# Thermodynamic Evaluation of the Forced Convective Hybrid-Solar Dryer during Drying Process of Rosemary (Rosmarinus officinalis L.) Leaves

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## Abstract

**:**

## 1. Introduction

_{eff}) is a significant transport characteristic in food and other materials. It also identifies the function of moisture content and temperature in materials. Physical and thermal characteristics of food products, for instance, the parameters of the moisture diffusion coefficient and activation energy, are needed for the ideal dryer design [4].

## 2. Materials and Methods

#### 2.1. Sample Preparation

#### 2.2. Dryer Equipment

#### 2.3. Experimental Procedure

_{0}and W

_{0}are initial humidity (% d.b.) and mass of fresh samples (kg), respectively. The rosemary samples were dried until the moisture content reached about 12% (% d.b.) based on fresh weight.

#### 2.4. Data Analysis

#### 2.4.1. Moisture Content Analysis

_{t}is the mass humidity (% d.b.), and M

_{e}is the equilibrium moisture. MC is the moisture content at t and t + dt. Due to the low value of M

_{e}compared to M

_{0}and M

_{t}, Equation (2) was simplified as MR = M

_{t}/M.

#### 2.4.2. Effective Moisture Diffusivity Coefficient (D_{eff})

_{eff}) was obtained from the slope (K) of the Ln(MR) diagram relative to time, as follows:

_{eff}is the defined effective diffusivity coefficient (m

^{2}/s) and L is the semi-thickness of each sample.

#### 2.4.3. Activation Energy

_{a}is activation energy (kJ/mol), T

_{abs}is the temperature inside the dry chamber (k), R

_{g}is the universal gas constant equal to 38.143 (kJ/mol.K), and D

_{0}is the Arrhenius pre-exponential factor (m

^{2}/s) with a constant value. T is also the absolute air temperature. To obtain E

_{a}, linear relation (8) was used:

_{eff}) versus 1/T

_{abs}, the slope of K

_{2}was obtained as below:

#### 2.4.4. Energy and Exergy Analysis

_{a,i}and h

_{a,o}are input and output air enthalpy of the dryer (J/kg), respectively; ${\stackrel{\u2022}{m}}_{PF}$ and ${\stackrel{\u2022}{m}}_{PD}$ are mass flow rates of fresh and dried products (kg/s), respectively; h

_{PF}and h

_{PD}are enthalpy of fresh input and dried products (kJ/kg), respectively; and ${\stackrel{\u2022}{Q}}_{defl}$ is the heat loss from the dryer body (kJ/s).

^{3}) and V

_{a}is the linear velocity of the input air flow to the dryer chamber (m/s). To calculate the dry air density of ρ

_{a}(kg/m

^{3}), Equation (14) was used [27]:

_{a}is air temperature (°C). The input and output air enthalpy of the drying chamber is calculated using the following equation [28]:

_{a}is the specific heat of the air at constant pressure (kJ/kg °C) and T

_{∞}is the temperature of the output air (°C), h

_{fg}is the latent heat of evaporation of water (kJ/kg), and w is the absolute humidity of the input or output air.

_{p}is the specific heat of the input or output product (kJ/kg °C) and T

_{p}is the temperature of the input or output product (°C). To specify the enthalpy of input or output air, Equation (18) is used:

_{ai}is the specific heat of the input air (kJ/kg °C); T

_{ai}and T

_{ao}, are the temperature of the input and output air (°C), respectively; U

_{def}is the thermal degradation coefficient of the dryer body (Kw/m

^{2}°C); A

_{def}is the contact surface with the dryer body (m

^{2}); and T

_{mvdef}is the average temperature at three points of the dryer body.

_{in}), exergy at the outlet of the drying chamber (Ex

_{out}), and exergy loss (Ex

_{loss}) were calculated:

_{eff}) is defined as the ratio of outflow exergy to input exergy to the dryer chamber, and calculated by applying Equation (26):

#### 2.4.5. Specific Energy Consumption

## 3. Results

#### 3.1. Moisture Content

#### 3.2. Drying Rate

#### 3.3. Determination of D_{eff}

_{eff}values for the drying of rosemary. D

_{eff}values range from 8

^{−10}to 12

^{−10}m

^{2}/s for foods and crops [30]. With increasing air velocity and temperature, effective moisture diffusivity coefficients increase. The maximum effective moisture diffusivity coefficient at 70 °C and an air velocity of 2 m/s was 1.57 × 10

^{−9}m

^{2}/s. In addition, the lowest value (4.8 × 10

^{−10}m

^{2}/s) was recorded at 40 °C and an air velocity of 1 m/s. D

_{eff}in the rosemary foliage occurred as a result of cell wall degradation caused by increased input air velocity and temperature. The range obtained for D

_{eff}has been confirmed by other researchers [25,27,31,32].

#### 3.4. Activation Energy

^{2}value of 0.994, whereas the lowest value of 16.9 kJ/mol occurred at 1.5 m/s, and the R

^{2}value was 0.998. Similar results have been reported for apple slices and Chilean berry [33,34].

