Solidification problem for the wavy mold

The solidification process on the wavy mold is studied. It is assumed that the mold temperature is kept at a constant level below the melting point of material. The boundaries of the solidified layer are folded . The approximate technique, known as the heat-balance integral method, is applie d to determine the location of the solidification line and its perturbations . The solution is obtained with neglecting the square of small quantities. The effect of the folded boundary on the solution is shown in diagrams.