# Discretization of transient calculation region and determination of heat transfer in solidification process and mold vibration of centrifugal casting furnace tube

The mold and its internal area are discretized. The mold is divided into M1 grids in the radial direction, M2 grids in the pipe direction, n grids in the circumferential direction, and P grids in the axial direction

As shown in Figure 1, where l is the total length of centrifugal casting mold, R1, R2 and R3 are the inner radius of casting pipe, outer radius of casting pipe (inner radius of casting mold) and outer radius of casting mold respectively.

Next, the heat transfer analysis of a single grid is carried out without considering the heat transfer in the circumferential direction. Obviously, the heat transfer mode of the cast pipe body and the cast cylinder is heat conduction, the heat transfer mode of the outer surface of the cast mold is convective heat transfer and radiation heat transfer, and the heat transfer mode of the inner surface of the cast pipe is convective heat transfer.

There are two kinds of grids in the whole computational domain: internal grid and boundary grid. The boundary grid refers to the grid close to boundary 1, 2, 3 and 4 in Figure 1, and other grids are internal grids. The heat transfer mode of internal grid is heat conduction, while the heat transfer mode of boundary grid is not unique. The heat exchange calculation formula of each part is given in detail below.

(1) At boundary 1, the heat transfer mode is convection and heat conduction

(2) The heat transfer mode is heat conduction

(3) The heat transfer mode is heat conduction

(4) The heat transfer modes are heat transfer, convection and radiation

(5) The heat transfer mode is heat transfer

(6) The heat transfer mode is heat transfer

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