# Modeling and Optimization of Energy and Exergy Parameters of a Hybrid-Solar Dryer for Basil Leaf Drying Using RSM

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## Abstract

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## Highlights

- An exergy and energy analysis during basil leaf drying is performed.
- Factors investigated include drying rate, energy utilization, energy utilization ratio, exergy efficiency, exergy loss, improvement potential rate, and sustainability index.
- Exergy efficiency varied in the range of 31.78–86.55%.
- The optimal conditions for basil drying were at an air temperature of 63.8 °C and a bed thickness of 2 cm.

## Abstract

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Preparation of Sample

#### 2.2. Drying Equipment and Empirical Method

^{3}. In this type of dryer, the frame of the solar collector was made of aluminum and black aluminum sheets with air-conducting blades to absorb sunlight. The solar collector was inclined at 34° from the horizontal, with 1.20 m of length, 1 m of width, and 0.07 m of internal height. In addition, a 1000 W electric element heated the inlet air of the dryer chamber, which could be varied by a fan located inside the collector. To measure the velocity of the air entering the dryer chamber, an AVM-07 vane velocity meter made in Taiwan with a measurement accuracy of 0.1 m/s was used. There was also an air outlet at the top of the solar drying chamber to direct the air outside. Additionally, five LM75 sensors (Sigma-Delta, Ann Arbor, MI, USA) with a measurement accuracy of −55 °C to 125 °C (±2 °C), and two HS101 sensors (model HS1101, Apollo Electronics Co., Ltd., Guangdong, China) with a measurement accuracy of ±2% were applied to measure the air circulation temperature and relative humidity, respectively. During the experiments, the solar radiation that reached the absorber plate was in a range between 36–49 MJ/m

^{2}, while the relative humidity and the temperature of the ambient air were 17 ± 2%, and 30–35 °C, respectively. Moreover, the relative humidity of the air leaving the dryer was 55% at the beginning of the test and 15% at the end of the process.

#### 2.3. Data Analysis

#### 2.3.1. Moisture Ratio and Drying Rate Analysis

#### Energy Utilization

#### Energy Utilization Ratio

#### Exergy Evaluation

#### 2.3.2. Experimental Design and Statistical Analysis

^{2}), adjusted regression coefficient (Adj-R

^{2}), predicted regression coefficient (Predicted-R

^{2}), and analysis of variance (ANOVA) with statistical and response plots were used to analyze the results and evaluate the significance and accuracy of the model. The specific RSM was used and evaluated in relation to the actual data along with the corresponding F and p values at the 95% confidence level.

_{1}), exergy improvement potential rate (d

_{2}) sustainability index (d

_{3}), and drying rate (d

_{4}), and to minimize the exergy loss rate (d

_{5}), energy utilization (d

_{6}), and energy utilization ratio (d

_{7}) to perform the optimization process.

## 3. Results and Discussion

#### 3.1. The Influence of Air Temperature and Bed Thickness on the Drying Rate

#### 3.2. Drying Rate

^{2}) and (p-value < 0.0030) for the bed thickness (B

^{2}), were significant, and this was in a good agreement with the results of Karami et al., [7]. In Table 3, the results of the lack of fit were not significant (p ≥ 0 0.05). The drying results showed no significant lack of fit, indicating that the model was well fitted. Based on the coefficient of variation (CV) of 2.35%, it can be seen that the selected model has a good signal-to-noise ratio and can be used to move around the design space [23].

^{2}value (0.9964), predicted R

^{2}(0.9640), adjusted R

^{2}(0.9939), and PRESS (0.0015) was the best model for the drying rate. Additionally, the cubic model was considered to be over fitted compared to the other evaluated models.

#### 3.3. Energy Utilization

^{2}and B

^{2}) were 0.0003 and 0.0047, respectively. This shows that these parameters had a significant effect on the response of the energy utilization at a confidence level of 95% (p < 0.05) (Table 5).

^{2}(0.9960), adjusted R

^{2}(0.9931), predicted R

^{2}(0.9598), and a value of PRESS = 0.0000 was significant at p < 0.01. The selected model had a good fit with no significant lack of fit. The difference between the predicted and adjusted R

^{2}values was less than 0.20, which was in a reasonable fit (Table 6).

#### 3.4. Energy Utilization Ratio

^{2}) was not significant at all.

