Reconstruction of radial thermal conductivity depth profile in case hardened steel rods

In this work the surface thermal-wave field (ac temperature) of a solid cylinder illuminated by a modulated light beam is calculated first in two cases: a multilayered cylinder and a cylinder the radial thermal conductivity of which varies continuously. It is demonstrated numerically that, using a few layers of different thicknesses, the surface thermal-wave field of a cylindrical sample with continuously varying radial thermal conductivity can be calculated with high accuracy. Next, an inverse procedure based on the multilayered model is used to reconstruct the radial thermal conductivity profile of hardened C1018 steel rods, the surface temperature of which was measured by photothermal radiometry. The reconstructed thermal conductivity depth profile has a similar shape to those found for flat samples of this material and shows a qualitative anticorrelation with the hardness depth profile.