^{1}

^{2}

^{2}

The objective of this work is to analyse the extent to which a change in the drying air velocity may affect the drying kinetics of tomato in a forced-convective solar tunnel dryer. 2 m⋅s
^{−1} (
*V*
_{1}) and 3 m⋅s
^{−1} (
*V*
_{2}) air speeds were applied in similar drying air temperature and humidity conditions. Main drying constants calculated included the drying rate, the drying time and the effective water diffusivity based on the derivative form of the Fick’s second law of diffusion. Henderson and Pabis Model and Page Model were used to describe the drying kinetics of tomato. We found that solar drying of tomato occurred in both constant and falling-rate phases. The Page Model appeared to give a better description of tomato drying in a forced-convective solar tunnel dryer. At
*t *= 800 min, the drying rate was approximately 0.0023 kg of water/kg dry matter when drying air velocity was at 2 m/s. At the same moment, the drying rate was higher than 0.0032 kg of water/kg dry matter when the drying air velocity was 3 m/s. As per the effective water diffusivity, its values changed from 2.918E−09 m
^{2}⋅s
^{−1} to 3.921E−09 m
^{2}⋅s
^{−1} when drying air velocity was at 2 and 3 m⋅s
^{−1} respectively, which is equivalent to a 25% increase. The experimentations were conducted in Niamey, on the 1st and 5th of January 2019 for
* V*
_{2} and
*V*
_{1} respectively. For both two experiments, the starting time was 9:30 local time.

Drying is the most common preservation technique used to extend the shelf life of fresh vegetables and fruits as well as to facilitate their transportation and storage [

The drying kinetics of tomato was established by plotting ΔX against time. ΔX represents the difference between absolute humidity of the drying at the exit and the entrance of the tunnel dryer. The absolute humidity X of the inlet and outlet drying air was calculated based on Formula (1):

X = 0.622 ∗ φ ∗ P v s a t P − φ ∗ P v s a t (1)

φ represents the relative humidity (%).

P v s a t the saturation vapour pressure of water at the operating temperature (T_{a}).

P total pressure equals to the atmospheric pressure (Pa). Nadeau J. P. et al. [

P v s a t = exp ( 23.3265 − 3802.7 T a + 273.18 − ( 472.68 T a + 273.18 ) 2 ) for 0 < T a < 45 ˚ C (2)

P v s a t = 23.1964 − 3816.44 T a + 273.18 for T a > 45 ˚ C (3)

The general form of a curve characterizing the drying kinetics of solids is obtained by plotting the product moisture content dry basis (M_{p}) against time (t). The most completed form of a drying curve consists of a transition phase where the product is eventually being heated, a constant-rate drying phase corresponding to the evaporation of free water on the surface of the product [

Drying constants are determined from graphical representation of moisture content M_{p} ((kg water)/(kg dry matter)) of tomato slices, the drying rate DR = ((kg water)/(kg dry matter))/min and the moisture ratio MR (Equation (4)) over time.

M R = M t − M e M 0 − M e (4)

M t is the moisture content of the product at any time (kg water/kg dry matter), M e the moisture content at equilibrium (kg water/kg dry matter) and M 0 the initial moisture content (kg water/kg dry matter). Variation of moisture ratio over time is governed by Luikov equations derived from the second law of Fick on diffusion. Water diffusivity in tomato slices can be calculated from Luikov Equations (5) and (6) used to predict the gradient of temperature (T) and moisture (M) inside tomato slices.

∂ M ∂ t = D e f f [ ∂ 2 M ∂ x 2 + a 1 x ∂ M ∂ x ] (5)

∂ T ∂ t = α [ ∂ 2 T ∂ x 2 + a 1 x ∂ T ∂ x ] (6)

Parameter a_{1} = 0 for planar geometries, a_{1} = 1 for cylindrical shapes and a_{1} = 2 for spherical shapes [

M R = M t − M e M c r − M e = A 1 ∑ i = 1 ∞ 1 ( 2 i − 1 ) 2 exp ( − ( 2 i − 1 ) 2 π 2 D e f f t A 2 ) (7)

M c r is the moisture content of the tomato slices at critical point. A 1 and A 2 are constants (

Henderson and Pabis [

M R = M t − M e M c r − M e = A 1 exp ( − π 2 D e f f A 2 t ) (8)

Assuming D e f f is constant during the drying process, Equation (8) can be written as:

M R = M t − M e M c r − M e = a ⋅ exp ( − k ⋅ t ) (9)

where a and k are drying constants in the Henderson and Pabis Model.

The Page Model was developed by Page, C. [

exponential model, which approximated the 8 π 2 ratio as being equal to unity but introduced new constants as follows:

M R = exp ( − k t y ) (10)

where k and y are drying constants associated with this model.

Calculation of effective water diffusivity was based on Equation (7). Assuming slab geometry for tomato slices, Equation (7) can further be simplified in a linear form as follows:

ln ( M R ) = ln ( 8 π 2 ) − ( π 2 D e f f 4 H 2 t ) (11)

Product geometry | A 1 | A 2 |
---|---|---|

Infinite slab with H as half thickness | 8 π 2 | 4 H 2 |

Sphere with r as radius | 6 π 2 | 4 r 2 |

where, D e f f is given by the slope π 2 D e f f 4 H 2 .

