**3. Case studies**

In order to study the ultrasound waves behavior and their thermal effects on apple and tomato samples, we proposed an ultrasound-assisted dehydration system based on the forced convection dehydration system shown in **Figure 1** considering two case studies. In the first case study, represented by **Figure 2a**, we used one piezoelectric

**Figure 1.** *Ultrasonic dehydration chamber.*

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

#### **Figure 2.**

*Proposed geometry for the thermo-acoustic simulation when apples and tomatoes were dehydrated using: (a) one PZT, and (b) three PZT's.*

transducer of size (0.5 cm 4 cm). In the second case study, represented by **Figure 2b**, we use three piezoelectric transducers as the first case study. Considering a transversal cut at (*x*, *z*)-plane, note in **Figure 2** that the dehydration system has a (27 cm 20 cm 20 cm)-chamber composed of five gridded trays spaced 3 cm from each other, an electronic module to regulate the dehydration temperature, an ultrasound waves generator, and up to three piezoelectric transducers placed at the dehydration chamber base.

In both case studies, we consider 0.5 cm-thick apple and tomato plates placed in the five gridded trays and assumed that the dehydration chamber is in equilibrium conditions at a temperature of 60°C. From the geometries proposed in **Figure 2**, and considering that the simplified geometry of the dehydration chamber derived by the transversal cut at (*x*, *z*)-plane can help to simplify the thermo-acoustic analysis of the proposed system, we show an example of the FEM simulation results for both case studies considering the effects of the ultrasound waves on apple and tomato when a conventional convection dehydration system is used.

### **3.1 Food composition and properties**

In order to perform a thermal and acoustic FEM analysis for apple and tomato inside an ultrasonic-assisted convection dehydrator, in **Table 2**, we summarize the


#### **Table 2.**

*Thermo–acoustic parameters of apple and tomato.*

physical parameters of apple and tomato, such as density, sound propagation velocity, heat capacity, thermal conductivity, and sound absorption coefficient [36–39].

For the acoustic and thermal analysis for the apple and tomato, we defined the parameters shown in **Table 2** in order to determine the dynamics produced by the drying chamber in the apple and tomato. We should emphasize that if any of these parameters are omitted, the FEM analysis cannot be performed properly and the spatial and temporal dynamics will have a significant error since acoustic and thermal phenomena are completely interrelated.

#### **3.2 Acoustic waves and piezoelectric transducers**

Firstly, a wave can be defined as the energy and momentum transfer from one point in a medium to another point in the same medium without net matter transport between the two points [40]. When the waves require a medium for their propagation are called mechanical or elastic waves [41]. In this case, the medium particles perform a periodic motion around a mean position as the wave propagates through the medium. A mechanical wave is produced when a particle is perturbed in the propagating medium and interacts with the neighboring particle and its energy is transmitted to the next particle (due to the inertia of the medium) [42]. The perturbed particles return to equilibrium due to the medium elasticity after a finite time. Thus, when the mechanical wave motion is produced the following parameters must be considered: frequency, propagation velocity, period, phase, and wavelength.

On the other hand, the piezoelectric transducer is an important component of ultrasound instrumentation systems [43]. Piezoelectric transducers convert electrical waves into mechanical vibrations and mechanical vibrations into electrical waves [44]. These devices are mainly used to generate waves in the ultrasound range (frequencies higher than 20 kHz) at low, medium, and high intensity. Piezoelectric transducers can be produced by using ceramics, quartz, Rochelle salts, and metal alloys to be used in ultrasound wave generators applicable in multiple industrial areas [45]. For example, drying, ultrasonic cleaning, fuel oil injection into burners, and medical treatments, among others.

#### **3.3 Simulation environment**

To describe the acoustic and thermal behavior of apple and tomato in the proposed dehydrator, COMSOL Multiphysics*™* has been chosen as the simulation environment, which is a software tool for finite element analysis useful in various physics and engineering applications, especially for couple or multiphysics phenomena [46]. The possibility of analyzing different physical phenomena integrated into COMSOL Multiphysics*™* allows the user to model and analyze scenarios involving multiple interacting physical phenomena. The phenomena that can be modeled in COMSOL Multiphysics*™* are related to acoustics, electromagnetism, micro-electromechanical systems (MEMS), microwaves, radio frequency components, semiconductor devices, and wave propagation, among many others. In this work, the acoustics and heat transfer modules have been used to perform the acoustic and thermal analysis of the proposed system.

The finite element method is based on dividing the body, structure, or domain over which the equations characterizing the phenomena physical behavior are defined into subdomains called finite elements [47]. The finite elements set forms a domain partition also called discretization or mesh. Due to the subdivisions generated in the geometry, the mathematical equations that govern the phenomena physical behavior

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

could not be solved in an exact way, but in an approximate way, since the solution that results in the simulation environment depend on the nodes and elements number, as well as of the elements size and type defined in the mesh [48]. From the approximation provided by the solution of the equations describing the desired physical phenomenon from the generated finite elements, it is possible to describe the desired system behavior.

Using a COMSOL Multiphysics*™* simulation environment and the FEM, the acoustic and thermal analysis of the proposed system for apple and tomato has been performed from the geometry shown in **Figure 2**. Additionally, we have used the mathematical models developed in Subsection 4.1, and we have shown the obtained results in Subsections 4.2 and 4.3.
