从典型冶金过程问题看现象相似的数理本质

指出了现象相似的数学物理本质是它们在同一个量纲为1的单元坐标体系中有相同的量纲为1的模型:模型的结构相同且各特征数数值一一对应相等.以冶金工程中常见的问题--一维非稳态传导传热问题为例进行了说明与讨论.指明在量纲为1的单元坐标体系中不同现象的规律性之区别仅在于变量之间的关系不同,并不依赖于描述实际现象的方程.只要现象相似,它们在量纲为1的单元坐标体系中有相同的模型且有相同的解.在量纲为1的单元坐标体系中具有相同结构模型的现象是同类现象,同类现象中特征数数值对应相等的现象才是相似现象.

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 here discussed 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.