# Mathematical model of heat transfer in solidification process of sand castings

In the process of sand casting, liquid metal is poured into the mold and then dissipated heat to the surrounding environment through the mold. In this process, three heat transfer modes of heat conduction, convection and radiation work together, and the temperature of liquid metal decreases continuously.

This is an unstable heat conduction process, in which the computer simulation of liquid metal solidification process is based on the transient heat conduction partial differential equation：

Where:

T = (x, y, Z, t) – temperature, which is a function of time and space;

ρ— Density;

C – specific heat;

λ x， λ y， λ Z-value of heat conduction coefficient in X, y, z direction;

QL – internal heat source (latent heat of crystallization).

λ x， λ y， λ z， ρ， c。 The values of are related to temperature. For simplicity of calculation, only isotropy (i.e λ x= λ y= λ z= λ) The situation. At this time, the formula can be written in the following form:

Scroll to Top