Solute boundary layer on a rotating crystal

In order to obtain the directional microstructure of different supersaturation and growing velocity, three simulations is calculated with different initial temperature. When the initial temperature is 1576K, and the supersaturation and growing velocity are smaller. The average space length of columnar crystals is bigger, and the directional microstructure grows by the wide columnar crystals. Microsegregation is smaller; when the initial temperature is 1574K, the supersaturation and growing velocity increase. when the initial temperature falls to 1566K, the planar interface comes back, and microsegregation decreases rapidly. The directional microstructure grows by the thinnest columnar crystals. At the same time, the transverse solute profiles and solute boundary layer are also talked in this paper.

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The Czochralski crystal growth system with a periodic crystal growth rate and back-melting

Proceedings of the Royal Society of London Series A - Mathematical and Physical Sciences ◽

10.1098/rspa.1982.0019 ◽

1982 ◽

Vol 379 (1777) ◽

pp. 327-343 ◽

Cited By ~ 4

Keyword(s):

Boundary Layer ◽

Growth Rate ◽

Crystal Growth ◽

Solid Phase ◽

Harmonic Component ◽

Preceding Paper ◽

Crystal Growth Rate ◽

Czochralski Crystal Growth ◽

Solute Boundary Layer ◽

Growth System

This paper considers the effect upon the Czochralski crystal growth process of modulating the crystal growth rate periodically, by imposing upon a constant mean growth rate a harmonic component. The case is considered when the amplitude of the harmonic component is sufficiently large that the crystal melts during part of the periodic cycle. The model of the Czochralski system discussed in the preceding paper is adopted. The system is considered in the realistic limit of Sc → ∞, σ → 0 ∆ → 0, where Sc = v / D L is the Schmidt number, σ= v / K L is the Prandtl number, and ∆ = D S / D L is the ratio of the solute diffusivities in the liquid and solid phases, v being the kinematic viscosity of the liquid, and K L the thermal diffusivity of the liquid. When the crystal melts back, large solute gradients are formed in the solid phase. It is due to the presence of these that the diffusion of solute in the solid becomes important, being responsible for the formation of a time-dependent solute boundary layer adjacent to the interface in the crystal. Four distinct periods throughout the cycle are identified in which this boundary layer has different structures. The results of numerical calculations arising from this work are presented.

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Morphological and thermosolutal instabilities inside a deformable solute boundary layer during directional solidification. I.— Theoretical methods

Journal de Physique ◽

10.1051/jphys:01987004802017300 ◽

1987 ◽

Vol 48 (2) ◽

pp. 173-183 ◽

Cited By ~ 13

Author(s):

M. Hennenberg ◽

A. Rouzaud ◽

J.J. Favier ◽

D. Camel

Keyword(s):

Boundary Layer ◽

Directional Solidification ◽

Theoretical Methods ◽

Solute Boundary Layer

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Study on MHD Flow over a Stretching Surface with Convective Boundary Condition by Numerical Method

Biointerface Research in Applied Chemistry ◽

10.33263/briac125.64376446 ◽

2021 ◽

Vol 12 (5) ◽

pp. 6437-6446

Keyword(s):

Boundary Layer ◽

Velocity Ratio ◽

Mhd Flow ◽

Convective Boundary Condition ◽

Convective Boundary ◽

Velocity Boundary Layer ◽

Convective Parameter ◽

Solute Boundary Layer ◽

Non Linear ◽

Schmidt Numbers

The thermal and mass diffusive MHD flow through a stretching sheet has been inspected in the presence of a chemically reactive solute under convective boundary conditions in the present paper. The non-linear PDEs of the system concerning the flow, temperature, and species are recasted into a set of non-linear ODEs using ST. The consequential system of the differential equations is numerically resolved by using an implicit FDS in combination with the QL technique. The velocity ratio factor plays an important role in reducing the thickness of the velocity boundary layer, whereas the presence of magnetic parameters decreases the thickness of the velocity boundary layer profile. The study reveals that the fluid moves away from the surface during injection, resulting in a fall of the velocity gradient, whereas the opposite effect is observed in suction. The thermal and concentration boundary layer thicknesses are influenced by non-dimensional numbers, namely Prandtl and Schmidt numbers. The reaction rate parameter acts as a decelerating agent, and it thins the solute boundary layer formed in the neighborhood of the sheet. An increase in the convective parameter leads to an increase in the plate surface temperature. The present results of the paper are compared with the existing one, and good agreement is found between them.

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