Estimation of the Evolution of Solid Fractions in Constant Volumes of Cylindrical Samples Unidirectionally Solidified

Abstract

An estimation of the evolution of solid fractions in cylindrical samples with predominantly lower heat extraction have been performed, considering approximately constant finite volume constituting the alloy samples of Zn commercial grade and Zn - Al diluted alloys, with concentrations ranging from Zn-1wt.%Al to Zn-5wt.%Al. From decreasing exponential functions that simulate the experimentally determined temperature versus time curves, for materials in the liquid state, in a state of superheated liquid, superheated solid state, solid state and after the disappearance of the thermal transient, typically determines the evolving of solid fractions as functions depending on time and position. We concluded that the variation with time of solid fraction between zero and unity, during the phase change, was not linear and was estimated by hyperbolic tangent functions such as modified or approximated by third degree polynomials in the intervals of local solidification. Also, the form that presented the variation of the solid fraction depends on the position considered along the sample, exhibiting different behaviors conditional on the distance from the base of the sample, and depending on cooling rates imposed, thermal effects of heating of liquid and solid due to the release of latent energy of the movable and resizable region where liquid and solid coexists during solidification.