H is the half thickness of the slices. In our experiments, drying was taking place through both sides of the slices. Plotting ln ( M R ) = f ( t ) allow the determination of the slope of Equation (11) and subsequently the determination of D e f f . Application of Fick’s second law of diffusion in the calculation of water diffusivity required assumptions of moisture migration being governed by diffusion, negligible or constant shrinkage of slices, constant diffusion coefficients and temperature [

Thermo hygrometers

The thermo hygrometers served to measure relative humidity and temperature of the inlet and outlet drying air. The specifications of these thermo hygrometers are summarized in

The thermo hygrometers act as data loggers with automatic and manual logging modes. In the automatic logging mode, the thermo hygrometers’ memory can store up to 8124 records at time intervals of 10 s to 24 h.

Thermo anemometer

A Kestrel type thermo anemometer (0.3 to 40 m/s sensibility) served to measure the speed of the drying air. Air temperature and relative humidity ranges are −29˚C to 70˚C ± 1˚C and 5 to 95% ± 3% respectively.

The precision balance

A SCALIX CB-310 model balance was used to weight the tomato slices before and after the drying process. The capacity and the precision of the balance are 300 g and 0.01 g respectively.

The cutting tools

Cutting tools were used to for peeling and trenching the tomatoes into regular slices in preparations for drying. These cutting tools include a kitchen slicer and few knives.

Moisture analyser

A PCE-MA Series moisture analyser was used to determine the initial ( M 0 ) and final moisture contents ( M f ) of tomato samples. Three heat-up modes are

Relative Humidity range | 0% to 100% ± 2.5% with a resolution of 0.1% |
---|---|

Temperature | −30˚C to 105˚C ± 0.4˚C with a resolution of 0.1˚C |

Dew point | −60˚C to 80˚C ± 1.5˚C with a resolution of 0.1˚C |

Data storage capacity (auto mode) | Up to 8124 records |

Software | Compatible with Windows |

Data format | .txt and .db |

available. The Standard heat-up mode is the default mode which is suitable for most sample types. In this heat-up mode, 120˚C are reached after approximately 4 minutes. The Quick heat-up mode is suitable for samples with a high moisture content. In this heat-up mode, 120˚C are reached after approximately 1 minute. The Slow heat-up mode is suitable for samples with low moisture content. In this heat-up mode, 120˚C are reached after approximately 8 minutes. Dry matter, initial and final moisture content of tomato samples were determined by using the Standard heat-up mode. The measurement is stopped automatically when the measured value is constant over a certain period of time.

Experimental dryer

Our locally manufactured experimental dryer is a forced-convective tunnel dryer made up of a one-millimetre thick metallic sheet. The experimental appliance in

Around twelve kilograms of ripen tomatoes were selected bearing in mind to avoid fruits that are either too ripe (broken) or hard (not ripe enough). The product is then weighted, washed, wiped and cut into regular circular slices. Since the drying rate reduces—by 4.5% as a result of a 1 mm thickness increase [

The drying experiments were launched at 09:30 am. The dryer was placed under sun heat. The entire drying energy is therefore coming from the sun. In order to capture a maximum solar heat, the tunnel dryer was placed in a West-East direction. The tomatoes to be dried were evenly placed on shelves in the drying chambers. A fan powered by a solar panel was used for air convection throughout

the tunnel dryer. After every minute, the two thermo hygrometers automatically record the values of the drying air relative humidity, temperature and dew point at the entry and exit of the experimental dryer. In order to eliminate the maximum of water content from the product and predict its storage conditions, the drying process was conducted continuously and over two consecutive days without interruption.

After the two days of experimentation, the recorded data (temperature, relative humidity and dew point of the drying air) was transferred from the data loggers to a computer in the form of tables.

The values of relative humidity were converted into absolute humidity. The difference ΔX between absolute humidity of the drying air at the exit and the entrance of the dryer was therefore calculated. We assumed that ΔX represents the actual moisture content being removed from the product every minute.

This experimental procedure was repeated in one hand with a drying air velocity of V_{1} = 2 m/s and in another a drying air velocity of V_{2} = 3 m/s.

In our work, the method we used for characterizing drying kinetics for tomato was based upon the “indirect” method, which consisted in recording over time, the inlet and outlet variation of the humidity of the drying air instead of the humidity of the product itself.

From a mass balance, the amount of water transported by the inlet and outlet drying air was calculated. Assuming that, the moisture gains (ΔX) of the drying air was taken from the tomato slices, dry basis moisture content and drying rate were calculated. Moisture ratio at any time was therefore calculated based on Formula (4).

Moisture ratio versus moisture content dry basis curves were adjusted in one hand with the Henderson & Pabis Model, given by Equation (9) and in another with the Page Model given by Equation (10) to determine the values of drying constants k, a and y. The adjustment was performed by the use of Solver Tool from Microsoft Excel 2011 software, minimizing the root mean square error between the experimental values and those calculated based on the models.