^{2}) and bed thickness (B

^{2}) were significant at the 95% probability level with p-values of 0.0004 and 0.0022, respectively (Table 7). Nevertheless, the experimental data were well expressed by the model, and estimated the energy utilization ratio very closely while the p-value of the model with a low C.V. value (1.65%) was less than 10% [54].

^{2}and R

^{2}show that the developed models were suitable for predicting the energy utilization ratio so that the predicted values of R

^{2}were close to the adjusted R

^{2}; however, the analysis of variance showed that the quadratic model was the best model to explain the energy utilization ratio, as shown in Table 8. It is important to note that the values of R

^{2}and adjusted R

^{2}, predicted R

^{2}, and PRESS for the selected model to estimate the response of the energy utilization ratio were 0.9988, 0.9979, 0.9878, and 0.0012, respectively, as shown in Table 8.

^{2}) had a direct relation with the EUR and the drying air temperature had the highest effect between the parameters and the terms. In contrast, the quadrative term of the drying air temperature (A

^{2}) was inversely related to this response.

#### 3.5. Exergy Efficiency

^{2}) with a p-value < 0.0001 and the interaction effect of the drying air temperature and bed thickness (AB) with a p-value < 0.0064, were significant only at the 5% level, while the second-degree term of the bed thickness (B

^{2}) had a p-value < 0.0129. The p-values were obtained for these parameters: 4722.40, 552.42, 186.49, 14.76, and 10.98, respectively (Table 9). The non-significance of the lack of fit parameter and the low value of the variation coefficient (C.V. = 1.20%) indicated that the chosen model was suitable for the estimation of the exergy efficiency.

^{2}= 0.9987 had a good performance for fitting the experimental and predicted data, which represented only 0.23% of the total changes not accounted for by the RSM model (Table 10).

^{2}, predicted R

^{2}, and PRESS values were 0.9978, 0.9885, and 35.36, respectively, which were statistically acceptable values for predicting the exergy efficiency (Table 10).

^{2}) and (B

^{2}) were significant. Accordingly, the temperature and the thickness of the sample bed and their interactions had a positive effect on the exergy efficiency, while the second-order term had the opposite effect. In general, the drying air temperature had a greater effect on exergy efficiency than the sample bed thickness.

#### 3.6. Exergy Loss Rate

^{2}of 0.9829, adjusted R

^{2}of 0.9771, predicted R

^{2}of 0.9458 and PRESS of 0.0000 showed a suitable fit and a very good correlation with the values of the predicted exergy losses, indicating this parameter could have caused a higher proportion of changes in the experiment.

^{2}of 0.9771 and the predicted R

^{2}of 0.9458, the fit of the model shows that it was properly used to predict the exergy loss (Table 12).

#### 3.7. Exergetic Improvement Potential Rate

^{2}, were the significant variables of the model at 95% (p < 0.05) and 99% (p < 0.01), confidence levels, respectively, so that the A

^{2}with the value (p = 0.0234) was significant only at a 95% confidence level (p < 0.05) (Table 13). According to the results, B

^{2}with a value (p = 0.8438) was also the only non-significant variable in the model (p ˃ 0.05). The ANOVA also showed that the lack of fit for the models at the response level of the exergy improvement potential rate was not significant at the 95% confidence level with a coefficient of variation of 1.25%, which also indicated the proper performance of the corresponding model (Table 13).

^{2}of 0.9997, and an adjusted and predicted R

^{2}of 0.9995 and 0.9971, respectively, are presented in Table 14.

^{2}) and (B

^{2}) were directly related to the exergetic improvement potential rate. Since the coefficients of all the terms were positive, the drying air temperature was more effective than the variable of the sample bed thickness due to a higher coefficient of 0.7982.

#### 3.8. Sustainability Index

^{2}) based on the probability (p < 0.01), except for the quadratic term of sample thickness (B

^{2}) with (p ˃ 0.05), were highly significant. Reducing the size of a model may be beneficial if it contains many meaningless terms. Based on the results obtained to evaluate the sustainability index, both the drying air temperature and sample bed thickness had a positive effect on this response. In other words, the sustainability index increased when these factors increased. The coefficient of variation in this analysis was 2.73%.

