**4.3 Thermic behavior analysis**

In order to perform the thermal analysis on the apple and tomato samples, a multiphysical analysis is performed in which the energy produced in the food samples by the ultrasound waves is used to obtain the temperature change in each of them during a dehydration time of 40,000 seconds. To perform the thermal analysis of the ultrasound-assisted convection dehydration system, the following steps are established:


variable values ! settings ! user-controlled ! method ! solution ! study ! study in frequency ! frequency parameter value ! selected according to the optimum operating frequency for each food ! compute. In this way, the simulation environment will be able to give the approximation of the temperature change in the food samples as a function of the frequency that is radiating them.

5.*Results:* to visualize the results obtained, simply select the results option and the temperature contour graphs of the dehydration system and the temperature rise curve for each food sample will be displayed. Thus, the thermal analysis according to the optimum operating frequency of the dehydration chamber is finished.

Using the above steps, we can determine the temperature change in the dehydration system. Note that the food mass should not exceed 70°C. This temperature limit is given according to Michelice and Ohaco [53] in their guide to food dehydration and drying, and as experimentally proven by Tao *et al.* [54] in their tests carried out in the dehydration of blackberries. This temperature has been established since the use of higher temperatures may cause structural and nutritional damage to foods. For this purpose, simulation runs must be performed by varying the ultrasound waves pressure until the food samples temperature do not exceed 70°C.

For the first case study, **Figure 7** shows the thermal analysis performed on the five levels of apple samples at 34 kHz, 80 kPa, and an initial temperature of 60°C. **Figure 7a** shows the isothermal curves generated inside the dehydration system after 40,000 seconds. **Figure 7a** shows the effect of ultrasound waves radiation on food samples. Note that the food samples closest to the piezoelectric transducer reaches a maximum temperature of 70.8°C, while the other samples have minimal increases in temperature. The temperature change in the apple samples is shown in **Figure 7b**. Note that the first food samples have the greatest influence on their temperature change. It should be noted that in **Figure 7b** each food sample is denoted with its Cartesian coordinates (x,z) within the system, being so for the first sample (0, 6.7), the second (0, 9.7), the third (0, 12.7), the fourth (0, 15.7), and the fifth (0, 18.7).

**Figure 7.** *Temperature of the apple samples radiated with a piezoelectric transducer.*

*Acoustic and Thermal Analysis of Food DOI: http://dx.doi.org/10.5772/intechopen.108007*

#### **Figure 8.**

*Temperature of the tomato samples radiated with a piezoelectric transducer.*

Similarly, **Figure 8** shows the temperature changes of five tomato samples radiated with ultrasound waves using a piezoelectric transducer at 70 kHz and 22 kPa for 40,000 seconds. **Figure 8a** shows the isothermal curves inside the dehydration system, in which it is observed that the first and second samples have a significant increase in temperature reaching a maximum of 70.1°C, while the other samples have smaller temperature changes. In **Figure 8b**, these temperature changes can be better observed from the curves plotted as a function of time.

However, **Figure 9** shows the temperature change of the apple samples radiated with ultrasound waves using three piezoelectric transducers at 34 kHz, 52 kPa, for 40,000 seconds. Note that the maximum temperature reached was 70.2°C. **Figure 9a** shows the isothermal curves generated after 400,000 seconds in apple samples located at the five levels are more homogeneous compared to the isothermal curves in **Figure 7a**. These temperature changes are more visible in **Figure 9**. These curves show that all the apple samples have a significant temperature change due to the ultrasound waves radiation and that the difference between each of them is not so large compared to those obtained for a single transducer in **Figure 7**.

**Figure 10.**

*Temperature change of tomato when radiated with three piezoelectric transducers.*

Now, the temperature change in the tomato samples radiated by ultrasound waves using three piezoelectric transducers at 70 kHz and 5 kPa during 40,000 seconds is shown in **Figure 10**. Note in **Figure 10a** that the isothermal curves for the tomato samples show homogeneous temperature changes reaching a maximum temperature of 70.8°C. These temperature changes in the tomato samples are more evident in **Figure 10b**. Note the temperature increase on five levels of food samples occurs to a greater extent when radiated with three piezoelectric transducers than if the samples are radiated with a single transducer as shown in **Figure 9b**.

From the thermal-acoustic analysis performed, it is possible to highlight different aspects that are relevant at the moment of designing a convection dehydration system assisted by ultrasound waves: (a) the distribution of the acoustic field produced by the ultrasound waves depends on the frequency, the number of transducers and the dimensions of the dehydration chamber, (b) the increase in the temperature of the food samples is a function of the frequency and pressure with which the samples are radiated, and (c) it is possible to radiate more than one sample simultaneously within the same dehydration chamber placed at different distances from the radiation source. Thus, in this way, it is possible to give an approximation of the thermo-acoustic behavior of different foods within the processes of dehydration by convection assisted by ultrasound waves.
