A scientific methodology for foundry has been developed in order to have a constant connection between foundry and the continuous development of solid state physics. This is achieved through the continuous expansion of the minimum scientific knowledge based on the historical development of metal physics, solid state physics, and today mathematics is placed in the first place. Metal science is a pure application of metal physics and solid state theory based on foundry, today it is materials science. The natural mathematical theory of foundry is the theory of thermal conductivity describing phase transitions of the first and second kind through Stefan-type problems – solidification together with modern software products for descriptions.
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