Raw materials adopted for the present study were fresh tea leaves, one bud with two leaves, or one bud (Varieties “Fuyun No.6”), which were purchased from a local farmer in Shaoping County, Guangxi Zhuang Autonomous Region.

Since the moisture content of fresh tea was commonly 72–73%, sample preparation for drying experiments required a series of pretreatments before drying. (1) Fresh tea leaves: one bud and two leaves, undamaged. (2) Withering: the tea leaves were spread on the withering board and placed in a calm and ventilated place; the ambient temperature was 8–20°C, and the withering time was 16 h. (3) Rolling: The length of the kneading operation was 60 min. (4) Fermentation: the tea leaves were placed on the fermentation board after kneading, and the pile of leaves was 5–12 cm thick. It was put in a constant-temperature and constant-humidity environment, in which the temperature was 25°C, the humidity was 90%, and the duration of the fermentation time was 10 h. Tea leaves at the end of fermentation were used for drying test.

The test equipment selects a laboratory-grade blast type constant temperature hot air drying oven; the model is shown in Figure 1. The working principle of the blast type constant temperature drying oven includes setting the target temperature, the blower at the bottom of the drying chamber introduces the outside natural air into the drying chamber, and heats the materials in the drying chamber, the exhaust air is discharged from the rear exhaust port at the upper end of the drying chamber, and the air velocity is 1.26 m/s, measured by the anemometer, and the parameters in the drying chamber are displayed in real time by the anemometer. A paperless recorder displays the parameters in the drying chamber in real time. The sample preparation and test procedure are shown in Figure 2. The ambient temperature of the test is 8–20°C, and the humidity of the air is 60–70%, which is in line with the working environment conditions of the blast constant temperature drying oven.

Preheating the drying cabinet before conducting the drying experiment is to reduce the impact of the thermal inertia on the drying experiment (Zeng et al., 2022). A laboratory scale constant temperature hot air cabinet drier was applied to conduct the drying experiment with the hot air temperatures of 70°C, 80°C, and 90°C. The fermented tea sample was spread with the thickness of the thin layer of 10 mm, 15 mm, and 20 mm in food grade circular trays (note: diameter of trays is 200 mm) and placed on a cabinet drier for drying experiment. The initial moisture content of each experimental group was determined by adopting a halogen lamp moisture detector. An electronic precision balance was applied to measure the weight of the sample during the drying process with an interval of 5 min. Until the error between two consecutive weightings was less than 0.1 g (moisture content of less than 5%), the present group of the drying experiment was over. Each set of the above tests was repeated three times, and the recorded data were averaged. The detailed information on the relevant equipment used in the present study is shown in Table 1.

The calculation of MR can be adopted from a moisture diffusion model developed by Crank, (1979) based on Fick’s Second Law, which is expressed in Equation (3):

where D_eff is the effective moisture diffusivity, and l_t is the half thickness of thin layer (Dehghannya et al., 2018).

The drying of materials requires a longer time, the Equation (3) above can be abbreviated as Equation (4) follows:

Taking the Equation (4) to logarithm and can be simplified into linearization as shown in Equation (5), and fitting the ln (MR) with drying time (t) to obtain the slope of the linear equation and further estimate the moisture diffusivity (k), detail Equation (6) as shown in following:

where k denotes the slope.

The relationship between moisture diffusivities and drying air temperature were indicated by Arrhenius relationship as shown Equation (7), expression of following Equation (8) was linearized from Arrhenius relationship and plotted it to determine the slope and y-intercept, further to obtain the activation energy of tea and pre-exponential factor (Midilli and Kucuk, 2003).

where E_a refers to the activation energy of tea, R_a refers to the ideal gas constant, T_abs refers to the kelvin temperature, and D₀ refers to the pre-exponential factor.

In the present study, energy consumption for the convective dryer includes energy of thermal and electrical, can be calculated using Equation (9):

where P_dryer indicates the power of the dryer, and ∆t means interval time for data collection.