All drying experiments were conducted under uncontrolled temperature and air humidity conditions. The drying air velocity was however maintained at a constant value of V_{1} = 2 m/s and V_{2} = 3 m/s over two sets of experiments. The inlet section of the experimental drier was 24 × 24 cm^{2}, which gives an applied airflow of 6.912 m^{3}/min and 7.488 m^{3}/min when the drying air velocity was 2 m/s and 3 m/s respectively.

It appears that despite experiments under V_{1} and V_{2} were conducted over different days, ambient air temperature and humidity governing the experimental

conditions, remained relatively constant. Maximum difference of drying air temperatures was less than one degree Celsius (

The relative humidity of the drying air also remained basically constant (

Show in Figures 4-9.

Figures 4-7 show that drying of tomato takes place over two drying phases namely the constant-rate (BC) and the falling-rate (CD) phases.

our experiments. Under both V_{1} and V_{2} drying air velocities, the constant-rate phase occurred at a drying rate of around 0.03 kg water/kg dry matter/min. Several authors reported the non-existence of the constant-rate drying phase in different experimental conditions. Hadi Samimi-Akhijahani et al. [

On the other hand, few authors reported the existence of both a constant-rate and a falling-rate drying phases. Reyes A. et al. [

In our experiments under V_{1} and V_{2} air velocity, the critical points occurred after 200 and 175 minutes respectively (

We used two drying models to describe drying kinetics of tomato slices. These models are the Henderson & Pabis Model and the Page Model. Both models were derived from Fick second law of diffusion. Drying constants associated with the Henderson & Pabis Model are summarized in

In the Henderson and Pabis Model, k is an empirical drying constant (s^{−1}) and a, a constant dependent on the geometric shape of the material [_{1} and with V_{2}. Drying constants associated with the Page Model are summarized in

V_{1} = 2 m/s | V_{2} = 3 m/s | |
---|---|---|

a | 1.082 | 1.104 |

k | 0.0032 | 0.0036 |

χ^{2} | 0.2604 | 0.6090 |

V_{1} = 2 m/s | V_{2} = 3 m/s | |
---|---|---|

y | 1.176 | 1.158 |

k | 0.00103 | 0.00071 |

χ^{2} | 0.1584 | 0.0205 |

As per constant k, it is sensitive to experimental conditions so the variation in its values when drying air velocity varied from 2 to 3 m/s. The values of constants a and k we obtained are summarized in

In the Page Model, constants y and k (

Diffusivity is a key parameter for designing and calculating of industrial dryers. It is a function of the product to be dried but it is mainly a function of operating conditions. The effective moisture diffusivity ( D e f f ) increases with increasing air velocity and temperature. From our experiments, we found values of D e f f in tomato slices equal to 2.918E−09 m^{2}/s and 3.921E−09 m^{2}/s when the drying air velocity was 2 m/s and 3 m/s respectively. These values were calculated from Equation (11) and slopes of ln ( M R ) = f ( t ) (^{−11} to 10^{−9} m^{2}/s. Moreover, Zafer Erbay et al. [^{−10} to 10^{−8} m^{2}/s. These values are both in line with those we found for tomato drying.

An increase in air velocity corresponds to a decrease in external resistances to heat and mass transfer. This has resulted in faster drying [

Our results revealed the existence of both a constant and a falling-rate drying phases. The constant-rate phase occurred at a drying rate of around 0.03 kg water/kg dry matter/min in both experiments with V_{1} and V_{2} drying air velocities. It appeared that the existence of a constant and a falling rate phases is strongly related to the continuous but indirect measurements of water losses in the product being dried during the experiments. This is in contrast with intermittent disruption of experiments in order to measure weight loss on the product, which is likely to disturb the system and prevent from observing a constant rate phase. Conducting our experiments in real-world conditions with uncontrolled temperature and drying air humidity was another significant difference compared with drying experiments conducted in laboratories. The drying constants we obtained from modelling of drying kinetics for tomatoes are in the range of values obtained by other authors who worked on forced convective solar drying experiments. The values we found for effective diffusivity ( D e f f ) of water (2.918E−09 m^{2}/s under V_{1} and 3.921E−09 m^{2}/s under V_{2}) are in the range of values (1E−10 to 1E−8 m^{2}/s) agreed by majority of authors we reviewed. Our study demonstrated that drying air velocity has a significant impact on the drying kinetics. Increasing the air velocity from 2 to 3 m/s has led to 25% increase in effective diffusivity of water in tomato slices during drying. Greater drying air velocity leads to earlier critical point and shorter drying time during the drying process.

We would like to thank Professor Eric DUMONT (Service de Thermodynamique—Ecole Polytechnique de Mons—Université de Mons, Belgique), Professeur Emérite Jacques BOUGARD (Ingénieur Civil AIMs—Ecole Polytechnique de Mons—Université de Mons, Université Libre de Bruxelles—Belgique) for providing valuable help in data analysis.

The authors declare no conflicts of interest regarding the publication of this paper.

Moussa Na Abou, M., Madougou, S. and Boukar, M. (2019) Paper Title. Journal of Sustainable Bioenergy Systems, 9, 64-78. https://doi.org/10.4236/jsbs.2019.92005