## 1 Introduction
[14] presented a straightforward application of an indirect method based on a three-microphone impedance tube setup to determine the non-acoustic properties of a sound-absorbing porous material. [PERSON] et al. [15] presented a review on acoustic waves in porous media. Particular emphasis was placed on the relationship between the full Biot-Allard model and the simpler approximations presented by [PERSON], [PERSON] and [PERSON], and others. Acoustics and vibrations: Since thermoacoustic refrigerators use sound waves to generate pressure changes and, thus, cooling, they can be studied from the perspective of acoustics and vibrations. This includes optimizing acoustic resonator geometry and system design to maximize acoustic-to-thermal energy transfer efficiency. For example, [PERSON] [16] correlated the results of the theory with those of an earlier theory by [PERSON] as long as the attenuation in the duct was not large. However, wide divergences appeared, particularly where the attenuation in the duct began to approach that characteristic of the propagation of sound through bulk lining material. [PERSON] [17; 18] aimed to establish a compromise between the acoustic resonance frequency and the thermal penetration depth without paying attention to the need for the driver resonance to be matched to the resonator frequency, for the high efficiency of the driver. [PERSON] et al. [19] highlighted the impact of the resonance tube on the performance of a thermoacoustic stack. The appropriate resonance tube's length led to an increase in the performance of the stack, in terms of the temperature difference. [PERSON] et al. [20] found that the viscous component of the pressure drop follows a quadratic trend with respect to the velocity inside the stack, while the inertial component is also linear in high-velocity regimes. The largest value of the non-linear coefficient related to the Forchheimer coefficient is found at low frequencies, as the fluid particle displacement is comparable to the stack length. Control and electronics: Electronic control of the thermoacoustic cycle can be crucial to optimizing the stability and performance of the refrigerator. Control algorithms, temper ature and pressure sensors, and the integration of electronic components can be studied, to improve system accuracy and efficiency [21]. In the literature, the efficiency of a thermoacoustic device is given by the coefficient of performance (\(COP\)) [22], defined as the ratio between the heat flow (\(Q_{c}\)) and the acoustic work (\(W\)) on the stack. From an energy efficiency optimization perspective, the \(COP\) generated in the stack must be maximized. Regarding geometrical optimization parameters, several studies have been carried out, including intelligent optimization techniques such as genetic algorithms [4; 10], response surface methodology (RSM) [23; 24], and non-linear programming models with discontinuous derivatives (DNLPs) [9]. Most of these works have been based on linear thermoacoustic theory (LTT), which assumes that acoustic wave amplitudes are small compared to the mean pressure [25; 26]. This implies that the oscillations are weak and that non-linear effects are negligible. LTT simplifies the interaction between acoustic waves and thermal gradients, often using linearized heat transfer and fluid dynamics equations. Thus, LTT can provide a first-order approximation of the behavior of a thermoacoustic system by solving simplified versions of the governing equations. It is most useful for understanding the basic operation principles, stability analysis, and preliminary design of thermoacoustic devices. Following this, a computational fluid dynamics (CFD) model can be employed to represent multi-dimensional effects and design optimization [27], complex geometries, non-linear losses of a parallel plate stack [20], and realistic boundary conditions solving the full Navier-Stokes equations along with heat transfer and thermodynamic relations, capturing detailed flow and temperature fields [28] not considered by LTT [29].