## Abstract

A group classification of equations describing the motion of a liquid metal with the inclusion of nanopowder inoculators is carried out in relation to the dependence of the viscosity coefficient on temperature and the fraction of the solid phase in the melt. The motion of a liquid metal with the inclusion of nanopowder inoculators will be described by the Navier - Stokes system of equations in an axisymmetric coordinate system taking into account the force of gravity directed against the axial coordinate and the heat transfer equation in a liquid, taking into account crystallization. The viscosity of a liquid is considered dependent on temperature and the fraction of the solid phase in the melt. The widest permissible group is obtained in the case of a constant viscosity coefficient. Also, the expansion of the permissible group occurs with some special types of dependence of the viscosity coefficient on temperature and the fraction of the solid phase in the melt.

Original language | English |
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Article number | 012012 |

Number of pages | 6 |

Journal | Journal of Physics: Conference Series |

Volume | 1268 |

Issue number | 1 |

DOIs | |

Publication status | Published - 16 Jul 2019 |

Event | All-Russian Conference and School for Young Scientists, devoted to 100th Anniversary of Academician L.V. Ovsiannikov on Mathematical Problems of Continuum Mechanics, MPCM 2019 - Novosibirsk, Russian Federation Duration: 13 May 2019 → 17 May 2019 |