3.1. Drying Characteristics
The drying curves of the walnut at different
IMCs and drying temperatures are shown in
Figure 2. As shown in
Figure 2, the
MCs of walnuts decreased gradually with the drying time, which was commonly observed for food and agricultural materials [
5,
21,
28,
38,
39]. It was found that as the
IMC was larger, the drying time was substantially longer, and the drying curves were flatter. When the
IMC was 0.35, 0.39, and 0.43 g water/g wet mass, the drying time at 50 °C was 1300, 1600, and 1950 min, respectively; the drying time at 60 °C was 1000, 1200, and 1500 min, respectively; the drying time at 70 °C was 800, 950, and 1250 min, respectively; and the drying time at 80 °C was 660, 800, and 1000 min, respectively (
Table 3). This is attributed to the different water removal required for walnuts with different
IMC [
19].
In addition, it was found that the drying time was significantly reduced with the increase in drying temperature. When the drying temperature increased from 50 °C to 80 °C, the drying time decreased from 1300 min to 660 min for walnuts with an
IMC of 0.35 g water/g wet mass, and the drying time decreased by 49.23%; the drying time decreased from 1600 min to 800 min for walnuts with an
IMC of 0.39 g water/g wet mass, and the drying time decreased by 50%; and the drying time decreased from 1950 min to 1000 min for walnuts with an
IMC of 0.43 g water/g wet mass, and the drying time decreased by 48.72% (
Table 3). The results indicated that the drying time was reduced by about 50% when the drying temperature was increased from 50 °C to 80 °C, regardless of the
IMC. This may be due to the increased kinetic energy and activity of water molecules in walnuts at high temperatures and the increased rate of water migration [
40].
The average temperature curves of the walnut at different
IMC and drying temperatures are shown in
Figure 3. As shown in
Figure 3, the average temperature of walnuts rises continuously with the drying time and maintains a stable value when it rises to a certain value. A hysteresis in the temperature curves was found in
Figure 3A–D, as it took a longer time for the preheating of walnuts with high
IMC than walnuts with low
IMC. This may be due to the fact that the specific heat of water is much higher than the dry mass of walnut, and the higher
IMC required more heat energy to evaporate, resulting in a slow increase in the temperature of the walnuts [
12]. It was found that the preheating time for walnuts decreased with increasing drying temperatures. This was attributed to the fact that higher temperatures provided more heat energy, thus reducing the preheating time [
29]. On the other hand, since the heat energy of the drying medium is transferred from the surface to the interior, the higher temperature resulted in large temperature gradients, thus accelerating the heat transfer [
18]. In addition, it was also found that the lag time for temperature changes became shorter as the temperature increased. Therefore, we considered that it should be applied with high temperature treatment at the early stage of drying to improve the heat transfer effect and the drying performance and then enhance the drying rate of walnuts.
As can be seen from the temperature curves, the walnut temperature was always lower than the drying temperature during the
HAD process. When walnut samples are placed in hot air, theoretically, the walnut temperature and drying temperature should be the same, but due to material moisture evaporation during
HAD, the surface temperature is lower than the air temperature. At the same time, moisture evaporation by heat after the
HA is properly cooled down during
HAD, allowing the
HA to reach the walnut surface on the way to heat diffusion. When the
HA reaches the walnut center position, the heat diffusion is the most serious, resulting in the center temperature always being the lowest. Similar behavior was observed for the
HAD of the almond, where the material temperature was lower than the drying temperature [
41].
The rate curves of the walnut at different
IMCs and drying temperatures are shown in
Figure 4. As shown in
Figure 4, the drying of walnuts occurred mainly in the falling-rate periods, which indicated that the walnut drying process is controlled by the internal mass transfer rate and the transfer mechanism is diffusion [
35,
40]. This drying rate curve is a typical drying behavior for food materials with porous structures or cellular structures, i.e., garlic [
42], brown rice [
43], apple [
44], wolfberry [
45], and cistanche [
46]. As can be seen in
Figure 3, the drying rate curve shows two falling-rate drying periods: the first and second falling-rate drying periods. In the first falling-rate drying period, the surface and internal free moisture of walnuts evaporated rapidly, resulting in a high drying rate. As the drying progressed, the drying evaporation zone gradually moved inward from the outside surface to the internal. This results in elongated inner moisture transfer paths, and therefore the drying rate dropped rapidly, indicating that the drying entered the second falling-rate drying period [
12,
40].
