Kinetics, energy efficiency and mathematical modeling of thin layer solar drying of figs (Ficus carica L.)

First convectional thin layer drying of two fig (Ficus carica L.) varieties growing in Morocco, using partially indirect convective dryer, was performed. The experimental design combined three air temperature levels (60, 70 and 80 °C) and two air-flow rates (150 and 300 m3/h). Fig drying curve was defined as a third-order polynomial equation linking the sample moisture content to the effective moisture diffusivity. The average activation energy ranged between 4699.41 and 7502.37 kJ/kg. It raised proportionally with the air flow velocity, and the same patterns were observed for effective moisture diffusivity regarding drying time and velocity. High levels of temperature (80 °C) and velocity (300 m3/h) lead to shorten drying time (200 min) and improve the slices physical quality. Among the nine tested models, Modified Handerson and Pabis exhibited the highest correlation coefficient value with the lowest chi-square for both varieties, and then give the best prediction performance. Energetic investigation of the dryer prototype showed that the total use of energy alongside with the specific energy utilization (13.12 and 44.55 MWh/kg) were inversely proportional to the velocity and drying temperature. Likewise, the energy efficiency was greater (3.98%) in drying conditions.

www.nature.com/scientificreports/ This work contributes to a detailed research and information about figs drying proprieties and modeling growing in Morocco. In the present study is the first systematic investigation of thin layer behavior in figs during hot air forced convection, alongside with the energy consumption and efficiency in a solar dryer under the Moroccan conditions. It, therefore, investigates, the possibility of adopting forced convection solar drying to reduce postharvest losses of figs, harvesting and optimizing free solar energy, and helping local farmers economically. The herein proposed solar dryer prototype can be manufactured locally; cheaply, thus it will be totally affordable by smallholder farmers along with traditional cooperatives clusters. This prototype can have wide application especially in remote mountainous areas as well as in the south area where sunshine is abundant during the whole year.

Materials and methods
Preparation. Fresh  Drying experiments. The samples were cut in thin slices of 70 g following a uniform thickness of ~ 6 mm using ceramic knife. The experimental design combined three air temperatures levels (60, 70 and 80 °C) and two drying velocity levels 150 and 300 m 3 /h. The dryer was started about 40 min before drying experiments to achieve steady-state conditions. The fig slices were spared uniformly on the first rack of stainless-steel mesh (mesh size 10 × 10 mm) to ensure homogeneity of diffusion during the process. The heated air goes through the drying chamber trays, from the bottom and flowed upwards to carry out the samples' moisture. The auxiliary heater served for controlling and keeping the air temperature constant.
The fig slices wet Mh(t) was monitored through time using a precision balance (± 0.01 g). Initially, the samples weighing M h (t) was performed every 5 min for the first hour, then increased to 10 min for the second hour and 20 min until constant weight. Dry weight M d was measured after each experiment by keeping samples at 105 °C for 24 h. The moisture content was determined using Eq. (1). The temperature and air humidity at drying entrance unit were measured using a HI 9564 Thermo Hygrometer (Hanna Instruments Ltd, Bedfordshire, UK). Experimental set up. Figs slices were dehydrated in hybrid convection solar dryer (Fig. 1). The prototype produces 80% of solar radiation, and is basically composed of four main parts that are: solar air collector, drying chamber, circulation fan and auxiliary heater. The solar collector was a 10° inclined black galvanized sheet iron with dimensions of 1 m by 2.5 m and a thickness of 0.5 mm. It was a non-selective surface-oriented southward with a single circulation and glazed. The drying chamber was 1.40 m of height, 0.5 m width, and 0.90 m depth and has 10 racks. A centrifugal fan (0.0833 m 3 /s; 80 mm CE, 220 V) provides a theoretical velocity of 1.7 m/s with a regulator which allows to fixed the air flow rate within a range of 150 to 300 m 3 /h. The circulation fan that supplies fresh air has a power of 0.1 kW. The auxiliary heater has a power of 4 kW. It was connected to a thermoregulator which allows to set the temperature (0 to 99 ± 0.1 °C) of drying chamber. Further details regarding accuracy of different drying compartments alongside that of other devices herein are summarized in the Table 1.  (13)  : drying rate at a specific drying time (kg water/ (kg dry matter.min)).