^{2}, adj-R

^{2}, and predicted R

^{2}, respectively (Table 16); however, according to the results of the analysis of variance, the quadratic model was the best model for predicting the sustainability index (SI) according to the relationship between the set of independent variables and the response of SI.

^{2}) and (B

^{2}) showed that higher values of these variables increased this index. Consequently, according to Equation (27), the effect of the drying air temperature (A) on the sustainability index with a coefficient value (+0.0075) was much greater than the effect of the sample bed thickness (B) with a coefficient value (+0.0024). On the other hand, the drying air temperature parameter (A

^{2}) had the most positive effect on the sustainability index with a coefficient of 0.0040 (Equation (27)), based on the combined effects.

#### 3.9. Optimization Analysis

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Nomenclature

Notations | |

MR | moisture ratio (dimensionless) |

M | moisture content (% dry weight) |

DR | drying rate |

t | time (min) |

$\stackrel{\xb7}{En}$ | energy rate (kJ/s) |

n | mass flow rate (kg/s) |

T | temperature (°C) |

P | atmospheric pressure (kPa) |

A | area (m^{2}) |

V | air velocity (m/s) |

c_{p} | specific heat (kJ/kg°C) |

$R$ | gas constant (8.3143 kJ/mol) |

U | overall heat transfer coefficient (kW/m^{2} °C) |

h | enthalpy (kJ/kg) |

h_{fg} | latent heat of vaporization (kJ/kg) |

EU | energy utilization (kJ/s) |

EUR | energy utilization ratio (kJ/s) |

EX | exergy rate (kJ/s) |

Q | heat transfer (kJ/s) |

IP | improvement potential rate (kJ/s) |

SI | stainability index |

x | coded variable of model in RSM |

RSM | response surface method |

D | total desirability function |

d | desirability function of each response in RSM |

Greek letters | |

$\rho $ | density (kg/m^{3}) |

${\psi}_{ex}$ | exergy efficiency (%) |

$\phi $ | relative humidity of air (%) |

$\omega $ | humidity ratio (kg water/kg dry air) |

t | time difference |

$\alpha $ | coefficient term of RSM’s model |

Subscripts | |

$\infty $ | ambient |

$a$ | air |

e | equilibrium |

vs | saturated vapor |

0 | initial |

L | heat loss |

ij | numerator |

in | inlet |

$L$ | loss |

w.b. | wet basis |

out | output |

ph | physical |

in | inlet air |

out | outlet air |

b | basil |

fp | fresh product |

dp | dried product |

da | drying air |

tp | triple point |

evp | evaporation |

hdb | hybrid dryer body |

dc | drying chamber |

p | pressure |

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**Figure 2.**Changes in the drying rate of basil during the drying period at different temperatures and bed thicknesses.

**Figure 3.**The effect of bed thickness and air temperature on the predicted response surface of drying rate (kg water/kg dry matter min), (

**a**) 3D response surface and (

**b**) 2D contour plot.

**Figure 4.**The effect of bed thickness and air temperature on the predicted response surface of energy utilization, (

**a**) 3D response surface and (

**b**) 2D contour plot.

**Figure 5.**The effect of bed thickness and air temperature on the predicted response surface of energy utilization ratio, (

**a**) 3D response surface and (

**b**) 2D contour plot.

**Figure 6.**The effect of bed thickness and air temperature on the predicted response surface of exergy efficiency, (

**a**) 3D response surface and (

**b**) 2D contour plot.

**Figure 7.**The effect of bed thickness and air temperature on the predicted response surface of exergy loss rate, (

**a**) 3D response surface and (

**b**) 2D contour plot.

**Figure 8.**The effect of bed thickness and air temperature on the predicted response surface of improvement potential rate, (

**a**) 3D response surface and (

**b**) 2D contour plot.

**Figure 9.**The effect of bed thickness and air temperature on the predicted response surface of sustainability index, (

**a**) 3D response surface and (

**b**) 2D contour plot.

**Figure 10.**The values of individual desirability of input and response parameters for hybrid-solar dryer.

**Table 1.**Experimental layout of independent factors, related levels, criteria and goals utilized for central composite design.

