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The presented work shows the results of numerical modeling of the bronze solidification process in a permanent mold made of cast iron in a three-dimensional space, incorporating thermophysical phenomena. The model considers the effect of the air gap between the mold and the casting, which has a variable width, on the rate of the solidification process. Employing the Finite Element Method (FEM) with independent spatial discretization of the casting and the mold, the model accounts for the thermal deformations of the casting, while the mold is assumed to be undeformable. This approach involves the use of two separate meshes to obtain temporary temperature fields. The thermal interaction between the bronze casting and the mold is described by appropriate boundary conditions. The solution is obtained sequentially in each time step independently for each volume.