The determination of the drying kinetics is achieved using appropriate software calculation (DOS Smoothing, Curve Expert 3.1 and Originpro 8.1). The drying rate corresponding to each experiment was calculated using Lissage software under MS-DOS.
The effective moisture diffusivity. The effective moisture diffusivity D eff is an important transport property in food drying processes modeling. It indicates the flow of moisture within the drying product. Moisture migrates from the inside of the product and reaches the outer surfaces under the action of various moisture transport mechanisms that can be combined (i.e. capillary flow, Knudsen diffusion, surface diffusion, evaporation and condensation, pure diffusion, ect.). This moisture thereafter, is evaporated through the air due to convection 28 . Fick's equation might be performed to depict the drying behavior through falling rate period. It is presented in Eq. (4): Assuming that the transport of moisture carries out by diffusion, the shrinkage is neglected, the particle is homogenous and isotropic, initial moisture and temperature distribution are uniform, the analytical solution of Fick's can be developed as shown in Eq. (5) 29 .
For a sufficiently long drying period, the above equation becomes 30 : where L (in m) is the half-thickness of the used samples. D eff could be determined through the slope method. Indeed, Eq. (6) is transformed into Eq. (7): The D eff may be deduced from the slope of Eq. (8) by fitting the drying experimental data. The activation energy E a , is the lowest energy level (minimum), that must be exceeded for this process to occur. The E a value is www.nature.com/scientificreports/ related to D eff and its dependence on temperature is expressed by Arrhenius model 11 . The self-diffusion origin is closely related to the thermal agitation. Afterword, the diffusion is activated, and the D eff is calculated following the Arrhenius law as shown in the Eq. (8): where D 0 is the Arrhenius law pre-exponential factor (m 2 s −1 ), E a is the activation energy (kJ mol −1 ), R is the perfect or ideal gas constant (8.314 kJ mol −1 ), and T (in K) is the air temperature 31 . The activation energy is calculated by plotting the ln(D eff ) as a function of the reciprocal of the temperature Drying curves modeling. To describe and predict the fig thin-layer drying kinetics and model its moisture content ratio, nine mathematical models were used ( Table 2). The experimental data were fitted using nine empirical and semi-empirical mathematical models (Table 2). Fitting robustness was evaluated based on to the following criteria: • highest coefficient of correlation (r); • the lowest reduced chi-square (χ 2 ).
These statistical parameters are defined by: where MR* pre,i : i eme Moisture ratio predicted by model; MR* exp,i : i eme Experimental moisture ratio; N: Number of experimental data; n: Number of constants.
Energy consumption of the solar dryer. The total energy consumed (kWh) of convective solar dryer was obtained using Eq. 6 42 .
where E t is the total energy consumption (kWh) of drying system, A is the tray area (m 2 ), ν is the air velocity (m/s), ρ a is the air density (kg/m 2 ), C a is the air specific heat (kJ/kg °C), ΔT is the temperature difference (°C), D t is the time of the entire drying process (h) and ρ a is the microwave power (kW) 42 . The inlet heat capacity 43 and microwave power 44 were calculated using Eqs. (7) and (8): E mec is the mechanical energy (consumed by the fan and the auxiliary heater) used during each drying experiment and measured by the mean of an electric energy meter (accuracy of 0.01 kWh).
