Depth profile reconstruction of the thermal conductivity of inhomogeneous solids: application to laser-hardened Al alloys

Zhao, Yirong; Zhang, S.Y.; Cheng, Jinquan; Zhang, Y.K.; Xu, Wen

doi:10.1007/s003390000527

Cited by 3 publications

(1 citation statement)

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“…Note that in order to represent the reconstructed K͑r͒ of the two steel rods in the same figure we have taken the origin of r at the cylinder surface. Their shapes are very similar to those found in flat surface geometries, [22][23][24][25][26] and they are in good qualitative anticorrelation with the hardness depth profile obtained by mechanical indentation testing performed on these rods ͑see Fig. 6 in Ref.…”

Section: ͑12͒supporting

confidence: 74%

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

Celorrio

Mendioroz

Apiñaniz

et al. 2009

Journal of Applied Physics

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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.

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Section: ͑12͒supporting

confidence: 74%

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

Celorrio

Mendioroz

Apiñaniz

et al. 2009

Journal of Applied Physics

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Two-dimensional reconstruction theory of thermal conductivity profiles based on the thermal wave technique

Zhou

Zhang

et al. 2002

Journal of Applied Physics

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A two-dimensional (2D) theory of thermal wave reconstruction is presented. By using a pulse spectrum technique and a Newton-like iteration method, the 2D inverse problem is expressed by a 2D Fredholm integral equation of the first kind. Further, the integral equation is approximated by a set of ill-posed linear algebraic equations, and a regularization method is introduced to overcome the singularity of the ill-posed linear algebraic equations. Finally, an error function is defined to choose the regularization parameter automatically to converge the iteration rapidly. The important developments in 2D inverse problem, compared with the one-dimensional problem, are that a line source is used instead of the source with a large cross section, and a finite difference method is adopted for numerical solution of the 2D heat equation. Numerical simulations demonstrate that this approach is effective and stable even with 5% random noise disturbance in the signal.

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Reconstruction of thermal properties of inhomogeneous materials from one dimension to two dimensions

Zhang

Zhou

2003

Review of Scientific Instruments

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Based on one-dimensional theory of thermal wave reconstruction, a two-dimensional theory of thermal conductivity profile reconstruction is developed. The important developments in the two-dimensional (2D) inverse problem are that a line source is used instead of the source with a large cross section in one dimension, and a finite difference method is adopted for the numerical solution of the 2D heat equation. Numerical simulations demonstrate that this approach is effective and stable even with 5% random noise disturbance in the signal.

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Depth profile reconstruction of the thermal conductivity of inhomogeneous solids: application to laser-hardened Al alloys

Cited by 3 publications

References 0 publications

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

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

Two-dimensional reconstruction theory of thermal conductivity profiles based on the thermal wave technique

Reconstruction of thermal properties of inhomogeneous materials from one dimension to two dimensions

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