Specific energy consumption (SEC) for drying the unit mass (1 kg) of the drying tea sample can be calculated by the following equation (Yahya et al., 2016):

Except for the parameter of SEC, specific moisture extraction rate (SMER) is also a significant parameter to depict the drying characterization, which is defined as per unit energy required to evaporate the moisture. SMER is expressed as the following equation (Ibrahim et al., 2015):

In addition, another parameter to describe the efficiency of the energy consumption of the drying system is the efficiency of the drying process, defined as the ratio of the energy utilized usefully to remove the moisture content from the materials to the total energy, which is calculated by the following equation:

where h_fg refers to latent of vaporization with a value of 2.26 kJ/kg.

Unlike energy, which denoted “quantity,“exergy was defined as the “quality” of energy, indicating the most significant amount of usable work input in the drying system as the system reached equilibrium with the surrounding environment. Electricity is the primary source of energy employed in this endeavor. Since the total beneficial work of the dryer in the current study can be estimated, the Equations (13–20) utilized is shown in Table 2.

The heat and mass transfer coefficients for thin layer drying of tea can be obtained via dimensionless numbers, such as the Nusselt number, Sherwood number, and Schmidt number. Accordingly, the calculation depicted the correlations for dimensionless as following Equations (18–20) to estimate the heat and mass transfer coefficients for thin layer drying of tea.

Thin layer drying models have been conducted in scientific studies to describe the drying characteristics of the materials during the drying process based on Fick’s Second Law of moisture content by previous researchers (Azizpour et al., 2014). In the present study, the most commonly used classic thin layer models, Equations (30-34) as shown in Table 3, were selected to fit experimental MR to depict the drying curves. Applied the data processing software of Origin 2023b (Student Free Trial Edition) to fit experimental MR with the thin layer model and adopted the coefficient of determination (R²) and Chi-Square (χ²) along with drying kinetic factors to evaluate the goodness-of-fit of the drying curve and determine the best descriptive model. Corresponding calculations of R² and χ² have been given as follows Equations (28-29):

where,

R² is the coefficient of determination;

MR_{exp, i} is the experimental moisture rate;

MR_pre,i is the predicted moisture rate;

M R ¯ exp , i is the mean experimental MR;

χ² is the chi-square;

z is the number of parameters.

The impact of the relationship between different drying temperature and different tea layer thickness and tea moisture rate is shown in Figure 3. As the result shown that increasing drying temperature and keeping the thin layer thickness unchanged, or keeping the temperature constant decreasing the thin layer thickness can significantly to accelerate moisture transfer, decreasing drying time and improving drying efficiency simultaneously. Taking Figures 3A,B for instance, when thin layer at the same thickness of 10 mm and at the drying temperature of 90°C, 80°C, and 70°C, time required for the experimental group to complete drying was 45 min, 65 min, and 85 min, respectively. Similarly, completing the drying process need to consume 40 min and 55 min at 10 mm and 15 mm thickness under the same temperature of 80°C. Therefore, it can be also put in the other word, lower thickness thin layer and higher drying temperature may be providing an environment exist pressure difference to develop driving force of the moisture content migration to accelerate migrating rate of the moisture content result in rapid moisture content evaporation. Similar study in tobacco leaves have been reported (Chen et al., 2019).

The entire drying process under various temperatures and drying lamella thickness conditions is shown in Figures 3C,D. At the start of drying, the rate of drying stays high. On the other hand, when the drying temperature rises, or the drying layer thickness decreases, the drying rate gradually increases. Furthermore, the data shown in Figure 3D support the idea that the drying rate increases with decreasing drying layer at a given drying temperature throughout the drying process. The reason is that a higher temperature or lower thickness of the layer can encourage the migration of internal moisture to the material’s surface and accelerate the evaporation of free water from the material’s surface. As the drying process progresses, the drying rate for all drying conditions decreases as the moisture content of the material decreases. This is because most of the water in the material at the later drying stages is bound to water with a specific binding force with the internal material, which is difficult to migrate and evaporate, resulting in a lower drying rate. Similar trends in drying rate and moisture content have also been reported (Varhan et al., 2019; Khan et al., 2021).

