Dimensional analysis of the thermomechanical problem arising during through-hardening of cylindrical steel components

This article concerns the dimensional analysis of the complex thermomechanical problem arising during through-hardening of cylindrical steel components. A complete and independent set of physically based dimensionless numbers was derived using the weak formulation method and the individual effects of dimensionless numbers with sensitive material parameters were investigated by finite element simulations. The results demonstrate potential of the approach in simplification of the model and the identification of physically relevant dimensionless combinations.