Is it reasonable to assume a uniformly distributed cooling‐rate along the microslide of a directional solidification stage?

Abstract

It is commonly assumed that the cooling-rate along the microslide of a directional solidification stage is uniformly distributed, an assumption which is typically applied in low cooling-rates studies. A new directional solidification stage has recently been presented, which is specified to achieve high cooling-rates of up to 1.8 x 104 degrees C min-1, where cooling-rates are still assumed to be uniformly distributed. The current study presents a closed-form solution to the temperature distribution and to the cooling-rate in the microslide. Thermal analysis shows that the cooling-rate is by no means uniformly distributed and can vary by several hundred percent along the microslide in some cases. Therefore, the mathematical solution presented in this study is essential for experimental planning of high cooling-rate experiments.