Moreover, Figure 3D shows the variation curve of the drying rate with moisture content at 20 mm thickness. The reasons for generating the zig-zag pattern plot are as follows: First, the drying process is carried out in a constant temperature drying chamber, and the fluid inside the drying chamber is pressurized by a fan that applies pressure to pressurize the drying air to flow from the bottom to the top and out of the drying chamber, and the moisture is taken away by the hot air as it flows out. This study collected more data because the drying process is more complicated and takes longer at 20 mm thickness. The large thickness of the material, and the high drying temperature may lead to the removal of water through the material layer, there is a repeat humidification, resulting in large fluctuations in the drying rate, and the higher the moisture content of the fluctuation is more significant, in Figure 3D at the horizontal coordinate of the stage of 0.4–1.0 characterizes the stage of the higher moisture content. It can also be observed that the smaller the thickness, the less the secondary humidification, the flatter the curve, and the larger the thickness, the larger the fluctuation; this is the reason why the zig-zag plot is not generated at 10 mm thickness because it does not have the secondary humidification. Second, the moisture content in the process of tea drying is in the state of non-linear change, when the slight change in moisture content will cause the drying rate to exist an inevitable fluctuation due to the existence of systematic errors in the test process, including the measurement error of the weight of the samples and the error of the sensor. In conclusion, the overall trend of the curve is that the drying rate decreases gradually with the decrease in moisture content, which has proven the drying rate of tea in the drying process with the change in moisture content, and at the same time proved that the thickness of the tea spreading would also have a specific effect on the drying rate.

The present study was applied five thin layer model, namely, Lewis model, Logarithmic model, Page model, Modified Page model, and Wang & Singh model, to perform non-linear fitting on the moisture content measured in the experiment. The statistical parameters, coefficient of determination (R²) and chi-square (χ²) given by the calculation Equations (7, 8), were adopted to evaluate the goodness of fit to the model curve. Since existed multiple group experiments that calculate the average value of coefficient of determination (R²) and chi-square (χ²) and selected the group with the highest average value of R² and the lowest average value of χ² to determine the appropriate model, detailed values of statistical parameters are presented in Table 3 (Madamba et al., 1996; Mishra et al., 2021).

As shown in Table 4, within the five models, the logarithmic model had excellent performance in fitting the experimental moisture content, with the highest average value of R² and the lowest average value of χ² being 0.99877 and 8.80 × 10–5, respectively. Therefore, in the following analysis of drying behavior, the logarithmic model was the best option in the present study. Results of the fitting coefficient of the Logarithmic model fitting experimental data are shown in Table 5. In addition, with the further and careful observation can clearly reveal that under the condition of low drying temperature (experimental group with 70°C), model constant act out certain assured of correlation with the drying temperature and thickness of thin layer. However, this correlation was not observed under the drying temperature of 80°C and 90°C. Similar observation has reported by previous studies for drying plant porous materials, such as vegetable and fruits (Brar et al., 2020; Mishra et al., 2021).

To assess the accuracy of the logarithmic model, Figures 4A–C display the linear correlations between the experimental moisture content and the moisture content predicted by the model. Under the same thickness (selected 15 mm as an example to demonstrate), the coefficient of determination (R²) for drying temperature of 70°C, 80°C, and 90°C was 0.99882, 0.99872, and 0.99687, respectively. Meanwhile, the above results further indicate that the Logarithmic model was suitable for describing the drying characteristics.

The original intention of development of many theories of effective moisture diffusivity in drying process was to describe the phenomenon of moisture content diffusion. To obtain the effective moisture diffusivity, the slope of the line plotted by fitting the natural logarithmic of moisture rate with drying time should be obtained first. As shown in the following Figures 4D–F, the linear relationship plotted between natural logarithmic of moisture rate and drying time under conditions of drying temperatures and thin layer thickness, the value of the coefficient of determination (R²) acquired from 0.96499 to 0.98913, and the slope can be further calculated. Description in Figures 4D–F can be obvious to observe that the natural logarithmic of moisture rate was performance downward trend, especially at the same thickness higher the temperature with the faster the decrease. Similar findings also have been reported in a few studied works on drying dynamics of agricultural products (Doymaz, 2017). Immediately after, effective moisture diffusivity can be calculated based on the Equation (6) mentioned above and listed the result in Table 6. At the same level of drying temperature, the effective moisture diffusivity presented an increasing trend accompanied by the thickness of the dry thin layer increases. Similar detection was also found expression in the same level of thin layer thickness that the water diffusion coefficient increases with increasing temperature. For example, with the condition at 70°C drying temperature, the effective moisture diffusivity of the 10 mm, 15 mm, and 20 mm thin layer thicknesses was 4.4969 × 10⁻⁷ m²·s⁻¹, 6.8875 × 10⁻⁷ m²·s⁻¹, and 1.0222 × 10⁻⁶ m²·s⁻¹, respectively. Similarly, at the level of thickness at 10 mm, the maximum effective moisture diffusivity was found at the level of drying temperature at 90°C, minimum effective moisture diffusivity appeared at the level of drying temperature at 70°C. Therefore, it can be taken as a deduction that increasing the thickness and drying temperature of the drying thin layer can increase the internal pressure of the drying thin layer and improve the activity of water molecules of the material contributed to increase the diffusion of moisture and further to improve the drying rate. This deduction was confirmed from previous some other similar studies reported for carrot slices (Susanti et al., 2021) and red sorghum (Dehghannya et al., 2019).

