In the process of lining plate forming, there are both heat absorption and cooling processes. During the heating process, the casting is in a fluid state, which has no direct impact on the casting stress. Therefore, the heat transfer analysis during the cooling process of the casting liner forming is focused on, as shown in the figure below. Assuming that the mold cavity has been filled instantaneously, the initial temperature of carbon steel, high chromium cast iron, the initial temperature of molding sand, and the heat transfer between metal interfaces is mainly in the form of heat conduction, The heat transfer between high-temperature castings, air and molding sand is mainly by convection and radiation. The arrows in the figure indicate the direction of heat transfer.
The cooling process of casting liner forming can be regarded as an unsteady heat conduction process. The micro unit is established in the Cartesian coordinate system. Based on the energy conservation theorem, the three-dimensional mathematical model can be deduced as follows:
