A comparative study of approximations to the RG model in a differential photoacoustic system in reflection mode
DOI:
https://doi.org/10.37636/recit.v9n3e478Keywords:
Thermal effusivity, Photocoustic response, Approximations of complex relative pressure, Differential photoacoustic cellAbstract
This paper presents a comparative study of approximations to the photoacoustic response obtained from the Rosencwaig-Gersho (RG) model for a differential photoacoustic cell in reflection mode, and in this way to evaluate its use in determining thermal effusivity. An integrated configuration consisting of two identical conventional photoacoustic cells is proposed, in which the ratio of the photoacoustic responses allows a reduction in the number of geometric, optical, and thermal parameters, simplifying the mathematical treatment. Zero-order, first-order, and second-order approximations are developed for the ratio of complex relative pressures, and their performance is evaluated by the percentage error with respect to the complete expression of the RG model. The analysis is performed for modulation frequencies between 1 and 2000 Hz, using air as the working gas and aluminum as the thermal transducer in both cells, and, in one cell, steel is used as support material and as a reference, while in the other cell, thermal effusivities between 5.85 and 36500 Wꞏs1/2ꞏm-2ꞏK-1 are worked on in the support material under study. The results show that the zero-order approximation exhibits significant deviations, while the first-order approximation offers an optimal balance between simplicity and accuracy, making it the most suitable for describing the photoacoustic response of the differential system. The proposed method constitutes a non-intrusive, reproducible, and low-cost alternative for the thermal characterization of materials, with potential applications in liquid systems, cooling processes, biomaterials, and various engineering fields.
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