Photothermal Thermoelastic Bending for Media with Thermal Memory

Abstract

Photothermal thermoelastic bending depends on an optically generated dynamic thermal field distribution within a sample. A generalized description of the distribution is proposed, including the effects of a finite heat propagation velocity and a finite, non-zero time of thermal relaxation (known as thermal memory effects in generalized heat conduction theory), and finally the generated thermoelastic bending is calculated by using both a thin solid-plate approximation and a decoupling system of thermoelastic equations. The comparison between this model and the classical one, which does not account for thermal memory influence, has been made. If the sample is thicker than the value of its minimal thermal diffusion length, the difference between the two models becomes insignificant. Otherwise, it has been shown that the two models tend to overlap at low and high modulation frequencies of the excitation light, while in the mid-frequency range, some deviations become more apparent and thermal memory properties of the sample must be taken into account. The suggested model enables evaluation of thermal memory properties for such a solid.M. Nesic (B) · S. Galovic · M. Popovic

Developing the Techniques for Solving the Inverse Problem in Photoacoustics

“…Based upon previous research and in accordance with literature defined norms [5], the following designation of thermodynamic properties of the system is introduced: Thermal relaxation time and heat propagation velocity are the properties of materials which exist in the generalized theory of heat transfer [6][7][8][9][10][11][12]. Explanation attempts regarding the meaning of thermal relaxation time can be found in several papers [13][14][15].…”

“…Basing the approach upon literature considerations [4,8,18,19,22,23], the starting expression of the model (for the measured signal directly proportional to the pressure change in the PA cell) can be written in the form: (1) where pth denotes the pressure change due to the thermoconducting(TH) component of the PA response (the component that originates from the periodic expansion of a thin gas layer closest to the Thermal relaxation time and heat propagation velocity are the properties of materials which exist in the generalized theory of heat transfer [6][7][8][9][10][11][12]. Explanation attempts regarding the meaning of thermal relaxation time can be found in several papers [13][14][15].…”

“…Instead, theoretical predictions are presented for reference samples (Aluminum, two thickness levels) in Figure 6. The most important result of these considerations is the expression which directly links the position of the first peak (the frequency value) with heat propagation velocity through the observed medium [9,10,12,21,26]:…”

Thermal Fractional Diffusion: Experimental Evidence from the Discrepancies in the Amplitude and Phase in Photothermal Technique

“…[17,18,28] In some cases, the classical model of heat propagation does not fit the results obtained for non-homogeneous samples because the values obtained for the thermal diffusivity do not match the expected value. This leads to the application of mathematical models that better explain the propagation of heat in non-homogeneous materials [4,15,19,22,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. The thermal memory theory, which employs the hyperbolic equations of heat propagation (HHE), or Cattaneo equations [44], that account for thermal relaxation time, was used to develop an extended model for the TD and TE phenomena [41,42].…”

“…This leads to the application of mathematical models that better explain the propagation of heat in non-homogeneous materials [4,15,19,22,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43]. The thermal memory theory, which employs the hyperbolic equations of heat propagation (HHE), or Cattaneo equations [44], that account for thermal relaxation time, was used to develop an extended model for the TD and TE phenomena [41,42]. The generalization of Cattaneo equations (GCE) by considering the fractional equations was applied to the study of PA signal generated by TD and TE [39].…”