Parameters | Coded Symbol | Targets | Coded | Actual | Importance | |
---|---|---|---|---|---|---|

−1 | 2 | |||||

Air temperature, T (°C) | A | In range | 0 | 4 | 3 | |

Input parameters | 1 | 6 | ||||

−1 | 40 | |||||

Bed thickness, BT (cm) | B | In range | 0 | 55 | 3 | |

1 | 70 | |||||

Drying rate (g water/g dry matter min) | DR | Maximum | 0.1127–0.3227 | 3 | ||

Energy utilization (kJ/s) | EU | Minimum | 0.0124–0.0438 | 3 | ||

Energy utilization Ratio (-) | EUR | Minimum | 0.1181–0.4612 | 3 | ||

Responses | Exergy loss rate (kJ/s) | - | Minimum | 0.0078–0.0297 | 3 | |

Exergy efficiency (%) | ${\psi}_{ex}$ | Maximum | 31.78–86.55 | 3 | ||

Improvement potential rate (kJ/s) | $\stackrel{\xb7}{IP}$ | Maximum | 0.2424–2.549 | 3 | ||

Sustainability index (-) | SI | Maximum | 0.0116–0.0324 | 3 |

**Table 2.**Experimental central composite design of input and response factors for basil dried under hybrid-solar dryer conditions.

Input Variables | Responses | ||||||||
---|---|---|---|---|---|---|---|---|---|

Run | Air Temperature °C | Bed Thickness cm | Drying Rate g Water/g Dry Matter min | Energy Utilization kJ/s | Energy Utilization Ratio - | Exergy Loss kJ/s | Exergy Efficiency % | Improvement Potential Rate kJ/s | Sustainability Index - |

1 | 40 | 2 | 0.1420 | 0.0125 | 0.1181 | 0.0079 | 31.79 | 0.2424 | 0.0325 |

2 | 55 | 4 | 0.1958 | 0.0201 | 0.2558 | 0.0175 | 65.28 | 1.1358 | 0.0162 |

3 | 55 | 4 | 0.1958 | 0.0201 | 0.2558 | 0.0175 | 65.28 | 1.1358 | 0.0162 |

4 | 70 | 4 | 0.2958 | 0.0290 | 0.3357 | 0.0251 | 79.53 | 1.9675 | 0.0127 |

5 | 55 | 4 | 0.1958 | 0.0201 | 0.2558 | 0.0175 | 65.28 | 1.1358 | 0.0162 |

6 | 70 | 6 | 0.2219 | 0.0418 | 0.4612 | 0.0298 | 86.56 | 2.5495 | 0.0117 |

7 | 55 | 6 | 0.1561 | 0.0276 | 0.3394 | 0.0213 | 71.23 | 1.5069 | 0.0148 |

8 | 40 | 6 | 0.1127 | 0.0196 | 0.1777 | 0.0122 | 42.24 | 0.5050 | 0.0242 |

9 | 55 | 2 | 0.2132 | 0.0152 | 0.1915 | 0.0106 | 55.12 | 0.7501 | 0.0182 |

10 | 55 | 4 | 0.1958 | 0.0201 | 0.2558 | 0.0175 | 65.28 | 1.1358 | 0.0162 |

11 | 40 | 4 | 0.1315 | 0.0155 | 0.1399 | 0.0092 | 37.58 | 0.3358 | 0.0273 |

12 | 55 | 4 | 0.1958 | 0.0201 | 0.2558 | 0.0175 | 65.28 | 1.1358 | 0.0162 |

13 | 70 | 2 | 0.3227 | 0.0225 | 0.2511 | 0.0195 | 70.40 | 1.3555 | 0.0144 |

Source | Sum of Squares | df | Mean Square | F-value | p-Value | |
---|---|---|---|---|---|---|

Model | 0.0424 | 5 | 0.0085 | 390.54 | <0.0001 ** | significant |

A-Air temperature | 0.0344 | 1 | 0.0344 | 1584.10 | <0.0001 ** | |

B-Bed thickness | 0.0058 | 1 | 0.0058 | 268.99 | <0.0001 ** | |

AB | 0.0013 | 1 | 0.0013 | 59.04 | 0.0001 ** | |

A^{2} | 0.0008 | 1 | 0.0008 | 35.00 | 0.0006 ** | |

B^{2} | 0.0004 | 1 | 0.0004 | 19.70 | 0.0030 ** | |

Residual | 0.0002 | 7 | 0.0000 | |||

Lack of Fit | 0.0002 | 3 | 0.0001 | |||

Pure Error | 0.0000 | 4 | 0.0000 | |||

Cor Total | 0.0425 | 12 | ||||

C.V.% | 2.35 |

Source | Std. Dev. | R^{2} | Adjusted R^{2} | Predicted R^{2} | PRESS | |
---|---|---|---|---|---|---|

