Heat transfer coefficient in rapid solidification of a liquid layer on a substrate

The heat transfer coefficient at the bottom surface of ar splat rapidly sol idified on a cold substrate is self-consistently, and quantitatively invest igated. Provided that the boundary condition at the bottom surface of the s plat is specified by introducing the obtained heat transfer coefficient, so lutions of the splat can be conveniently obtained without solving the subst rate. In this work, the solidification front in the splat is governed by no nequilibrium kinetics while the melting font in the substrate undergoes equ ilibrium phase change. By solving one-dimensional unsteady heat conduction equations cmd accounting fbr distinct properties between phases and splat a nd substrate, the results show that the time-dependent heat transfer coeffi cient or Biot number can be divided into five regimes: liquid splat-solid s ubstrate, liquid splat-liquid substrate, nucleation of splat, solid splat-s olid substrate, and solid splat-liquid substrate. The Blot number dr the bo ttom surface of the splat during liquid splat cooling increases and nucleat ion time decreases with increasing contact Biot number, density ratio, and solid conductivity of the substrate, and decreasing specific heat ratio. De creases in melting temperature and liquid conductivity of the substrate and increase in latent heat ratio further decrease the Biot number at the bott om surface of the splat after the substrate becomes molten. Time-dependent Biot number at the bottom surface of the splat is obtained from a scale ana lysis.