Photothermal microanalysis of thermal discontinuities in metallic samples

Finite element modelling for micro-scale thermal investigations using photo-thermal microscopy data inversion

“…Let us consider the following notation: i ∈ R 3 is the space domain corresponding to the component i; X = (x, y, z) ∈ ∪ i is the space variable; t ∈ T is the time variable. In [15], the periodic heat flux focused on the surface at point I is expressed in the form φ (r X , t) = φ 0 e −r 2 X /r 2 0 e jωt (1) where φ 0 is the heat flux amplitude (W m −2 ), r X is the distance XI (in m), r 0 is characteristic of the heat flux spatial distribution (m), ω is the pulsation (rad s −1 ). The evolution of temperature θ(X, t) in ∪ i is described by the following equations,…”

“…Simulated values are deduced from a mathematical model describing the heat transfer induced by periodic excitation. Semi-analytical solutions are proposed in [9,18] for homogeneous samples and in [6,15,19] for several types of discontinuities. In [6], the partial differential equation system is solved considering the analogy between the Helmholtz equation and the Laplace transform of the heat diffusion equation in order to obtain the Laplace transform of the solution.…”

Microscale Thermal Characterization by Inverse Method in the Frequency Domain

“…x y z = ∈ Ω ∪ is the space variable, t T ∈ is the time variable. In (Pruja et al, 2004), the periodic heating flux focused at the surface Γ on point I is expressed in the form :…”

“…In specific configurations such as homogeneous solid, semi infinite geometry, temperature nondependent parameters, particular multicomponent configurations (for which thermal interface are well identified), calculation of the inverse Fourier transform leads to semi analytical solution, see theoretical aspects and applications in (Gervaise et al, 1997(Gervaise et al, , 2001, (Milcent et al, 1998), (Gagliano et al, 2001), (Pruja et al, 2004). From the experimental point of view, for heterogeneous materials which not verify previous assumptions, thermal diffusivity identification according to semi analytical solution can lead to erroneous estimation.…”

“…Simulation values are deduced from mathematical model describing heat transfer induced by periodic excitation. Semi analytical solutions are proposed in (Gervaise et al, 1997) for homogeneous samples and in (Pruja et al, 2004) for several types of discontinuities. In both previous communications, partial differential equation system is solved using a space Fourier transform; calculation of the inverse Fourier transform is carried out numerically and temperature amplitude and phase lag values are compared to the incident heat flux.…”