Abstract
With the preliminaries of the structure, thermodynamics, and energy balances encountered in crystal-melt systems and their transformations discussed in earlier chapters, one may now consider additional details of the progressive freezing of a pure melt phase with some initial thickness L, for a slab casting, or with a radius, R 0, for solidification of a circular right cylinder. These representative casting geometries serve to elucidate some important findings from heat transfer theory and help describe interfacial motion that quantify the kinetic behavior of freezing events occurring on macroscopic scales.
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Notes
- 1.
Extensions using fast-convergent analytic methods to solve transient heat conduction problems at high Biot numbers in finite solid bodies, including plates, cylinders, and spheres, were developed recently by Ostrogorsky and Mikic [1].
- 2.
The differences between using numerical simulations and analytical solutions are that the latter quickly give the analyst or engineer an intuitive grasp of a system’s behavior over as wide a range of the process parameters as required. Numerical simulations provide enormous flexibility and breadth in their application, and become indispensable when dealing with complexities introduced by variable thermal properties and complicated casting geometries. Computer simulations, however, still pose considerable interpretive challenges when one explores wide regions of a multi-parameter space that many solidification problems require. Clearly, each methodology—numeric and analytic—can assist the casting engineer.
- 3.
This chapter, despite its focus on classical analytic solutions for casting and crystal growth problems, is also included to encourage the use of mathematics software and computers to explore more deeply the details and nuances of heat flow during solidification.
References
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Glicksman, M.E. (2011). Solidification of Pure Materials. In: Principles of Solidification. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-7344-3_4
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DOI: https://doi.org/10.1007/978-1-4419-7344-3_4
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