AUTHORS’ CONTRIBUTION

S. K. Natarajan designed the experiments, reviewed and edited the drafted manuscript, and also performed the critical revision and data interpretation. E. Elangovan conducted and performed all the experiments related to open sun drying, natural convection and forced convection, and based on that drafted the manuscript. Both authors have read and approved the final manuscript. Final approval of the version of the manuscript to be published was made by S. K. Natarajan.

Traditionally, open sun drying method serves to dry the products for long time preservation. Solar drying is also employed to minimise the drying time to achieve the required moisture content. This method inherently contains complex heat and mass transfer mechanisms, which makes difficult to describe drying kinetics at the micro level.

In this paper, research is carried out to investigate the drying of 5 mm thick slices of red banana (^{2}) of 0.997 is in very good agreement with other well-known models. Based on the model, we calculated the moisture diffusivity and activation energy of the red banana drying process.

It was found that the moisture diffusivity of the red banana samples was in the range 0.87-1.56·10^{-9} m^{2}/s for natural convection solar drying and 0.84-2.61·10^{-8} m^{2}/s for forced convection solar drying. The activation energy of the red banana varied from 24.58 to 45.20 kJ/mol for passive and 22.56 to 35.49 kJ/mol for active drying. Besides, we carried out energy and exergy analyses of red banana in the dryers and found that the average exergy losses in the forced and natural convections were 16.1 and 6.63 kJ/kg and the average exergic efficiency of the natural and forced convection dryers was 57.7 and 70.9%, respectively.

A single slope direct solar dryer was designed and built to maintain the desired temperature for a specified period in both natural and forced convection mode. A novel drying kinetics model with higher correlation coefficient (R^{2}) than the other drying kinetic models is proposed for the preservation of red bananas.

Banana is one of the most popular fruits around the world. Among all the developing countries, India is one of the largest producers of banana (

Akbulut and Durmuş (^{-10} m^{2}/s and its activation energy was 32.65 kJ/mol. Mierzwa

Hempattarasuwan ^{-10} m^{2}/s. Using the first and second law of thermodynamics, Midilli and Kucuk (

Simo-Tagne ^{2}·K) and from 1.0·10^{-8} to 5.5·10^{-8} m/s, respectively. Komes

Based on the literature review, very few research works analysed the energy and exergy efficiencies of the banana drying. Most researchers concentrated on the drying process of commonly available species of yellow banana and no research has been carried out on red banana. Hence, in this article, we have attempted to study the drying characteristics of red banana and to estimate the moisture diffusivity and activation energy in a single slope direct solar dryer under passive and active mode. Besides, we compared the results with open drying, as well as other existing drying models and developed a new correlation between the drying moisture ratio and drying time.

The experiments were performed in a single slope direct solar dryer, which has a trapezoid shape with base dimensions of 1290 mm×850 mm with two different heights of 500 and 260 mm, respectively. Sides of the solar dryer were constructed using a dual 1.5 mm thick galvanized sheet with a gap of 50 mm between the inner and outer walls of the sheets, which were filled with coconut husk to reduce the heat loss from the sides of the dryer. Top of the dryer was covered with a flat transparent glass of 5 mm thickness with an inclination of 10.9° (latitude of the place, Karaikal District). Outer surfaces were enclosed in an insulation chamber that consists of two layers of thermocol each 25 mm thick with an air gap of 25 mm between them to reduce significantly heat loss. An aluminium mesh of dimensions 1190 mm×750 mm was constructed and placed inside the dryer at about 50 mm vertically from the absorber plate of the dryer. This mesh served as the plate for placing red banana slices for drying. The inlet air was supplied to the dryer through a 22 mm diameter mild steel pipe placed horizontally in the lower side of the drying chamber. A similar outlet pipe was placed vertically on the opposite end of the dryer (perpendicular to the inlet of the system). The entire drying chamber was placed on a stand of mild steel L brackets of 25 mm thickness, dimensions 1290 mm×1000 mm with a height 750 mm. Two similar set-ups were made. One was used for natural convection and the other one for forced convection with a blower (model M4000B; Makita, Bangalore, India), providing air velocity of 1.5 m/s. In addition, open drying method experimental set-up was made and the same quantity of red banana was dried to compare the drying time of forced and natural convection. The photographs of natural convection, forced convection single slope dryer and open sun drying experimental set-ups are shown in ^{2}, was used to measure the intensity of global radiation. The thermocouples and the pyranometer were connected to a data acquisition unit (model 34972A; Keysight, New Delhi, India) to measure the temperature and global radiation (

