Introducing non-locality into solidification models

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A non-local flux, constructed as a weighted sum of local gradients, is introduced into a standard solidification model. A particular choice of weights leads to a flux expressed as a Caputo fractional derivative. Numerical solution, indicates that-in modeling solidification at microstructure scales of ∼5 mm-the presence of non-locality influences the distribution of temperature and liquid fraction and also increase the expected exponent in the characteristic solidification time scale.

Original languageEnglish (US)
Pages (from-to)515-519
Number of pages5
JournalTransactions of the Indian Institute of Metals
Issue number6
StatePublished - Dec 2012


  • Enthalpy solution
  • Fractional derivative
  • Non-locality
  • Solidification model


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