Color and water activity determination. The L*, a* and b* color coordinates were determined before and after each drying experiment using a NH310 colorimeter (Shenzhen 3NH Technology, China) 47 . The colorimeter was calibrated to a white calibration plate. The peels color measurements were obtained from two spots located on opposite sides of the slice diameter, while the pulp color was determined from two arbitrary spots on the both sides of the slice. The mean of the two measurements was considered as one replicate. Color differences of fig peels and pulp between the dry and fresh samples were used to describe the color change during drying, defined using Eq. (14), as follows: where L*represents on the scale CIELAB the lightness of the sample ranging from 0 (black) to 100 (white), coordinate a* represents red color ( +) or green (−), and coordinate b* represents yellow color ( +) or blue (−). Subscript 0 refers to the color of the fresh fig slices. High DE values indicate large color changes compared to the reference. Water activity of fresh and dried slices was assessed by a calibrated electric hygrometer (HygroLab, Rotronic, Bassersdorf, Switzerland). All measurements were carried out in triplicates.

Statistical analysis.
The results herein reported are expressed as means ± SE (standard error). Analysis of variance was performed by GLM procedures (SPSS 22 for Windows). The p value < 0.05 was considered statistically significant.

Results and discussions
All experiments started at 9:00 a.m. and continued till 6:00 p.m., during which the city receives the maximum of solar radiation. Figure 2 shows data of the ambient air temperature, relative humidity and solar radiation for fig drying experiment at 60 °C and velocity of 300 m 3 /h. The temperature of the ambient air was found between 30 and 40 °C, while the ambient air humidity varied between 23 and 44%. Horizontal solar radiation was slightly higher than the inclined. Thus, the values ranged from 280 to 850 W/m 2 and 280 to 830 W/m 2 , respectively. The initial moisture content of the studied samples (wet basis) was 78 ± 1% for 'Rey Blanche' and 75 ± 1.2% for 'Conidria' . This initial moisture was reduced for both samples to a final moisture content of 23 ± 1%. Drying curves. Drying time was determined by jointly using drying temperature and velocity variables.
It defines the time required to lower the moisture content of samples to the moisture content suitable for their conservation. The drying time of fig slices for different aero-thermal conditions is given in Fig. 3. According to the results, drying temperature and volume velocity displayed a significant effect on drying time, particularly due the osmotic pressure increase. Hence, at a constant air velocity, arising the air temperature from 60 to 80 °C decreased significantly the drying time. Also, at a constant air temperature, increasing air velocity from 150 to 300 m 3 /h decreased substantially the drying time, as a result of increasing convective heat and mass transfer coefficient between the drying air and the samples. For almost all agricultural products, the drying process took place in the falling rate period where the water molecule is strongly linked to the structure of the product; therefore, the effect of the drying temperature is more important comparatively to the air velocity. Indeed, drying temperature of 80 °C coupled to air flow rate of 300 m 3 /h, provide the optimum condition for fig slices drying in a shortened period of 200 min. These results are consistent with those reported by Garba et al. 48 , Ouaabou et al. 19 and Bahammou et al. 49 , who attributed the great impact on drying kinetics, primary to the temperature and then velocity.
As observed from Fig. 4, the drying curves showed a sharp decrease of moisture content as the drying time increases. The figure shows an absence of phase 0, period of the increasing drying-rate, where the sample temperature increased without any significant loss of moisture, and phase I, known as the period of constant drying-rate. Therefore, only the falling drying rate period (phase II) was observed. This may be due to the small difference between the wet air temperature and the sample initial temperature. These results are in agreement with previous reports 19, [48][49][50][51] . Obviously, increasing the drying temperature implies an important rise of the drying rate, and thus a substantial decrease of the drying time. It is noteworthy that the drying flow rate of 300 m 3 /h leaded to sharp decrease of the moisture content and drying time shortening. Similar pattern was observed at a low flow rate (150 m 3 /h), but the drying time was lengthened. The varieties 'Rey Blanche' and 'Conidria' showed approximately the same behavior to different air-drying conditions on account of small difference in their initial moisture. In general, the time needed to obtain the targeted moisture content to any given level was dependent on     Change in physical and color characteristics. Figure 6 shows      Table 3, ΔE of both peels and pulp decrease significantly when temperature and D v increase. It is noteworthy that all these parameters were significantly higher at low temperature and air flow rate (D v ). Therefore, best physical conditions of figs' slices conservation were obtained at high temperature and air-drying flow rate (80 °C and 300 m 3 /h, respectively). Table 4 shows a highly significant impact of temperature and D v on the quality of samples. However, both varieties displayed similar behavior an then no statistically significant difference was spotted. Furthermore, the interaction between temperature, D v and variety was statistically significant.