It can also be seen from
Figure 4 that the drying rates at the early drying stages increase with the increase in
IMC. During the drying process of the material, the dissipation of surface moisture and the diffusion of internal moisture occur simultaneously, but the drying rates at the early drying stages are mainly influenced by the rate of surface moisture dissipation [
13,
40]. Therefore, the larger the
IMC of walnut, the greater the surface moisture, and thus the greater the drying rates at the early drying stages. It was found that an increase in drying temperature could significantly increase the highest drying rate and average drying rate of walnuts (
Table 3). This is due to the high temperatures improving heat transfer and increasing the thermal energy absorbed by the walnuts, which in turn increases the drying rate [
29]. The highest drying rates increased from 0.00053 to 0.00084 g water/g wet mass/min for walnuts with an
IMC of 0.35 g water/g wet mass, from 0.00061 to 0.00116 g water/g wet mass/min for walnuts with an
IMC of 0.39 g water/g wet mass, and from 0.00075 to 0.00124 g water/g wet mass/min for walnuts with an
IMC of 0.43 g water/g wet mass, respectively (
Table 3). The combination of high
IMC and drying temperature leads to a significant increase in highest drying rates, reaching a peak of approximately 0.00124 g water/g wet mass/min.
3.2. Effective Moisture Diffusivity
Generally, the
Deff is employed and represents an internal moisture diffusion characteristics in the material since the limited information on the moisture movement mechanism during drying [
22]. It can be seen from Equation (9) that the natural logarithm of the moisture ratio (ln
MR) of walnuts during
HAD is linearly related to the drying time.
Figure 5 shows the changes of ln
MR of walnut with drying time under the drying condition. The
Deff were determined by linear regression, as shown in
Table 4.
In order to quantitatively analyze the effect of
IMC and drying temperature on the internal moisture diffusion characteristics of the walnut,
Figure 6 shows the variation of
Deff with
IMC and drying temperature. It was also found that the
Deff of the lower
IMC walnuts was generally higher than the higher
IMC walnuts. When walnuts with different
IMCs were dried to the same
MC, walnuts with higher
IMCs underwent a longer drying time and excluded more water, and water loss was controlled by more internal water diffusion, while internal water diffusion is much more difficult than surface water dissipation, resulting in smaller
Deff values [
19]. At the same time, for materials with a porous structure in their organization, the volume of pore shrinkage during drying is almost entirely used to compensate for the loss of moisture in the pores [
40]. As a result, higher
IMC walnuts have a greater degree of structural shrinkage, which in turn results in a more difficult diffusion of internal moisture. The results showed that walnuts with higher
IMC had a longer descending drying time, entered the internal control phase earlier, and were affected by internal diffusion control effects for a longer period of time. In addition, it was also found that as the drying temperature increased from 50 to 80 °C, the value of
Deff for walnut with an
IMC of 0.35 g water/g wet mass increased linearly from 6.82 × 10
−10~1.44 × 10
−9 m
2/s; the value of
Deff for walnut with an
IMC of 0.39 g water/g wet mass increased linearly from 5.85 × 10
−10~1.24 × 10
−9 m
2/s; and the value of
Deff for walnut with an
IMC of 0.43 g water/g wet mass increased linearly from 4.94 × 10
−10~9.98 × 10
−10 m
2/s (
Figure 6B and
Table 4). This is because the high temperature increases the thermal energy absorbed by the walnuts, which in turn enhances the diffusion of water molecules. Similar results were found for straw-based nutrient seedling-growing bowl trays in previous studies [
37].
Comparing
Figure 6A,B, drying temperature has a greater effect on the
Deff than the
IMC, which suggested that the
Deff is more sensitive to the increase in the drying temperature than to increases in the
IMC during the
HAD process of walnut. The values of
Deff found in this study were in the range of 4.94 × 10
−10 m
2/s to 1.44 × 10
−9 m
2/s, which is a typical range for drying of agricultural products [
5,
21,
22,
23,
24,
25,
28,
29,
31,
35,
36,
37,
46,
47,
48,
49,
50]. In order to quantify the effects of
IMC and drying temperature on the
Deff of walnut, a two factor relationship model of
Deff with
IMC and drying temperature was developed by multiple linear regression fitting analysis of the experimental data, as shown in Equation (21). The high value of the determination coefficient of the model (
R2 > 0.978) suggested the goodness of the regression fittings.
where,
Td was the drying temperature (°C).
3.3. Mass Transfer Coefficient
In order to quantitatively analyze the effect of
IMC and drying temperature on the mass transfer characteristics of the walnut,
Figure 7 shows the variation of
hm with
IMC and drying temperature. As shown, the value of hm decreased linearly with the increased of
IMC (0.35~0.43 g water/g wet mass) and increased linearly with the increased of drying temperature (50~80 °C). Comparing
Figure 7A,B, drying temperature has a greater effect on the
hm than the
IMC, which suggested that the
hm is more sensitive to the increase in the drying temperature than to increases in the
IMC during the
HAD process of walnut. Unsurprisingly, the higher the drying temperature, the faster the water molecules in the walnuts evaporate, thus the higher the
hm accordingly [
24]. As the drying temperature increased linearly from 50 to 80 °C, the value of
hm for walnut with an
IMC of 0.35 g water/g wet mass increased linearly from 1.45 × 10
−7~3.86 × 10
−7 m/s; the value of
hm for walnut with an
IMC of 0.39 g water/g wet mass increased linearly from 1.34 × 10
−7~3.90 × 10
−7 m/s; the value of
hm for walnut with an
IMC of 0.43 g water/g wet mass increased from 1.24 × 10
−7~3.17 × 10
−7 m/s (
Figure 7B).
