In the present study, transient thermography, a nondestructive imaging technique, is applied to evaluate the transient temperature response in a graded medium without the use of embedded thermocouples. A layered composite sample was fabricated from Al2O3 and Y-ZrO2 powders using powder metallurgy (PM). This sample was irradiated on one side with a direct current laser while the transient temperature was measured along its depth by a midinfrared camera. Also, a MATLAB code based on the truly meshless radial point interpolation method (t-RPIM) was developed and implemented to solve the problem of quasilinear transient heat transfer in PM solids. In the t-RPIM formulation, the Cartesian transformation method and the Crank-Nicolson scheme were used for the evaluation of domain integrals and time discretization, respectively, thereby yielding a truly mesh-free technique. In the conducted experiment, the thermophysical properties were assumed to be independent of temperature because of the small amount of temperature increase. These properties and the volume fractions of the constituent powders were determined using a combination of the t-RPIM and the damped Gauss-Newton method in an inverse analysis. Good agreement was found between the measured temperature and the reconstructed temperature profile using the identified thermal parameters and volume fractions, thus validating the accuracy and ability of the applied t-RPIM as a tool in an inverse scheme to solve the inverse transient heat conduction problem in nonhomogeneous media.

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An efficient new thermal-wave inverse-problem approach based on an integral-equation boundary-value method coupled with an imperialist competitive algorithm was developed. The methodology was successfully applied to simultaneously reconstruct density and thermal conductivity depth profiles in a sintered powder metallurgy sample from an industrial automotive manufacturer with a surface layer of higher density than the bulk. The density and thermal conductivity depth profiles were validated independently using the manufacturer's data and in-house temperature and porosity measurements. The present non-destructive inverse problem approach represents a generalized formalism to thermal-wave reconstruction of dual depth profiles using frequency scan data measured from the interrogated surface. From a fundamental viewpoint, the method adds significant insights into the relationship between thermal conductivity and density distributions in inhomogeneous solids.