The red bananas (3 kg) were purchased from the local market in Karaikal, Puducherry, India. The skin was peeled off on the day of the experiment and the samples were cut into 5 mm thick cylindrical shapes with a uniform diameter of 50 mm. The samples were then carefully placed in the dryers for open sun drying, forced and natural convection drying from 9.00 am to 5.00 pm. Parameters monitored for the analysis were energy, exergy, effective moisture diffusivity and activation energy of the red banana samples.

The analyses of red banana were carried out based on the first and second law of thermodynamics, where the solar dehydration of red banana is considered as a steady flow process. The drying of red banana involves heating and humidification in the dryer chamber for effective removal of the moisture from the samples. The conservation of mass and energy in steady-state flow can be used to equate the processes (

where _{i} is mass flow rate of the inlet (kg/s), _{o} is mass flow rate of the outlet (kg/s), _{o} is humidity of the outlet air (g^{-1}), _{i} is humidity of the inlet air (g^{-1}), _{i} is velocity of the inlet air (m/s), _{o} is the velocity of the outlet air (m/s), _{i} is the enthalpy of the inlet air (kJ/kg) and _{o} is the enthalpy of the outlet air (kJ/kg).

The relative humidity of the solar dryer chamber is an important factor to control the drying samples. The amount of relative humidity inside the solar chamber highly influences the drying rate and time. The relative humidity (

where _{sat} is saturation pressure of air (kPa).

The enthalpy of the dehydrating air inside the dryer is computed by using the following equation:

where _{pda} is specific heat of drying air (kJ/(kg·K)), _{sat} is saturation enthalpy of air (kJ/kg).

The energy utilization ratio is a measurement of the amount of energy used in comparison to the total energy that could be used by the system. The _{ur} is important to calculate the amount of energy utilized by the dryer to perform its function and to calculate the amount of energy that the system does not utilize:

where _{ur}(dryer) is the energy utilization ratio of the dryer (%), _{dryi} is the enthalpy of the air at the inlet (kg/s), _{da} is the mass flow rate of the drying air (kg/s), _{dryo} is the temperature of the outlet air (K) and _{dryi} is the temperature of the inlet air (K).

In order to quantify the losses from the dryer, the exergy is also calculated. The calculation of exergy is based on the second law of thermodynamics under steady state by balancing the different forms of energy present inside the system using the first law of energy (

where ∞ is ambient condition, ^{2}), _{c} is constant.

Based on the solar dryer and source terms, the above equation is deduced to:

The amount of exergy in and out of system can be estimated by changing the parameters of Eq. 7 depending on the inlet or outlet condition. By applying this method, the amount of exergy inflow and outflow are computed. The exergy loss of the system can be calculated by analysing the difference between the inflow and outflow of exergy in the system:

where _{XL} is exergy loss (kJ/kg), _{Xi} is exergy inflow (kJ/kg) and _{Xo} is exergy outflow (kJ/kg).

The proposed solar dryer exergetic efficiency (_{EX}) is calculated by taking the ratio of the difference between the exergy inflow and exergy loss of the dryer to the exergy inflow of the dryer (

The drying kinetics of thin layer of red banana is evaluated in a developed single slope dryer in active and passive mode. Then, the moisture ratio is given as:

Where MR is the moisture ratio of red banana samples (%), _{i} is the initial moisture content of red banana sample (g).

Based on the moisture ratio, the drying parameters (moisture diffusivity and activation energy) can be estimated. The procedure for determining the moisture diffusivity is given below.

