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Journal Articles Scientific Reports Year : 2013

Why solidification has an S-shaped history


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.
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hal-01850834 , version 1 (14-06-2019)



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⟩
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