Linear | 0.0152 | 0.9456 | 0.9347 | 0.8697 | 0.0055 | |

2FI | 0.0107 | 0.9757 | 0.9676 | 0.9479 | 0.0022 | |

Quadratic | 0.0047 | 0.9964 | 0.9939 | 0.9640 | 0.0015 | Suggested |

Cubic | 0.0010 | 0.9999 | 0.9997 | 0.9866 | 0.0006 | Aliased |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 0.0007 | 5 | 0.0001 | 344.42 | <0.0001 ** | significant |

A-Air temperature | 0.0003 | 1 | 0.0003 | 892.68 | <0.0001 ** | |

B-Bed thickness | 0.0003 | 1 | 0.0003 | 640.80 | <0.0001 ** | |

AB | 0.0000 | 1 | 0.0000 | 95.33 | <0.0001 ** | |

A^{2} | 0.0000 | 1 | 0.0000 | 42.82 | 0.0003 ** | |

B^{2} | 6.494 × 10^{−6} | 1 | 6.494 × 10^{−6} | 16.61 | 0.0047 ** | |

Residual | 2.736 × 10^{−6} | 7 | 3.909 × 10^{−7} | |||

Lack of Fit | 2.736 × 10^{−6} | 3 | 9.120 × 10^{−7} | |||

Pure Error | 0.0000 | 4 | 0.0000 | |||

Cor Total | 0.0007 | 12 | ||||

C.V.% | 2.86 |

**Table 6.**Summarized statistical data of predictive models for energy utilization under hybrid-solar dryer.

Source | Std. Dev. | R^{2} | Adjusted R^{2} | Predicted R^{2} | PRESS | |
---|---|---|---|---|---|---|

Linear | 0.0028 | 0.8869 | 0.8642 | 0.7184 | 0.0002 | |

2FI | 0.0021 | 0.9420 | 0.9227 | 0.6973 | 0.0002 | |

Quadratic | 0.0006 | 0.9960 | 0.9931 | 0.9598 | 0.0000 | Suggested |

Cubic | 0.0002 | 0.9997 | 0.9993 | 0.9663 | 0.0000 | Aliased |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 0.0980 | 5 | 0.0196 | 1118.73 | <0.0001 ** | significant |

A-Air temperature | 0.0625 | 1 | 0.0625 | 3565.86 | <0.0001 ** | |

B-Bed thickness | 0.0291 | 1 | 0.0291 | 1658.77 | <0.0001 ** | |

AB | 0.0057 | 1 | 0.0057 | 323.33 | <0.0001 ** | |

A^{2} | 0.0007 | 1 | 0.0007 | 39.38 | 0.0004 ** | |

B^{2} | 0.0004 | 1 | 0.0004 | 22.18 | 0.0022 ** | |

Residual | 0.0001 | 7 | 0.0000 | |||

Lack of Fit | 0.0001 | 3 | 0.0000 | |||

Pure Error | 0.0000 | 4 | 0.0000 | |||

Cor Total | 0.0981 | 12 | ||||

C.V.% | 1.65 |

**Table 8.**Summarized statistical data of predictive models for energy utilization ratio under hybrid-solar dryer.

Source | Std. Dev. | R^{2} | Adjusted R^{2} | Predicted R^{2} | PRESS | |
---|---|---|---|---|---|---|

Linear | 0.0257 | 0.9329 | 0.9194 | 0.8173 | 0.0179 | |

2FI | 0.0101 | 0.9906 | 0.9875 | 0.9807 | 0.0019 | |

Quadratic | 0.0042 | 0.9988 | 0.9979 | 0.9878 | 0.0012 | Suggested |

Cubic | 0.0017 | 0.9998 | 0.9996 | 0.9825 | 0.0017 | Aliased |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 3060.98 | 5 | 612.20 | 1112.18 | <0.0001 ** | significant |