Determination of the characteristic drying curve. Drying rate and time vary continuously according to the experiment conditions. Based on the Van Meel concept 59 of the characteristic drying curve (CDC) may be exploited to establish a drying law for the samples from the experimental data. The principal interest of CDC is normalizing the kinetics of drying in a theoretical model to predict other drying curves under any aerothermal conditions, with regards to the sample initial water content and equilibrium moisture content. Indeed, to plot the CDC, it is required to gather all the data on a single curve using the non-linear optimization method of Levenberg Marquard. Figure 7a displays the dimensionless drying rate (f) as a function of the MR. The CDC was expressed in terms of the reduced moisture content as the following third-order polynomial function: f = 0.7945 MR-0.8774 MR2 + 0.6000MR3. Two criteria were used to evaluate fitting quality of the polynomial model, which were the standard error (SE = 0.1434) and the correlation coefficient (r = 0.9171).   Fig. 7b. This curve determines the values of the initial water content and that of equilibrium, which are needed to describe the kinetics of drying at variables air-drying conditions.
The fig slices moistures ratios spatial pattern versus dimensionless drying rates attained at polynomial models for the two fig varieties and their respective correlation coefficients and standard deviations values were provided in Table 5. It is noteworthy that these curves displayed almost similar correlation coefficients (r), which were 0.9192 and 0.9174 for Rey Blanche and Conidria, respectively, whereas, the standard deviations were successfully 0.1449 and 0.1406.
Effective moisture diffusivity (D eff ). D eff is an important indicator that helps in designing and modeling of the mass transfer processes, such as drying or moisture adsorption during storage. It is mainly linked to the product's temperature, the moisture content, and the structure. The D eff , is graphically determined using the logarithmic representation of the reduced moisture content X* as a function of the drying time. The plot of Ln(X*) versus drying period for different experimental sets was presented in Fig. 8. It illustrates the effect of temperature and velocity on the effective diffusion coefficient of fig slices. Thus, at a constant velocity level, D eff increases continuously as the drying temperature increased. It is also noted that for both varieties, the D eff increased subsequently as the drying air flow rate increases (Fig. 8). Table 6 presents D eff values for both varieties at different experiment conditions. In general, D eff varied between 1.9556 × 10 −9 and 4.0511 × 10 −8 , that lie within the range 10 −8 to 10 −12 m 2 /s for drying of food materials. In general, when fig slices were dried at higher air temperature and air flow rate, increased heating energy systematically accelerates the activity of water molecules leading to higher moisture diffusivity 2 . These results were in agreement with those reported by 60 on grape and 19 on sweet cherry, who revealed that the moisture effective diffusivity increased proportionally to the drying temperature.

Energy of activation. The energy of activation (Ea) was concluded by plotting Ln(D eff ) versus 1/T, which
the results were presented in the Fig. 9. Ea value was calculated in different drying experiments and listed in Table 7. The activation energy is considered as a great indicator of the required energy to remove moisture from the sample. Higher Ea value indicates high temperature sensitivity of diffusion coefficient. The obtained values of Ea were in the range of 4699.41 to 7502.37 kJ/kg. Ea required for water diffusion in "Rey Blanche" regardless the air velocity was lower than activation energy of "Conidria". The coefficient of determination was slightly superior to 0.95 with a small standard error that was in average inferior to 0.6 for the two variables considered together (Table 7). In general, at the beginning of drying a little energy is required to remove moisture, and passing the time, the Ea increases because of the moisture resistance in fig tissues 30 . The results are comparable to those reported in similar studies on sweet cherry 19 , on banana slices 61 and on peach and strawberry slices 62 .

