of convection cells which facilitate mass and heat transfer. Including turbulence led to a higher mixing effect due to the higher velocity of convection cells, resulting in a more uniform process with lower peak temperature and temperature gradients and higher heat transfer rate. In a melting process with Ra>10 11 , including convection and turbulence impact provides more realistic data of flow, mass and heat transfer.

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Dynamic simulation of the vertical zone-melting crystal growth

Cited by 21 publications

References 21 publications

Three-dimensional bifurcations in a cubic cavity due to buoyancy-driven natural convection

Three-dimensional bifurcations in a cubic cavity due to buoyancy-driven natural convection

Mathematical Equation for Impurity Distribution After Second Pass of Zone Refining

Numerical study of melting process of a high-temperature phase change material including natural convection and turbulence

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