## 3 Results and Discussion  
The temperature of the sample and the ambient temperature were measured during the experiments. Figure 2 shows the graphs of the averaged measurement data obtained for a small cylinder as an example. All curves are similar in nature. The temperature of the sample decreases over time due to convective cooling. In the absence of ultrasound, the temperature of the sample decreases to the temperature of the cooling air. When ultrasound is used, the temperature of the sample tends to be higher than the temperature of the cooling air. This is due to the absorption of the acoustic energy by the sample. The greater the power of the applied ultrasound, the higher the final temperature of the sample. The curves presented in Figure 2 have been drawn in the range until the temperature stabilizes. As can be seen, increasing the ultrasound power results in faster temperature stabilization. The change between the process time without ultrasound and the process time with the low power of applied ultrasound (50 W) is particularly noticeable. Increasing the ultrasound power resulted in a decreasing of the gain of cooling rate. Figure 2: \(Cont.\)  
It is worth noting the increase in the standard deviation for the sample cooled with ultrasonic support with a power of 200 W. This is probably due to the very intensive mixing of the boundary layer of air in the vicinity of the sample, at the same time increasing heat exchange with the surrounding air. This phenomenon occurred in all shapes. For lower ultrasonic powers it is not so clear; however, a detailed analysis of the numerical values confirmed a larger standard deviation for ultrasonic tests. On the basis of the measured temperature, the dimensionless temperature was calculated in accordance with Equation (13), and then its natural logarithm was determined. Examples of calculated values of this logarithm for a small cylinder are shown in Figure 3 for the initial period of the process. All the results obtained were approximated by a linear function defined by Equation (20). The approximations obtained were very accurate as the coefficient of determination \(R^{2}\) ranged from 0.9994 to 0.9999. On the basis of the above approximations, the values of the slope of the straight line (Equation (20)) were obtained. Then, using Equation (21),  
Figure 3: Small cylinder dimensionless temperature versus time. Figure 2: The temperature of small cylinder versus time: (a) 0 W (no ultrasound); (b) 50 W (ultrasound); (c) 100 W; (d) 150 W; (e) 200 W.  
the values of the heat transfer coefficient \(h\) were calculated. The values obtained for the coefficient \(h\) for all four samples and all applied ultrasound powers are presented in Table 2.  
To check whether the assumption that the resistance to heat conduction within the sample is much lower than the convective resistance to heat transport to the outside of the sample, the values of Biot's number were calculated according to Equation (19). These values vary in ranges (0.003-0.017) for the cube, (0.006-0.029) cuboid, (0.005-0.028) cylinder, and (0.006-0.0.057) small cylinder. This means that in all series of experiments, Biot's number was small, so the assumption is correct. As can be seen, the use of a low power of applied ultrasound (50 W) results in a very strong enhancement of convective heat exchange, from more than two times (cuboid) to almost five times (small cylinder). Further increase in ultrasound power results in improved heat transfer. [PERSON] and [PERSON] [40] present similar results obtained for forced convection. In that case, it was obtained that in the tested range, the increase in the heat transfer coefficient was a linear function of the applied ultrasound power. However, in the case of free convection, increasing the ultrasound power does not result in a linear increase in the heat transfer coefficient. In Figure 4, all the results obtained have been approximated by a function with the general equation.