Modified temperature-transforming model for convection-controlled melting

The temperature-transforming model developed in the 1990s is capable of solving convection-controlled solid-liquid phase-change problems. In this methodology, phase change is assumed to take place gradually through a range of temperatures. The heat capacity within the range of phase-change temperatures was assumed to be average to that of solid and liquid in the original temperature-transforming model. In this paper, a modified temperature transforming model is proposed, to consider the dependence of heat capacity on the fractions of solid and liquid in the mushy zone. The ramped switch-off method is used for a solid velocity-correction scheme. The results are then compared with existing experimental and numerical results for a melting problem is a rectangular cavity. The results show that the modified model is closer to experimental results with octadecane as pulse code modulation, even though its heat capacity ratio is close to one. The modified model is then tested on substances that have heat capacity further from one, such as 0.4437 for water and 1.2034 for acetic acid. The results show that the original model underpredicts the velocity of the solid-liquid interface when the heat capacity ratio is less than one and overpredicts the velocity when the ratio is higher than one.