Analytical Study of Temperature Fields in Aluminum Alloy Castings During Solidification in Sand and Metal Molds

The article presents the calculation of temperature fields for a casting (a cylinder 20 mm in diameter) made of Al–5%wt.Cu alloy, poured into sand (sand–clay) and metal (steel) molds at a temperature of 1123 K (with a metal mold temperature of 523 K). Many existing analytical approaches do not explicitly account for key features such as the time-dependent temperature evolution at the casting surface and center, as well as the variable temperature gradient within the casting. In this paper, the parameters calculated for the sand mold include the surface temperature change over time, as do the dynamics of the solidification front progression, and ultimately, the overall thermal field of the casting. For the metal mold, the process first determines the change in the center temperature over time, followed by the surface temperature dynamics, and finally, the complete thermal field of the casting. Particular attention is paid to determining the position of the mushy zone, namely the zero fluidity and feeding temperatures (the point at which the liquid phase loses mobility upon cooling). These temperatures are critical for casting structure formation and the initiation of shrinkage defects. To perform the calculations, the authors developed original mathematical models and provided solutions to the resulting differential equations. The study demonstrates the differences between the thermal fields in sand and metal molds: the maximum temperature difference is 195 K in the sand mold, compared to 90 K in the metal mold. Therefore, the solidification conditions for this casting in the metal mold are more favorable. The metal mold provides more favorable thermal conditions and a lower analytically predicted tendency toward shrinkage defects, but it does not guarantee their complete absence.