Why solidification has an S-shaped history

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Bejan A., Lorente S., Yilbas B. S., Sahin A. Z.

SCIENTIFIC REPORTS, vol.3, 2013 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 3
  • Publication Date: 2013
  • Doi Number: 10.1038/srep01711
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Istanbul Technical University Affiliated: No


Here we show theoretically that the history of solid growth during "rapid" solidification must be S-shaped, in accord with the constructal law of design in nature. In the beginning the rate of solidification increases and after reaching a maximum it decreases monotonically as the volume of solid tends toward a plateau. The S-history is a consequence of four configurations for the flow of heat from the solidification front to the subcooled surroundings, in this chronological order: solid spheres centered at nucleation sites, needles that invade longitudinally, radial growth by conduction, and finally radial lateral conduction to interstices that are warming up. The solid volume (B-s) vs time (t) is an S-curve because it is a power law of type B-s similar to t(n) where the exponent n first increases and then decreases in time (n = 3/2, 2, 1, ... ). The initial portion of the S curve is not an exponential.