## 3 Results and Discussion  
### Thermal History of Thermosonication Processing  
Figure 1 exhibits the thermal histories of the thermosonication-assisted extraction processes of phytochemicals from fennel at different nominal power and temperature conditions. The thermal history describes temperature behavior according to the extraction time.  
The initial temperature of the samples was standardized to 25 \({}^{\circ}\)C. Then, the samples were heated until the working temperature (40, 50, or 60 \({}^{\circ}\)C) was reached. The red dot line indicates the working temperature and the start of the extraction process assisted by thermosonication (Figure 1). The increase of nominal power and working temperature increased the maximum temperature reached by the thermosonicated sample. Thus, the combination between acoustic energy and an external heat source throughout the extraction process influenced the thermal history. The greater \(\Delta\)T (maximum temperature-working temperature) values were observed for the extractions employing 400 W. For this nominal power, \(\Delta\)T values of 35, 27, and 17 \({}^{\circ}\)C were observed for working temperatures of 40, 50, and 60 \({}^{\circ}\)C, respectively.  
The application of low-frequency (19 kHz) and high-power (100, 200, 300, and 400 W) ultrasound promotes the phenomenon of acoustic cavitation in the extraction medium. During the sonication treatment, cavitation bubbles are formed. These bubbles grow and explode violently, releasing mechanical and thermal energy in the sonicated liquid, increasing its temperature throughout processing [19]. The increase in nominal power from 100 W to 400 W intensified the acoustic cavitation effects resulting in greater \(\Delta\)T values. [PERSON] et al. [20] reported that increasing the ultrasonic power from 7.98 W to 32 W decreased the microbubble collapse time. Thus, the acoustic cavitation intensity was increased. Therefore, the nominal power and the working temperature affected the temperature of the thermosonication-assisted extraction processes. In this way, monitoring the temperature throughout the thermosonication is needed to prevent the fennel compounds' exposure to high temperatures, avoiding their bioactive compounds' thermal degradation.  
On the other hand, Figure 1 shows that higher \(\Delta\)T values are associated with lower working temperatures. In the extraction at 40 \({}^{\circ}\)C, \(\Delta\)T values of 5, 13, 29, and 35 \({}^{\circ}\)C were observed for the nominal powers of 100, 200, 300, and 400 W, respectively. The thermosonication-assisted extractions carried out at 60 \({}^{\circ}\)C exhibited lower \(\Delta\)T values of 2, 6, 14, and 17 \({}^{\circ}\)C for 100, 200, 300, and 400 W, respectively. The temperature can affect the physical properties of the solvent, such as saturation vapor pressure, surface tension, sound velocity, and viscosity. Our results demonstrated that the temperature rises gradually  
Figure 1: Thermal history of the processes of extraction by thermosonication.  
decreased the acoustic cavitation intensity since the nominal power increase did not cause the same response on maximum temperature for each working temperature evaluated.