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A general enthalpy method for modeling solidification processes

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Abstract

In the present work, a general implicit source-based enthalpy method is presented for the analysis of solidification systems. The proposed approach is both robust and efficient. The performance of the method is illustrated by application to a number of problems taken from recent metallurgical literature.

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Abbreviations

a, b, d :

coefficients of the discretization equation

Bi:

discrete Biot number

c :

specific heat capacity

C :

concentration (also weight percent)

dH/dT :

slope of the enthalpy temperature curve

Fo:

discrete Fourier number

g :

volume fraction of liquid

h :

convective heat-transfer coefficient

H :

enthalpy

k :

thermal conductivity

L :

latent heat of fusion

p :

pressure

r:

residue vector of a system of equations

S :

source term

t :

time

T :

temperature

u, v :

velocities

E :

eutectic

F :

fusion point

inf:

ambient

ini:

initial

l :

liquid, liquidus

L :

liquidus

M:

melting point

nb :

neighboring nodes top

p :

node pointp

Pr:

Prandtl number

ref:

reference

s :

solid, solidus

wall:

ingot/mold boundary

m :

iteration level

old:

old time value

— 1:

inverse

β :

compressibility

p :

density

k :

partition coefficient

μ:

viscosity

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Authors and Affiliations

  1. Department of Mechanical Engineering, University of Minnesota, 55455, Minneapolis, MN

    C. R. Swaminathan (Graduate Student)

  2. Department of Civil and Mineral Engineering, University of Minnesota, 55455, Minneapolis, MN

    V. R. Voller (Associate Professor)

Authors
  1. C. R. Swaminathan
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  2. V. R. Voller
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Swaminathan, C.R., Voller, V.R. A general enthalpy method for modeling solidification processes. Metall Trans B 23, 651–664 (1992). https://doi.org/10.1007/BF02649725

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