The filling process of horizontal centrifugal casting is characterized by free surface, viscous, incompressible and unsteady flow. Therefore, the fluid motion state conforms to the continuity equation and momentum conservation equation. The continuity equation and Navier Stokes equation of filling process are as follows:

(1) Continuity equation:

(2) Navier Stokes equation:

Where ρ－ Density, t-time, Ø – velocity component, V-velocity component.

In the simulation of the temperature field of the liquid metal filling flow process, the liquid metal should not only conform to the continuity equation and Navier Stokes equation describing the fluid motion state, but also conform to the following heat balance equation in the flow and solidification process of the liquid metal:

Where c – specific heat, T – temperature, k – thermal conductivity, Q is the internal heat source