#### 3.5. Energy Utilization Ratio (EUR)

#### 3.6. Energy Utilization (EU)

#### 3.7. Input Exergy, Output Exergy, and Exergy Loss

#### 3.8. Exergy Efficiency

#### 3.9. Exergetic Improvement Potential Rate (IP)

#### 3.10. Sustainability Index (SI)

#### 3.11. Specific Energy Consumption (SEC)

## 4. Discussion

_{eff}) values of rosemary samples varied between 4.8 × 10

^{−10}and 1.57 × 10

^{−9}m

^{2}/s at a temperature range of 40–70 °C using Fick’s diffusion model, and the activation energy changed from 16.9 to 25.3 kJ/mol. The lowest and highest specific energy consumptions were 24.854 and 64.836 MJ/kg, respectively. The EUR ranged from 0.246 to 0.502, and was higher at lower temperatures and air velocities. With increasing air velocity and temperature, EUR increased. The lowest and highest EU rates were 0.017 and 0.060 kJ/s. Increasing the temperature and air velocity of drying led to an increase in the rate of input exergy, output exergy, and exergy loss. The average exergy efficiency values ranged from 35.08% for the temperature of 40 °C and air velocity of 1 m/s, to 78.50% for the temperature of 70 °C and air velocity of 2 m/s. Finally, due to higher exergy efficiency, at lower velocities and temperatures, the sustainability index increased, leading to fewer environmental impacts. Hence, as a measure of the quality of energy, exergy analysis can be used to assess the loss of heat and reflect the thermodynamic values of the operation of an HSD. Thus, exergy analysis should be applied to the design of convective HSD systems with the largest possible thermodynamic efficiencies.

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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Temperature (°C) | Air Velocity (m/s) | ||
---|---|---|---|

1 | 1.5 | 2 | |

40 | 4.8046 × 10^{−1}^{0} | 6.28 × 10^{−1}^{0} | 7.43347 × 10^{−1}^{0} |

50 | 8.01047 × 10^{−1}^{0} | 8.40453 × 10^{−1}^{0} | 8.71977 × 10^{−1}^{0} |

60 | 9.24047 × 10^{−1}^{0} | 1.02903 × 10^{−9} | 1.11235 × 10^{−9} |

70 | 1.17427 × 10^{−9} | 1.2846 × 10^{−9} | 1.56832 × 10^{−9} |

Temperature | EUR | EU | ||||
---|---|---|---|---|---|---|

1 m/s | 1.5 m/s | 2 m/s | 1 m/s | 1.5 m/s | 2 m/s | |

40 (°C) | 0.246 | 0.274 | 0.323 | 0.017 | 0.019 | 0.021 |

50 (°C) | 0.293 | 0.316 | 0.363 | 0.025 | 0.028 | 0.032 |

60 (°C) | 0.340 | 0.367 | 0.432 | 0.034 | 0.039 | 0.042 |

70 (°C) | 0.375 | 0.414 | 0.502 | 0.043 | 0.048 | 0.060 |

Temperature | Exergy Input | Exergy Output | Exergy Loss | ||||||
---|---|---|---|---|---|---|---|---|---|

1 m/s | 1.5 m/s | 2 m/s | 1 m/s | 1.5 m/s | 2 m/s | 1 m/s | 1.5 m/s | 2 m/s | |

40 (°C) | 0.014 | 0.016 | 0.021 | 0.005 | 0.007 | 0.011 | 0.009 | 0.010 | 0.010 |

50 (°C) | 0.035 | 0.041 | 0.052 | 0.019 | 0.024 | 0.032 | 0.017 | 0.017 | 0.020 |

60 (°C) | 0.071 | 0.077 | 0.087 | 0.049 | 0.054 | 0.063 | 0.022 | 0.023 | 0.024 |

70 (°C) | 0.105 | 0.118 | 0.129 | 0.079 | 0.091 | 0.101 | 0.026 | 0.027 | 0.028 |

**Table 4.**SEC (MJ/kg) for thin-layer drying of rosemary at different air velocities and temperatures.

Temperature (°C) | Air Velocity (m/s) | ||
---|---|---|---|

1 | 1.5 | 2 | |

40 | 64.836 | 59.649 | 55.350 |

50 | 56.381 | 48.374 | 44.986 |

60 | 40.034 | 36.136 | 31.316 |

70 | 32.310 | 29.558 | 24.854 |

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**MDPI and ACS Style**

Karami, H.; Kaveh, M.; Golpour, I.; Khalife, E.; Rusinek, R.; Dobrzański, B., Jr.; Gancarz, M.
Thermodynamic Evaluation of the Forced Convective Hybrid-Solar Dryer during Drying Process of Rosemary (*Rosmarinus officinalis* L.) Leaves. *Energies* **2021**, *14*, 5835.
https://doi.org/10.3390/en14185835

**AMA Style**

Karami H, Kaveh M, Golpour I, Khalife E, Rusinek R, Dobrzański B Jr., Gancarz M.
Thermodynamic Evaluation of the Forced Convective Hybrid-Solar Dryer during Drying Process of Rosemary (*Rosmarinus officinalis* L.) Leaves. *Energies*. 2021; 14(18):5835.
https://doi.org/10.3390/en14185835

**Chicago/Turabian Style**

Karami, Hamed, Mohammad Kaveh, Iman Golpour, Esmail Khalife, Robert Rusinek, Bohdan Dobrzański, Jr., and Marek Gancarz.
2021. "Thermodynamic Evaluation of the Forced Convective Hybrid-Solar Dryer during Drying Process of Rosemary (*Rosmarinus officinalis* L.) Leaves" *Energies* 14, no. 18: 5835.
https://doi.org/10.3390/en14185835