Mathematical Physics Essentiality of Phenomenological Similitude Based on Some Typical Metallurgical Processes

The mathematical physics essentiality of phenomenological similitude is pointed out to have the same dimensionless models, including the same model structures and the same values of all characteristic numbers in a dimensionless normalized coordinate basis. As an example of metallurgical process, unsteady one-dimension heat transfer conduction is discussed here and one presents that the difference in variant physical phenomena in a dimensionless normalized coordinate basis depends upon the relationships between those parameters, not upon the equations themselves which describe physical phenomena. If there is an unique relationship between physical phenomena in the real world, then their dimensionless relationship in a dimensionless normalized coordinate basis can be found out. The phenomena with the same model structures are called as homogeneous phenomena. If the values of their characteristic numbers are also equal in homogeneous phenomena, then they belong to similar phenomena.