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Chapter 23
Solidification in a Casting Mold

## Excerpt

Exact temperature distribution solutions to unsteady-state one-dimensional heat conduction equations in rectangular, cylindrical, and spherical coordinates, for initial condition and different boundary conditions, have been provided in literature (see References [1], [6], [10] and [16]). The reference by Carslaw, H. S. and J. C. Jaeger [1] extended these exact solutions to moving boundary conditions with phase change.

In this chapter, sensitivity analysis for the solidification front of a semi-infinite liquid in a semi-infinite mold is considered. The unsteady-state one-dimensional heat conduction equation in rectangular coordinates for the mold region, solidified cast material region and liquid cast material region, with constant property assumptions, is given by:

$∂2T∕∂x2=(1∕α)∂T∕∂θ$

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