## 3 Results and Discussion  
### Drying Kinetics  
In Figure 2 the evolution of relative moisture content (MR) and temperatures of samples (T\({}_{\text{m}}\)) and drying agent (T\({}_{\text{a}}\)) are presented for convective (CV) and ultrasonically assisted convective (CVUS) drying of apples. Comparison of the obtained curves allows us to state that ultrasound visibly influenced the drying kinetics. In the case of ultrasound-assisted convective drying (CVUS), the time of drying was slightly shorter (10% reduction, cf. Figure 5a), and the material attained a higher temperature (Tm) at the end of the process compared to pure convective drying (CV). \begin{table}
\begin{tabular}{c c} \hline \hline
**Name** & **Formula** \\ \hline [PERSON] & \(MR=\exp(-kt)\) (6) \\ [PERSON] & \(MR=\exp(-kt^{n})\) (7) \\ [PERSON]–[PERSON] & \(MR=a\cdot\exp(-kt)\) (8) \\ [PERSON]–[PERSON] & \(MR=a\cdot\exp(-kt^{n})+bt\) (9) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Methods applied for the estimation of experimental data [22]. Small kinetic advantages may result from the relatively high temperature of the drying agent (T\({}_{\text{a}}\) = 343 K). It was stated in respective literature that the magnitude of ultrasound's influence on enhancing the drying process depends on the process variables employed. It is maximized when using low temperatures and high ultrasonic power levels. It is usually explained by the changes in air density and stronger attenuation of acoustic waves at higher temperatures. Ultrasound has a greater influence on enhancing the drying process when both external and internal resistances are present. At lower drying temperatures, ultrasound enhances both externally and internally controlled drying behavior [16]. Analysis of the temperature curves revealed the occurrence of the \"heating effect\" of ultrasound. One can see that the temperature of the material (T\({}_{\text{m}}\)) exceeded the temperature of the drying agent (T\({}_{\text{a}}\)--Figure 2b) at the end of the process, which may be attributed to the thermal effect of the acoustic waves. Such a phenomenon was not observed for convective processes (CV), where the temperature of the material during the process increased asymptotically to the value of the temperature of the ambient air. The \"heating effect\" of ultrasound results from the conversion of mechanical energy carried by the waves into heat. The magnitude of this phenomenon depends on many parameters, both of the material (material structure, density, porosity, chemical composition, etc.) and the process type (temperature and air velocity, flow direction). Properties of materials may affect the action of ultrasound due to their influence on the attenuation factor. The higher the attenuation of ultrasound, the more the waves' energy is converted to heat, the greater the \"heating effect\". On the other hand, it was stated in [24] that the growth of temperature or velocity of air negatively affects the effectiveness of ultrasound enhancement, thus lowering the \"heating effect\". Moreover, the growth of material temperature induced by the \"heating effect\" is usually quite small (does not exceed 5-10 K), thus its influence on the overall temperature of the material decreases with the growth of temperature of the drying agent. In Figure 3, the evolution of the relative moisture content (MR) and temperatures of samples (T\({}_{\text{m}}\)) and drying agent (T\({}_{\text{a}}\)) obtained during the convective-microwave processes (CVMW1 and CVMW2) are presented. Application of microwaves during the convective process meaningfully influenced the kinetics of the drying operation (compare Figures 2a and 3). Drying times were significantly shortened in comparison to CV or even CVUS processes, and the magnitude of reduction depends on the power of the applied radiation. If the CV schedule is chosen as a reference process, then the drying time reduction equals 47% and 66% for PMW = 100 and 250 W, respectively (cf. Figure 5a).