A parametric investigation of the photothermal radiometric signal under the Fourier and Maxwell-Cattaneo heat conduction laws

Abstract

Photothermal radiometry (PTR), which monitors the blackbody radiation emitted from a material under the excitation of an intensity-modulated light beam, has recently attracted the attention of the non-destructive research community in a variety of applications. The aforementioned optical excitation of the material results in a temperature with a spatiotemporal variation which is reminiscent of a damped wave, called a thermal wave. At first, we present the solution of the thermal wave problem in the framework of Fourier's heat transport equation for materials which are optically opaque or semitransparent and investigate how the excitation beam size and detector effective area affect the dimensionality of the thermal diffusion process. Having in mind that the classical Fourier heat conduction model violates the principle of causality, as was first argued by Maxwell, we employ the concept of thermal relaxation time as in the model proposed by Maxwell, Vernotte and Cattaneo, known as the MCV model. Using the MCV model, we conduct a parametric study to examine the impact of thermal relaxation time on the PTR signal for materials we consider to be interesting for industrial and biomedical applications like copper and animal tissue. Our numerical results show that the PTR technique is able to characterize the aforementioned materials and provide an accurate value of the thermal relaxation time.