Why solidification has an S-shaped history

Adrian Bejan (1) , Sylvie Lorente (2) , B. S. Yilbas (3) , A. Z. Sahin (3)

1 Department of Mechanical Engineering and Materials Science
2 LMDC - Laboratoire Matériaux et Durabilité des constructions
3 KFUPM - King Fahd University of Petroleum and Minerals

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.

Mots clés: kinetics; model; applicability; dendritic solidification; growth-rate; tin

Domaines: Génie civil

Adrian Bejan, Sylvie Lorente, B. S. Yilbas, A. Z. Sahin. Why solidification has an S-shaped history. Scientific Reports, 2013, 3 (1), pp.1711. ⟨10.1038/srep01711⟩. ⟨hal-01850834⟩