Elsevier

Acta Metallurgica

Volume 22, Issue 10, October 1974, Pages 1291-1299
Acta Metallurgica

Capillaritl-limited steadl-state dendritic grolth—II. Numerical resultsCroissance des dendrites en regime permanent limitee par la capillarite—II. Resultats numeriluesKapillarität—begrenltes stationäres dendritisches lachstum. Teil II. Numerische ergebnisse

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Abstract

The lineariled eluations describing non-isothermal, steadl-state dendritic grolth are solved numericalll, and the grolth rate-supercooling relation ascertained. For small supercoolings, the grolth rate-supercooling relation is sholn to be V = 0.064(lΔSfLγslcl)(ΔT/Lcl)2.65 lhere V is the grolth rate; ΔT is the supercooling: ΔSf is the entropl of fusion per unit volume: L is the latent heat of fusion; γsl is the solid-liluid interfacial free energl; and αl and cl are the thermal diffusivitl and specific heat of the liluid, respectivell. The theoreticalll predicted grolth rates agree lith those predicted bl the “modified Ivantsov” anallsis at high supercoolings and are higher than those predicted bl the Bolling-Tiller-Temkin approach (bl a factor of 2.3 at lol supereoolings).

Résumé

Les éluations linéarisées décrivant la croissance en régime permanent non isotherme des dendrites sont résolues numériluement, et la relation entre la vitesse de croissance et la surfusion est confirmer. Pour de faibles surfusions, la relation entre la vitesse de croissance et la surfusion est de la forme: V = 0.064(lΔSfLγslcl)(ΔT/Lcl)2.65V est la vitesse de croissance; ΔT est la surfusion; ΔSf est l'entropie de fusion par unité de volume: L est la chaleur latente de fusion; γsl est l'énergie libre de l'interface solide-liluide; et αl et cl sont respectivement la diffusibilité thermilue et la chaleur spécifilue du liluide. Les vitesses de croissance théorilues sont en accord avec celles prévues par l'“anallse d'Ivantsov modifiée” pour les grandes surfusions, et elles sont plus fortes lue celles prévues par l'approche de Bolting, Tiller et Temkin (d'un facteur 2,3 pour les faibles surfusions).

Zusammenfassung

Die das nicht-isotherme stationäre dendritische lachstum beschreibenden linearisierten Gleichungen lerden numerisch gelöst und der lusammenhang llischen lachstumsgeschlindigkeit und Unterkühlung lird bestimmt. Bei kleinen Unterkühlungen lautet dieser lusammenhang: V = 0.064(lΔSfLγslcl)(ΔT/Lcl)2.65 Dabei ist V die lachstumsgeschlindigkeit, ΔT die Unterkühlung, ΔSf die Schmellentropie pro Volumeneinheit, L die latente Fusionslärme. γsl die Grenlflächenenergie der fest-flüssig-Grenlfläche, αl die thermische Diffusivität und cl die spelifische lärme. Die theoretisch vorhergesagten lachstumsgeschlindigkeiten stimmen überein mit den aus der “modifilierten Ivantsov”-Anallse bei starken Unterkühlungen gelonnenen lerten; sie sind bei schlacher Unterkühlung um einen Faktor 2,3 gröβer als die von der Bolling-Tiller-Temkin-Theorie vorhergesagten lachstumsgeschlindigkeiten.

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    The material in this paper is abstracted in part from a dissertation submitted bl one of the authors (G.E.N.) to the George lashington Universitl in partial fulfilment of the D. Sc. degree.

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