Modelling of fig drying curves.
The samples moisture content at each drying temperature were converted afterwards to dimensionless moisture ratio and afterward fitted to nine empirical and non-empirical mathematical models ( Table 2) to determine the statistics values, that give the best fit of models. The statistics of these models were estimated using non-linear regression analysis and summarized in Table 8. The correlation coefficient (r) was the primary criterion for choosing the model with the highest accuracy in drying curve prediction. Other than r, the mean square of the deviations (khi-square) between the calculated and predicted values for the models was used to determine the accuracy of the fit. Indeed, the model presenting the best prediction of fig drying curve was determined as the one with the highest r and the lowest of χ 2 . In fact, the r values ranged from 0.5977 to 0.9997 for 'Conidria' and from 0.6009 to 0.9997 for 'Rey Blanche' , while χ 2 were in the range of 1.13 × 10 −3 to 0.2353 and 6.4 × 10 −3 to 0.59 for 'Conidria' and 'Rey Blanche' , respectively (Table 8). Among all the models tested, the modified Handerson and Pabis model provided the best prediction throughput resolution by displaying the highest r and the lowest value of χ 2 . In the literature, this model was successfully applied to pistachio 63 , kiwifruit 64 and coconut 65 to determine the drying curve.
The experimental moisture ratios and those predicted by the selected model were plotted according to different air temperatures and flow rates in order to validate the model (Figs. 10 and 11). The fitting results demonstrates that Modified Handerson and Pabis prediction is suitable to describe the kinetics drying of fig slices. Figure 10  Total energy consumption in solar convective drying. Figure 12. shows the total energy consumption in solar convection drying of fig at different air temperatures and flow rates. It was observed that the total energy consumption decreases as the air flow increases under the entire experimental temperature range. Likewise, at a constant air flow rate, the drying total energy consumption decreases substantially as the air temperature increases. That implies that the temperature increase leads to a substantial decrease of the drying time, which impacts significantly the dryer total energy consumption. These findings are in agreement with multiples studies previously published regarding several agri-foods products drying such as pomegranate arils, Russian olive, and chamomile [66][67][68] .  Energy efficiency. The Fig. 13 displays the values of energy efficiency for multiple drying conditions of fig.
The thermal efficiency represents the ratio between the amount of energy used for moisture elimination and the one supplied to the hybrid solar dryer. As it is described in the figure, the energy efficiency substantially decreases as the air flow rate and the drying temperature increase. According to this figure, the lowest energy efficiency was about 1.54%, and was found in the combination of a temperature of 60 °C and a velocity of 300 m 3 /h, while the maximum value was around 3.98%, and was achieved in the combination of 80 °C and 150 m 3 /h. The fig drying data generated using a solar convective dryer shows similar trends in comparison to the thin drying air convection of peppermint leaves (3.5-5.3%) and convective drying of chamomile (1.9-6.7%). The energy efficiency values obtained are in agreement with those found for most convection dryers 45,68 . Fundamentally, it was stated that the final moisture in biological products generally requires higher drying energy than the initial moisture, and the preparation of the samples prior to drying such as osmotic treatment 70 ,       -layer drying, evaluate and save energy consumption of the drying process. This study clearly shows that the air temperature as well as the velocity had a large impact on the overall energetic performance of the hybrid dryer, with a substantially low electrical power requirements, as these factors increase. The results suggest that the solar energy can be an effective renewable source in biological products drying process, which can become the most efficient and feasible way out to deal with the increasing energy demand and supply gap.