Accuracy of the two-iteration spectral method for phase change problems

Abstract

The accuracy of the solution of phase change problems using a spectral method is studied. Two iterations in the expansion are used to obtain the interface location of a solidification problem in semi-infinite domain. Asymptotic expansion of the current approach is compared to the existing analytical solution of the problem, and the validity of the expansion is studied. The results indicate the accuracy of a numerical application of the current approach to finite and semi-infinite geometries.

An approximate analytical solution of one-dimensional phase change problems in a finite domain

“…It is seen from the figure that the velocity of the interface is slower for higher value of diffusivity ratio. Thus the result conforms with the statement of Dursunkaya and Nair[13] that when ratio of thermal diffusivities is small, the interface motion is rapid.Fig. 2reveals the dependence of the moving interface on dimensionless time for three values of solid Stefan number S 1 = 0.65, 0.75, 0.85 and for fixed S 2 = 0.1, a 21 = 0.7.…”

“…In 2004, Lamberg [12] has developed a simplified approximate analytical method for two phase solution problem in a finned PCM storage which predicts the solid liquid interface location and temperature distribution of the fin in the solidification process. In 2006, Dursunkaya and Nair [13] has used two iteration spectral method to obtain the interface location of a two phase Stefan problem in semi infinite domain. They have discussed the accuracy and limitations of the two iteration spectral scheme and comparison was made with existing approximate analytical solutions.…”