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

Abstract

In this work the surface thermal-wave field ͑ac temperature͒ 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.

A flash characterisation method for thin cylindrical multilayered composites based on the combined front and rear faces thermograms

“…thermal response over time after a flash for front (1) and rear (2) faces. (2) signals; their sum (3) and a fit of equation [7] (4). right: logarithm of the difference (1) and a fit of equation [11] (2).…”

“…The experimental set-up is used in order to obtain front and rear faces thermal responses ( Figure 11). equation (7) has been used to fit the experimental sum of the thermal signals, Figure 11. thermal response over time after a flash for front (1) and rear (2) faces.…”

“…The developed experimental set-up seems to be a suitable solution for the study of heterogeneous tubular materials, as soon as the theoretical model is extended to a multi-layer model -currently available for lock-in experiments [7,8] -or even to a more complex imagebased model: this is the aim of current work in progress.…”

“…The validity of the analytical model [3,4] based on the quadrupoles formalism [6] and developed for flat samples has also been proved except for extremely curved samples. [4] The different existing thermal characterisation methods [3][4][5]7,8] use either front face or rear face signals obtained after a flash and lead to estimate the material thermal effusivity or diffusivity. In the case of highly diffusive and heterogeneous materials, the estimation accuracy is impaired, even more if they are cylindrical.…”

Optical and thermal depth profile reconstructions of inhomogeneous photopolymerization in dental resins using photothermal waves

“…10,13,15 Also, several algorithms to invert the depth profiles have been applied, using an inverse procedure to find the Taylor expansion parameters of the conductivity profile, 9,16 a least-squares one-parameter fit to reconstruct a polygonal approximation to the conductivity profile, 17,18 obtaining local thermal diffusivity at each frequency, 12,14,19 global optimization methods as genetic algorithm and neuronal networks, [20][21][22] and particle swarm optimization. 13 Experimentally, some of these theories have been applied to evaluate liquid crystals, 23,24 ceramics, 25 metallurgical specimens, 17,26,27 aluminum oxide thin films, 22 and dental resin composites, 28 to name a few. All these approaches concern only depth-dependent variations in the thermal parameters of materials while the optical properties remain either constant or the material is optically opaque ͑PT saturation͒.…”