Moisture diffusivity is used to estimate the diffusion of moisture during dehydration. The dehydration occurs in three stages; first a uniform drying time, followed by a falling rate period of drying, and the final stage when the moisture moves from the centre to the surface (

where _{eff} is the moisture diffusivity (m^{2}/s), ∇ is the gradient operator and

The general solution for the above equation can be obtained for different geometries (cube and cylinder respectively) and written as appropriated by the given boundary conditions (

where _{e} is the equilibrium moisture ratio (%), _{t} is the moisture ratio at a particular period (%), _{0} is the initial moisture ratio (%), _{c} is the radius of the sample (mm), _{n} is root of Bessel function (without units) and π is a constant.

The derived equations can be simplified by considering the first terms of the equations to compute moisture diffusivity (

The equations can be further simplified by taking natural logarithm on both sides to make the equation logarithmic:

where constant

The final equation can be represented as an Arrhenius type equation:

where _{a} is the activation energy (kJ/mol) and

The activation energy of the red banana drying is the minimum of energy required for the dehydration to occur. The prediction of activation energy of red banana drying is an important task to minimise the supply of required energy. The activation energy of convective dehydration can be calculated from Eq. 17 by taking a natural log on each side of the equation:

_{a} of the banana can be determined by plotting a graph between ln(_{eff}) and 1/

where

Three statistical criteria, namely root mean square deviation (RMSD), correlation coefficient (R^{2}) and reduced chi-square (χ^{2}) are calculated using Data fit v. 8.0 software to validate the goodness of the fit (^{2}, χ^{2} and RMSD were calculated as follows (

where SE is the standard error (%), _{i} is moisture ratio (%), MR_{(pr,i)} is the predicted value (%), MR_{(ex,i)} is the experimental value (%), and

The error analysis (w_{r}) of the experimental data depends on various factors such as environmental conditions (x_{1}), instrument error (x_{2}) and observation (x_{3}). The moisture content, solar radiation and temperature were measured using mass balance, pyranometer and thermocouple for open dehydration and solar dehydration of red banana.

where _{r} is the error analysis, _{a} represents environmental conditions, _{b} is instrument error and _{c} is observation.

The measured uncertainty for temperature and solar radiation was ±0.05 °C and ±5.7 W/m^{2}, respectively. Considering the above parameters, the uncertainty of drying rate was ±0.08 kg/s and kinetic parameters (moisture diffusivity and activation energy) of drying red banana in a single slope direct solar dryer were about ±0.42 m^{2}/s and ±0.18 kJ/mol, respectively (

Extensive experiments were carried out to estimate the moisture ratio of the red banana during open drying in active or passive mode. On 10 May 2020, three experiments were performed to compare the red banana drying rates. The same quantity (one kg) of the samples was used in each experiment. The investigations were carried out from 9.00 am to 5.00 pm under clear weather. The global radiation, surface and air temperature were recorded continuously from 9.00 am to 5.00 pm. The rate of dehydration curve was obtained.

Variation of moisture ratio of the samples with the drying time during open sun, natural and forced convection drying

From

It was observed that when maximum global radiation was 1029 W/m^{2} and ambient temperature 34.3 °C, under natural convection mode, the maximum average plate temperature was 71.3 °C and maximum average air temperature inside the dryer was 63.8 °C. Similarly, in the forced convection mode, the maximum average plate temperature and air temperature inside the dryer were 83 and 79.1 °C, respectively. It was evident that during the active drying, due to the presence of air current of 1.5 m/s, the plate and air temperature were higher than during the natural convection drying.