In order to quantify the effects of
IMC and drying temperature on the
hm of walnut, a two factor relationship model of
hm with
IMC and drying temperature was developed by multiple linear regression fitting analysis of the experimental data, as shown in Equation (22). The high value of the determination coefficient of the model (
R2 > 0.973) indicated the goodness of the regression fittings.
3.4. Activation Energy
The activation energy is a crucial indicator in the end analysis of the drying process since it shows the difficulty of dehydrating under certain drying conditions [
51].
Table 3 displays the walnut average temperatures during the
HAD. These walnut average temperatures were employed in Equations (16) and (17) to research the temperature dependence of the
hm and
Deff. Specifically,
Figure 8A shows the plots of the natural log of
Deff (ln
Deff) versus the reciprocal of sample temperature (1/
T) for the
HAD experiments of walnut. The high correlation between 1/
T and ln
Deff under different
IMCs was obtained with linear models (
R2 > 0.99). From the line slope in
Figure 8A, the
ED values of walnut were calculated to range from 21.56 to 23.35 kJ/mol, with an average value of 22.73 kJ/mol.
Figure 8B shows the plots of the natural log of
hm (ln
hm) versus reciprocal of sample temperature (1/
T) for the
HAD experiments of walnut. The high correlation between 1/
T and ln
hm under different
IMCs was obtained with linear models (
R2 > 0.99). From the line slope in
Figure 8B, the
EH values of walnut were calculated to range from 28.92 to 33.43 kJ/mol, with an average value of 31.05 kJ/mol. The results show that the range of energy required to remove 1 mol of water from walnuts during drying is 21.56~33.43 kJ.
3.5. Lightness of the Walnut Kernel
The lightness of the kernel is one of the key quality indicators of dried walnuts. The lightness values of walnut kernels under different
IMC and drying temperature conditions are shown in
Figure 9, with lightness values ranged from 35.87 to 52.61. As shown in
Figure 9, drying temperature has a greater effect on the walnut kernel lightness than the
IMC, which suggested that the walnut kernel lightness is more sensitive to changes in the drying temperature than to changes in the
IMC under the
HAD. It can be found that lightness slightly increases and then decreases with increasing drying temperature. The darkening of the color of food materials during the drying process may be caused by both non-enzymatic and enzymatic browning reactions [
52,
53]. The walnuts are dried under low-temperature drying conditions for long periods of time, which leads to increased browning [
13]. The high temperature heating induced the Maillard reaction of amino acids and reducing sugar within walnut kernels and led to more non-enzymatic browning [
54]. Meanwhile, it was also found that the lightness values of kernels after drying of high
IMC walnuts were lower than those of kernels after drying of low
IMC walnuts. It is due to the fact that the high
IMC walnuts require longer drying times, resulting in a higher browning degree of the kernels [
19]. Additionally, the combination of high
IMC (0.43 g water/g wet water) and drying temperature (70~80 °C) results in a significant decrease in lightness. This indicates that the combination of higher
IMC and drying temperature can exacerbate the browning of the kernel during
HAD.
3.6. Kinetic Analyses on the Hot Air Drying Process
Moisture movement in food is a dynamic and complex phenomenon. Drying kinetics studies were necessary for assessing and optimizing the walnut drying process [
37,
55,
56]. The
MR obtained from the
HAD process of walnut was investigated by the mathematical models presented in
Table 2, and the model results are summarized in
Table 5. As shown, the mean value of
R2 for the Verma et al model is 0.99965, which indicated that the Verma et al model could be used to describe the walnut
HAD processes. Additionally, the mean values of
RMSE and χ
2 are 0.00441 and 0.00027, respectively, which are the minimum values, which could also indicated the Verma et al model was the best model to describe the drying processes. The values of drying coefficients and constants in the Verma et al model at different conditions are summarized in
Table 6.
In order to further characterize the effect of drying factors on the Verma et al model, the equations between the drying model constants (a, g, and k) and the drying factors were developed using regression analysis. The regression equations between the Verma et al model constants and the drying factors were as follows:
IMC was 0.35 g water/g wet mass:
IMC was 0.39 g water/g wet mass:
IMC was 0.43 g water/g wet mass:
To verify whether the Verma et al model can accurately predict the walnut
HAD process,
Figure 10 shows the comparison of experimental
MR and predicted
MR by the Verma et al model. According to the literature, if the curves of the experimental and predicted values are approximately at a 45° angle, it means that the predicted values represent the experimental values well [
37]. As can be seen from
Figure 10, the model of Verma et al showed a good agreement between experimental
MR and predicted
MR during the
HAD processes of walnut. These data points are banded line plots at an angle of approximately 45°, which suggests that the model of Verma et al is able to make good predictions of walnut
HAD processes under different drying conditions.