The activation energy can also be calculated using a method similar to that used to calculate the effective moisture diffusivity. Applied the value of effective moisture diffusivity obtained above and plotted linear correlations between them against the reverse of the values of absolute drying temperature, as shown in the following Figure 5. Therefore, the activation energy value is determined by solving the slope of the linear correlations, as shown in Table 6. As shown in Table 5, in the present study, the activation energy values for the thickness of 10 mm, 15 mm, and 20 mm were 18.187 kJ mol⁻¹·K⁻¹, 22.344 kJ mol⁻¹·K⁻¹, and 14.030 kJ mol⁻¹·K⁻¹, respectively. The results obtained in this study can be considered reasonable due to a few relevant literature studies have cited that activation energy of vegetables and other plant-based materials ranged from 12.7 to 110 kJ mol⁻¹·K⁻¹. Meanwhile, Luthra and Sadaka pointed out that there is no significant correlation between the increase in grain layer thickness and activation energy, which can also explain the result where the activation energy of moisture does not show a certain correlation with drying temperature and thickness obtained in this study (Luthra and Sadaka, 2021).

The energy–exergy performance indicators, including specific moisture evaporation rate, specific energy consumption, energy efficiency, exergy efficiency, improvement potential rate, and sustainability index during the drying process, were calculated using the equations shown in Table 2 and presented as the average value of each indicator in Table 7 for convenient analysis.

In the present study, the results of dimensionless numbers, including Reynolds number, Prandtl number, Nusselt number, Schmidt number, and Sherwood number, are obtained according to Equations (21–27), as presented in Table 8. Additionally, the results of the heat and mass transfer coefficients are shown in Figure 6. As presented in Figures 6A,B, the heat transfer coefficient and mass transfer coefficient show a similar trend with changes in drying temperature and thickness. At the drying condition in the same level drying temperature, both heat and mass transfer coefficient showed a significantly opposite correlation with the thickness of the thin layer, whereas there was no significant change observed with different levels of drying temperature at the same level of drying thickness. Higher moisture content and thinner thickness in the early stages of drying process are beneficial for tea to heating up and accelerate the evaporation rate of moisture content which may be reasonably explained the above phenomenon of heat and mass coefficient. In addition, the water migration has a greater resistance reduced the drying rate and thus lowers the heat and mass transfer coefficient as the moisture content is lower at the later stage of drying process. Similar findings have also been reported in several literature studies (Kamali et al., 2021).

Description of Figure 6 can be only observed the variation of heat and mass transfer coefficients with drying temperature and thin layer thickness from an apparent level. In an effort to take a clearer and more intuitive knowledge of relationship of the heat and mass transfer coefficient and drying temperature and thin layer thickness, the multivariate linear regression method was applied to give the functions for the relationship between mass transfer coefficient and drying temperature and thin layer thickness. The functions were written as Equations (35, 36), respectively, with corresponding R² values of 0.967 and 0.951. The functions confirm the finding that heat and mass transfer coefficient is negatively correlated with the drying temperature and thin layer thickness. Moreover, the conclusion is drawn that the mass transfer coefficient is positively correlated with temperature and the heat transfer coefficient is negatively correlated with drying temperature. It should be noted that the heat and mass transfer coefficients in this study represent average values under a single drying process at different temperatures.