Literature review shows that most of the researchers developed thin layer drying kinetics of the yellow banana and separate moisture ratio models. The list of mathematical models for determination of moisture ratio is given in

Model name | Mathematical model | Reference |
---|---|---|

Newton | MR |
( |

Page | MR=exp(-k^{n}) |
( |

Modified Page | MR^{n}] |
( |

Henderson and Pabis | MR=a exp(-k |
( |

Logarithmic | MR=a exp(-k |
( |

Midilli-Kucuk | MR^{n})+b |
( |

Wang and Singh | MR=_{0}+a^{2} |
( |

Based on this study of active and passive drying (

where a=3.02225 and 1.23559, b=0.07711 and -0.05846, c=-2.03566 and -0.23589, k=0.07685 and 0.02300, n=1.02043 and 0.48056 in passive (natural convection drying at 53 °C) and active (forced convection drying at 64 °C) mode, respectively, and

Based on the existing mathematical moisture ratio models and constants, the moisture ratio in red banana was predicted for different drying time (h) for both passive and active dryer. Graphs in

Comparison of the proposed model with other drying models from the literature (

In order to compare the proposed model with other existing mathematical models, correlation coefficient (R^{2}) was calculated. The correlation coefficient (R^{2}) is considered as the primary parameter to check the compatibility of the experimental data with the developed model (^{2}, root mean square deviation (RMSD) and chi-square (χ^{2}) for both natural and forced convection are shown in ^{2}, χ^{2} and RMSD which are: 0.985 and 0.997, 0.003 and 0.009, and 0.0640 and 0.0873 for natural and forced convection drying respectively. Many researchers have reported similar results, where R^{2} for plantain banana (^{2}) and standard deviation (S.D.) for the parity plot of natural and forced convection drying respectively were: 0.985 and 0.997 for R^{2} and 0.046 and 0.0199 for S.D.

Model | Constant | R^{2} |
χ^{2} |
RMSE | Reference |
---|---|---|---|---|---|

Newton | k=0.17518 | 0.9798 | 0.0003 | 0.0640 | ( |

Page | k=0.14681 |
0.9830 | 0.0000 | 0.0592 | ( |

Modified Page | k=0.17691 |
0.9830 | 0.0000 | 0.0592 | ( |

Henderson and Pabis | k=0.17744 |
0.9800 | 0.0001 | 0.0658 | ( |

Midilli-Kucuk | a=0.98631 |
0.9839 | 0.0000 | 0.0536 | ( |

Logarithmic | k=0.12678 |
0.9840 | 0.0000 | 0.0495 | ( |

Wang and Singh | M_{0}=0.98718 |
0.9851 | 0.0000 | 0.0547 | ( |

Proposed model | a=3.02225 |
0.0001 | 0.0528 |

Model | Constant | R^{2} |
χ^{2} |
RMSE | Reference |
---|---|---|---|---|---|

Newton | k=0.22633 | 0.9901 | 0.0009 | 0.0868 | ( |

Page | k=0.23324 |
0.9902 | 0.0000 | 0.0873 | ( |

Modified Page | k=0.22592 |
0.9902 | 0.0000 | 0.0873 | ( |

Henderson and Pabis | k=0.22252 |
0.9906 | 0.0000 | 0.0840 | ( |

Midilli-Kucuk | a=0.99971 |
0.9977 | 0.0000 | 0.0696 | ( |

Logarithmic | k=0.18057 |
0.9921 | 0.0000 | 0.0726 | ( |

Wang and Singh | _{0}=0.96432 |
0.9900 | 0.0000 | 0.0851 | ( |

Proposed model | a=1.23559 |
0.0000 | 0.0562 |

In addition to the above-mentioned experimental analyses of passive and active drying, _{ur}, exergy loss and the exergic efficiency were predicted from experimental data based on Eq. 5. The _{ur} was predicted for both passive and active drying. _{ur} with dehydration period for passive and active drying. It was found that maximum _{ur} was reached at the time of high insolation. The maximum obtained _{ur} for natural and forced convection drying was 0.428 and 0.65 respectively. From the magnitude of the values, it was understood that the forced convection dryer efficiently sustained the _{ur} due to constant airflow and effective moisture removal from the system. Apart from that, the exergy loss was also predicted to examine the wastage of energy that could have been utilized for drying. The variation of exergy loss with dehydration period in natural and forced convection dryer is observable in