A-Air temperature | 2599.44 | 1 | 2599.44 | 4722.40 | <0.0001 ** | |

B-Bed thickness | 304.08 | 1 | 304.08 | 552.42 | <0.0001 ** | |

AB | 8.13 | 1 | 8.13 | 14.76 | 0.0064 ** | |

A^{2} | 102.65 | 1 | 102.65 | 186.49 | <0.0001 ** | |

B^{2} | 6.04 | 1 | 6.04 | 10.98 | 0.0129 * | |

Residual | 3.85 | 7 | 0.5504 | |||

Lack of Fit | 3.85 | 3 | 1.28 | |||

Pure Error | 0.0000 | 4 | 0.0000 | |||

Cor Total | 3064.84 | 12 | ||||

C.V.% | 1.20 |

**Table 10.**Summarized statistical data of predictive models for exergy efficiency under hybrid-solar dryer.

Source | Std. Dev. | R^{2} | Adjusted R^{2} | Predicted R^{2} | PRESS | |
---|---|---|---|---|---|---|

Linear | 4.02 | 0.9474 | 0.9368 | 0.8954 | 320.44 | |

2FI | 4.13 | 0.9500 | 0.9334 | 0.7890 | 646.62 | |

Quadratic | 0.7419 | 0.9987 | 0.9978 | 0.9885 | 35.36 | Suggested |

Cubic | 0.4797 | 0.9996 | 0.9991 | 0.9564 | 133.70 | Aliased |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 0.0005 | 3 | 0.0002 | 172.03 | <0.0001 ** | significant |

A-Air temperature | 0.0003 | 1 | 0.0003 | 384.40 | <0.0001 ** | |

B-Bed thickness | 0.0001 | 1 | 0.0001 | 121.82 | <0.0001 ** | |

AB | 8.692 × 10^{−6} | 1 | 8.692 × 10^{−6} | 9.86 | 0.0119 * | |

Residual | 7.931 × 10^{−6} | 9 | 8.812 × 10^{−7} | |||

Lack of Fit | 7.931 × 10^{−6} | 5 | 1.586 × 10^{−6} | |||

Pure Error | 0.0000 | 4 | 0.0000 | |||

Cor Total | 0.0005 | 12 | ||||

C.V.% | 5.47 |

**Table 12.**Summarized statistical data of predictive models for exergy loss under hybrid-solar dryer.

Source | Std. Dev. | R^{2} | Adjusted R^{2} | Predicted R^{2} | PRESS | |
---|---|---|---|---|---|---|

Linear | 0.0013 | 0.9641 | 0.9569 | 0.9126 | 0.0000 | |

2FI | 0.0009 | 0.9829 | 0.9771 | 0.9458 | 0.0000 | Suggested |

Quadratic | 0.0010 | 0.9859 | 0.9758 | 0.8714 | 0.0001 | |

Cubic | 0.0006 | 0.9955 | 0.9891 | 0.4716 | 0.0002 | Aliased |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 4.86 | 5 | 0.9717 | 4705.99 | <0.0001 ** | significant |

A-Air temperature | 3.82 | 1 | 3.82 | 18,514.77 | <0.0001 ** | |

B-Bed thickness | 0.8165 | 1 | 0.8165 | 3954.49 | <0.0001 ** | |

AB | 0.2169 | 1 | 0.2169 | 1050.39 | <0.0001 ** | |

A^{2} | 0.0017 | 1 | 0.0017 | 8.33 | 0.0234 * | |

B^{2} | 8.629 × 10^{−6} | 1 | 8.629 × 10^{−6} | 0.0418 | 0.8438 ^{ns} | |

Residual | 0.0014 | 7 | 0.0002 | |||

Lack of Fit | 0.0014 | 3 | 0.0005 | |||

Pure Error | 0.0000 | 4 | 0.0000 | |||

Cor Total | 4.86 | 12 | ||||

C.V.% | 1.25 |

**Table 14.**Summarized statistical data of predictive models for improvement potential rate under hybrid-solar dryer.

Source | Std. Dev. | R^{2} | Adjusted R^{2} | Predicted R^{2} | PRESS | |
---|---|---|---|---|---|---|

