### Abstract

The energy equation for solidifying dendritic alloys that includes the effects of heat of mixing in both the dendritic solid and the interdendritic liquid is derived. Calculations for Pb-Sn alloys show that this form of the energy equation should be used when the solidification rate is relatively high and/or the thermal gradients in the solidifying alloy are relatively low. Accurate predictions of transport phenomena in solidifying dendritic alloys also depend on the form of the solute conservation equation. Therefore, this conservation equation is derived with particular consideration to an accounting of the diffusion of solute in the dendritic solid. Calculations for Pb-Sn alloy show that the distribution of the volume fraction of interdendritic liquid g_{ L} in the mushy zone is sensitive to the extent of the diffusion in the solid. Good predictions of g_{ L} are necessary, especially when convection in the mushy zone is calculated.

Original language | English (US) |
---|---|

Pages (from-to) | 889-900 |

Number of pages | 12 |

Journal | Metallurgical Transactions B |

Volume | 22 |

Issue number | 6 |

DOIs | |

State | Published - Dec 1991 |

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### ASJC Scopus subject areas

- Condensed Matter Physics
- Metals and Alloys
- Materials Chemistry
- Mechanics of Materials
- Engineering(all)

### Cite this

*Metallurgical Transactions B*,

*22*(6), 889-900. https://doi.org/10.1007/BF02651165

**The energy and solute conservation equations for dendritic solidification.** / Poirier, David R; Nandapurkar, P. J.; Ganesan, S.

Research output: Contribution to journal › Article

*Metallurgical Transactions B*, vol. 22, no. 6, pp. 889-900. https://doi.org/10.1007/BF02651165

}

TY - JOUR

T1 - The energy and solute conservation equations for dendritic solidification

AU - Poirier, David R

AU - Nandapurkar, P. J.

AU - Ganesan, S.

PY - 1991/12

Y1 - 1991/12

N2 - The energy equation for solidifying dendritic alloys that includes the effects of heat of mixing in both the dendritic solid and the interdendritic liquid is derived. Calculations for Pb-Sn alloys show that this form of the energy equation should be used when the solidification rate is relatively high and/or the thermal gradients in the solidifying alloy are relatively low. Accurate predictions of transport phenomena in solidifying dendritic alloys also depend on the form of the solute conservation equation. Therefore, this conservation equation is derived with particular consideration to an accounting of the diffusion of solute in the dendritic solid. Calculations for Pb-Sn alloy show that the distribution of the volume fraction of interdendritic liquid g L in the mushy zone is sensitive to the extent of the diffusion in the solid. Good predictions of g L are necessary, especially when convection in the mushy zone is calculated.

AB - The energy equation for solidifying dendritic alloys that includes the effects of heat of mixing in both the dendritic solid and the interdendritic liquid is derived. Calculations for Pb-Sn alloys show that this form of the energy equation should be used when the solidification rate is relatively high and/or the thermal gradients in the solidifying alloy are relatively low. Accurate predictions of transport phenomena in solidifying dendritic alloys also depend on the form of the solute conservation equation. Therefore, this conservation equation is derived with particular consideration to an accounting of the diffusion of solute in the dendritic solid. Calculations for Pb-Sn alloy show that the distribution of the volume fraction of interdendritic liquid g L in the mushy zone is sensitive to the extent of the diffusion in the solid. Good predictions of g L are necessary, especially when convection in the mushy zone is calculated.

UR - http://www.scopus.com/inward/record.url?scp=0026407024&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0026407024&partnerID=8YFLogxK

U2 - 10.1007/BF02651165

DO - 10.1007/BF02651165

M3 - Article

AN - SCOPUS:0026407024

VL - 22

SP - 889

EP - 900

JO - Metallurgical and Materials Transactions B

JF - Metallurgical and Materials Transactions B

SN - 1073-5615

IS - 6

ER -