Design and control of interfacial temperature gradients in solidification

In a unidirectional solidification design problem, the solidification veloc ity and the liquid-side interfacial temperature gradient are of principle i nterest due to their effect on the morphology of the cast structure. The de sign challenge is prediction of the temporal conditions at the boundaries, such that the solidification velocity and the liquid-side temperature gradi ent at the solid-liquid interface follow a predetermined design scenario. T he stated problem requires the resolution of two inverse problems: one, in an expanding solid domain and the second, in a shrinking liquid domain. An innovative solution technique is proposed and demonstrated for design of th e liquid-side temperature gradient during unidirectional solidification. Du ring the early transient, the control of the interfacial temperature gradie nt presents a challenge due to the diffusion time between the boundary and the interface. This challenge is met using a combination of initial conditi on design and time structuring, which allows independent control of the int erfacial temperature gradient for the extent of the solidification process. The solution is developed in the context of a classic weighted-residual me thod, where the temporal variable is treated in an elliptic fashion. (C) 20 00 Elsevier Science Ltd. Ail rights reserved.