# Calculation method of solidification process and transient temperature field of mold vibration for centrifugal casting furnace tube

The solution domain is discretized into several nodes, and there is heat transfer between each node. The heat balance equation is set up for each node, and then the temperature of each node can be obtained by solving the heat balance equation.

In general, according to the law of conservation of energy, the heat balance equation of each node is as follows:

Where, Φ in, Φ, Φ out and Φ e represent the heat flux of the import node, the heat generated by the heat source in the node, the heat flux of the export micro element and the increment of the energy in the node respectively. Where the expression of Φ e is as follows:

Where, ρ, CP, V and t represent the material density, specific heat capacity, volume and temperature of the node respectively, and t is the time.

The equation can be solved by Euler method. Given the initial temperature value of each node, the temperature value at t + Δ t can be obtained from the temperature value at the previous time t (T + Δ T)

Where Δ t is the time interval between adjacent times. 