Variation in drying time of the red banana samples: a) energy utilization ratio and b) exergy loss

From the

Variation of exergetic efficiency with the drying time of red banana samples

The important parameters such as moisture diffusivity and activation energy were also predicted based on the experimental drying data of red banana using Eqs. 17 and 19. The moisture diffusivity depicts the rate of removal of moisture from the red banana. The least energy required for drying the sample is known as activation energy. Based on Eqs. 17 and 19, the predicted ranges of effective moisture diffusivity for the open sun drying, passive and active drying were: 3.86·10^{-11} to 1.10·10^{-10}, 8.74·10^{-10} to 1.56·10^{-9} and 8.43·10^{-9} to 2.61·10^{-8} m^{2}/s, respectively. In general, the value of moisture diffusivity falls in the range of 10^{-9} to 10^{-11} m^{2}/s for fruits, vegetables and grains (_{eff} value obtained for mushroom samples (9.619·10^{–10} to 1.556·10^{–9} m^{2}/s), pomegranate seeds (0.74·10^{–10} to 52.5·10^{–10} m^{2}/s) and sweet potato (9.32·10^{–11} to 1.76·10^{–10} m^{2}/s) were similar to previous research (^{–8} to 3.37·10^{–10} m^{2}/s (

Variation of ln(_{eff}) with temperature

The experimental analysis of red banana was carried out to develop the semi-empirical correlation between thin layer drying kinetics and moisture ratio in passive and active mode of drying in solar dryers. The results of drying time were compared with open sun drying. In order to achieve the same equilibrium moisture ratio percentage of 18.75%, forced convection drying was 28.5% faster than natural convection drying and 71.4% faster than open sun drying. The proposed semi-empirical correlation between thin layer drying kinetics and moisture ratio was in very close agreement with other existing models, with correlation coefficient for natural convection drying of 0.9846 and forced convection drying of 0.9977.Based on the uncertainty of the temperature (±0.05 °C) and solar radiation (±5.7 W/m^{2}), the uncertainty of drying rate and kinetic parameters for the single slope direct solar dryer was found to be ±0.08 kg/s and ±0.42 m^{2}/s and ±0.18 kJ/mol, respectively. Besides, moisture diffusivity and activation energy for red banana were found and the obtained values were within the range of fruit values. In addition to the above, energy and exergy analyses served to predict the losses from the system. In order to compare the dehydration characteristics of the red banana with other fruits, we compared the experimental results with other well-known models for broader scientific analysis. We observed that the drying characteristics of red banana are in good agreement with other well-known models. Thus, the developed single slope direct solar dryer can be effectively used for drying the agricultural products and the proposed semi-empirical moisture ratio correlation for forced and natural convection can also be used to analyse the thin layer drying kinetics of food products containing fruits and vegetables. Furthermore, our intention is to extend this study to analyse the drying rate of red banana indifferent dipping solutions.

CONFLICT OF INTEREST

The authors declare that they have no conflict of interest.

Photograph of the experimental set-up for banana drying: a) forced convection, b) natural convection single slope solar dryer and c) open sun drying

Variation of solar radiation, ambient temperature, drying air temperature, absorber plate temperature with the drying time of the samples: a) natural convection dryer and b) forced convection dryer

Parity plot for experimental moisture ratio (MR)

Parameter | Range | Uncertainty value |
---|---|---|

K type thermocouple | -270 to 1250 °C | ±0.05 |

J type thermocouple | 0 to 750 °C | ±0.03 |

Air velocity | 0 to 5 m/s | ±0.14 |

Relative humidity of air | 0 to 100% | ±0.14 |

Moisture quantity | 0 to 1000 g | ±0.001 |

Global solar radiation | 0 to 1650 W/m^{2} |
±5.77 |

Moisture diffusivity | -0.0 to 3.02 m^{2}/s |
±0.42 |

Activation energy | 0.0 to 2.05 kJ/mol | ±0.18 |

Drying rate | 0.002 to 0.24 kg/s | ±0.08 |