**5. Drying kinetics**

This section presents the mathematical formulation of important drying parameters including moisture content, moisture ratio, moisture diffusivity, activation energy, and various thin-layer mathematical model.

*Assessment of Solar Dryer Performance for Drying Different Food Materials: A Comprehensive… DOI: http://dx.doi.org/10.5772/intechopen.112945*

**Figure 5.**

*Schematic of the mixed-mode solar dryer [14].*

**Figure 6.** *Schematic of the hybrid-mode solar dryer [12].*

The moisture content (MC) of a drying product refers to the amount of moisture or water present in the product, expressed as a percentage of its total weight, as presented in Eq. (1), [30].

$$\text{MC} = \frac{m\_w - m\_d}{m\_w} \tag{1}$$

Where, *mw* is the mass of the drying product before drying and *md* is the mass of the dried product.

Activation energy is a crucial concept in the realm of drying products, denoting the energy required to initiate and propel the drying process [31]. This context refers explicitly to the energy necessary to surmount the molecular forces that bind water molecules to the product's surface, thus enabling their evaporation. This activation energy measures the minimum energy essential for the drying process to occur at a noteworthy rate. It is important to note that the activation energy is unique to the material undergoing drying and the specific drying conditions applied. Different materials and various drying methods may exhibit distinct activation energies. Empirical investigations are typically carried out to ascertain this value, involving the study of drying kinetics for the material at different temperatures.

Another fundamental property relevant to drying processes is moisture diffusivity. This parameter describes the rate at which moisture traverses a drying product during the drying procedure [31]. Understanding moisture diffusivity is paramount in modeling and comprehending the drying kinetics of diverse materials. The moisture diffusivity factor represents the capability of water molecules to move through the product's microstructure, and its value is influenced by several factors, including temperature, humidity, and the inherent nature of the material being dried. To determine the moisture diffusivity experimentally, the moisture content is measured at various locations within the drying product over time. The acquired data is then fitted into appropriate mathematical models, such as Fick's second law of diffusion, enabling the calculation of the diffusivity coefficient [13].

The diffusion mechanism governs the drying process of food substances at the rate of falling period. Fick's second law of diffusion governs effective moisture diffusion [30].

$$
\ln{MR} = \ln{\left(\frac{8}{\pi^2}\right)} - \frac{\pi^2 D\_{eff} t}{L^2} \tag{2}
$$

MR is a moisture ratio, and it represents the ratio of the current moisture content of the product to its initial moisture content. Deff is an effective moisture diffusivity (m<sup>2</sup> /s), t is the corresponding drying time (hrs), and L is the thickness of the drying sample (m). The slope of the ln MR with respect to time can be written as Eq. (3),

$$slope = \frac{\pi^2 D\_{\text{eff}}}{L^2} \tag{3}$$

$$MR = \frac{M\_l - M\_\epsilon}{M\_0 - M\_\epsilon} \tag{4}$$

Where *Mt*, *Me*, and *M*<sup>0</sup> are the instantaneous, equilibrium, and initial moisture content, respectively.

*Assessment of Solar Dryer Performance for Drying Different Food Materials: A Comprehensive… DOI: http://dx.doi.org/10.5772/intechopen.112945*

The diffusion of moisture during drying can be described as Eq. (5) by Fick's second law of diffusion as equation [13],

$$D\_{\sharp f} = D\_0 e^{\left(-E\_{\ast} \otimes T\right)} \tag{5}$$

Where *D*<sup>0</sup> is the diffusion factor (m<sup>2</sup> /s), *Ea* is the activation energy (kJ/mol), R is the universal gas constant (8.314 kJ/mol.K), and T is the temperature (K). The plot of ln *Deff* against 1/T gives a straight line of slope k where the relation between *Ea* and diffusivity coefficients can be defined through linear regression analysis and activation energy *Ea* is evaluated by Eq. (6),

$$k = \frac{E\_a}{R} \tag{6}$$

The thin-layer drying model is a mathematical representation that describes the drying kinetics of a material during the drying process [30]. It assumes that the drying occurs within a thin-layer on the material's surface and considers the moisture transfer from this layer to the surrounding drying medium (usually air) [32]. Several thinlayer models have been proposed over the years. The important thin-layer model is presented in **Table 3**.
