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Natural convection transients and their effects in unidirectional solidification

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Abstract

A formulation is given and computed solutions are presented for transient solidification accompanied by natural convection in a vertical slot. It was found that appreciable fluid velocities may be produced by natural convection, the values of which could be comparable to the terminal rising velocities of typical nonmetallic inclusions. The simplifying assumptions made limit the validity of the solutions to systems where GrPr < 500,i.e., to narrow slots or to low values of the superheat; nonetheless, the results should be indicative of the effects of convection at much higher values of GrPr.

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Abbreviations

Cp :

specific heat

g:

acceleration due to gravity

Gr:

Grashoff number

k:

thermal conductivity

L, Ĺ:

dimensionless and dimensional path travelled, respectively

Pr:

Prandtl number

q:

latent heat

Q:

dimensionless group

u, ú:

dimensionless and dimensional vertical velocity components, respectively

ú:

dimensional horizontal velocity component

y,’ y:

dimensionless and dimensional coordinates, respectively

Y:

half width of the liquid core

Yo :

half width of the slot

β:

coefficient of thermal expansion

v:

kinematic viscosity

p:

density

av:

average

m:

melting point

f:

flotation

s:

solid

i:

initial

t:

total

I:

liquid

w:

wall

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Authors and Affiliations

  1. State University of New York at Buffalo, Buffalo, N.Y.

    J. Szekely (Professor of Chemical Engineering)

  2. Institute of Chemical Process Fundamentals, Czechoslovak Academy of Science, Prague, Czechoslovakia

    V. Stanek

Authors
  1. J. Szekely
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  2. V. Stanek
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Formerly Post-Doctoral Research Associate, State University of New York at Buffalo

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Szekely, J., Stanek, V. Natural convection transients and their effects in unidirectional solidification. Metall Trans 1, 2243–2251 (1970). https://doi.org/10.1007/BF02643441

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  • DOI: https://doi.org/10.1007/BF02643441

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