Linear | 0.1485 | 0.9546 | 0.9456 | 0.8701 | 0.6314 | |

2FI | 0.0199 | 0.9993 | 0.9990 | 0.9964 | 0.0173 | |

Quadratic | 0.0144 | 0.9997 | 0.9995 | 0.9971 | 0.0139 | Suggested |

Cubic | 0.0069 | 1.0000 | 0.9999 | 0.9942 | 0.0280 | Aliased |

Source | Sum of Squares | df | Mean Square | F-Value | p-Value | |
---|---|---|---|---|---|---|

Model | 0.0004 | 5 | 0.0001 | 358.42 | <0.0001 ** | significant |

A-Air temperature | 0.0003 | 1 | 0.0003 | 1385.15 | <0.0001 ** | |

B-Bed thickness | 0.0000 | 1 | 0.0000 | 139.29 | <0.0001 ** | |

AB | 7.594 × 10^{−6} | 1 | 7.594 × 10^{−6} | 30.84 | 0.0009 ** | |

A^{2} | 0.0000 | 1 | 0.0000 | 183.75 | <0.0001 ** | |

B^{2} | 6.075 × 10^{−7} | 1 | 6.075 × 10^{−7} | 2.47 | 0.1602 ^{ns} | |

Residual | 1.723 × 10^{−6} | 7 | 2.462 × 10^{−7} | |||

Lack of Fit | 1.723 × 10^{−6} | 3 | 5.745 × 10^{−7} | |||

Pure Error | 0.0000 | 4 | 0.0000 | |||

Cor Total | 0.0004 | 12 | ||||

C.V.% | 2.73 |

**Table 16.**Summarized statistical data of predictive models for sustainability index under hybrid-solar dryer.

Source | Std. Dev. | R^{2} | Adjusted R^{2} | Predicted R^{2} | PRESS | |
---|---|---|---|---|---|---|

Linear | 0.0026 | 0.8473 | 0.8168 | 0.6756 | 0.0001 | |

2FI | 0.0026 | 0.8645 | 0.8193 | 0.3913 | 0.0003 | |

Quadratic | 0.0005 | 0.9961 | 0.9933 | 0.9612 | 0.0000 | Suggested |

Cubic | 0.0001 | 0.9998 | 0.9994 | 0.9722 | 0.0000 | Aliased |

Parameters | t (°C) | BT (cm) | Dr (kg Water/kg Dry Matter min) | EU (kJ/s) | EUR (−) | EX_{eff}(%) | EX_{loss}(kJ/s) | $\mathit{I}\dot{\mathit{P}}\phantom{\rule{0ex}{0ex}}(\mathbf{kJ}/\mathbf{s})$ | SI (−) | Desirability |
---|---|---|---|---|---|---|---|---|---|---|

Optimum values | 63.776 | 2.000 | 0.275 | 0.019 | 0.230 | 65.759 | 0.016 | 1.105 | 0.015 | 0.549 |

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## Share and Cite

**MDPI and ACS Style**

Parhizi, Z.; Karami, H.; Golpour, I.; Kaveh, M.; Szymanek, M.; Blanco-Marigorta, A.M.; Marcos, J.D.; Khalife, E.; Skowron, S.; Adnan Othman, N.;
et al. Modeling and Optimization of Energy and Exergy Parameters of a Hybrid-Solar Dryer for Basil Leaf Drying Using RSM. *Sustainability* **2022**, *14*, 8839.
https://doi.org/10.3390/su14148839

**AMA Style**

Parhizi Z, Karami H, Golpour I, Kaveh M, Szymanek M, Blanco-Marigorta AM, Marcos JD, Khalife E, Skowron S, Adnan Othman N,
et al. Modeling and Optimization of Energy and Exergy Parameters of a Hybrid-Solar Dryer for Basil Leaf Drying Using RSM. *Sustainability*. 2022; 14(14):8839.
https://doi.org/10.3390/su14148839

**Chicago/Turabian Style**

Parhizi, Zahra, Hamed Karami, Iman Golpour, Mohammad Kaveh, Mariusz Szymanek, Ana M. Blanco-Marigorta, José Daniel Marcos, Esmail Khalife, Stanisław Skowron, Nashwan Adnan Othman,
and et al. 2022. "Modeling and Optimization of Energy and Exergy Parameters of a Hybrid-Solar Dryer for Basil Leaf Drying Using RSM" *Sustainability* 14, no. 14: 8839.
https://doi.org/10.3390/su14148839