Analytical method for determination of cooling curves and cooling rates within the interval of temperatures of solidification of an alloy

Abstract

In this paper the analytical method for determination of cooling curves and cooling rates in a casting is presented. The type of casting structure is solid solution, which solidifies with low values of Die criteria, lielutibns which define curves are derived by mathematical model of a process of solidification of the casting. The model is based on the differential equation of heat conduction and generation of heat (latent heat). The solution of the model is derived by using the variational principle and is presented in analytical and functional form. Function 8 (y,F0 ) describes the temperature field within the wall of a casting. Using this function it is easy to determine cooling curve, cooling rate, temperature gradient, ratio of liquid and solid phase, time of solidification of a casting etc. Paper already presented drawing of cooling curves and cooling rates on the surface and the central area of a casting. It is obvious that the mathematical model is successful in describing the solidification process. Curve of cooling rate of a casting indicates that the intensity of cooling is smaller at the beginning than at the end of solidification. This indicates that at the beginning of the process of solidification is generating more significant amount of solid phase, r-pushing generation of great amount of latent heat and suppressing process of cooling.