
Research Article


Mathematical Modeling of Moisture Content of Apple Slices (Var. Golab) During Drying 

Elham Meisamiasl,
Shahin Rafiee,
Alireza Keyhani
and
Ahmad Tabatabaeefar



ABSTRACT

Drying is one of the primary methods of food preservation. Determining coefficients used in drying models is essential to predict the drying behavior. The present study was conducted to compute drying characteristics of apple slices. Thin layer drying kinetics of apple slices (varietyGolab) was experimentally investigated in a convective dryer and the mathematical modeling was performed by using thin layer drying models in the literature. Drying characteristics of apple slices were determined using heated ambient air at temperatures between 40 and 80^{o}C, velocities at 0.5 m/s and thickness of thin layer 2, 4, 6 mm. Beside the effects of drying air temperature, effects of slice thickness on the drying characteristics, drying time and quality of dried product were also determined. Drying curves obtained from the experimental data were fitted to twelve different thin layer drying models. All the models were compared according to three statistical parameters, i.e. Root Mean Square Error (RMSE), chisquare (X^{2}) and modeling efficiency (EF). The results showed that increasing drying air temperature resulted to shorter drying times. Midilli model had the highest value of EF (0.999611), the lowest values of 0.031806 and 0.001088 for RMSE and X^{2} respectively. The Midilli model was found to be the best model for describing the drying curves of apples. The effects of drying air temperature and thickness on the drying constant and coefficient were also shown.





INTRODUCTION Among fruits, apple is the more important one economically and industrially. It is consumed in different forms as fresh fruit, concentrated juice or thin dried slices (Wang et al., 2007). Apple was introduced into Iran many years ago. Iran with more than 2,000,000 tones produce in year, presently ranks 6th among the apple producing countries of the world (ASB, 2005). Drying, a complex process involving heat and mass transfer phenomena and frequent in most food processing industries (Cohen and Yang, 1995), is probably the main and the most expensive step after harvesting. It improves the product shelf life without addition of any chemical preservative and reduces both the size of package and transport cost. Fruits and vegetables are regarded as highly perishable foods due to their high moisture content (Simal et al., 1994). The fruits contain a high percentage of their fresh weight as water. Accordingly, they exhibit relatively high metabolic activity compared with other plantderived foods such as seeds. This metabolic activity continues after harvesting, thus making most fruits highly perishable commodities (Atungulu et al., 2004). Mathematical modeling and simulation of drying curves under different conditions is important to obtain a better control of this unit operation and an overall improvement of the quality of the final product. Models are often used to study the variables involved in the process, predict drying kinetics of the product and to optimize the operating parameters and conditions (Karathanos and Belessiotis, 1999). Drying process of food materials mostly occur in the falling rate period (Wang and Brennan, 1992). Thin layer drying equations are used to estimate drying times of several products and also to generalize drying curves. Several investigators have proposed numerous mathematical models for thin layer drying of many agricultural products. For example, apple (Wang et al., 2007), organic apple (Sacilik and Elicin, 2006), Golden apple (Menges and Ertekin, 2005), kiwifruit (Mohammadi et al., 2009), rough rice (Cihan, et al., 2007), red chilli (Kaleemullah and Kailappan, 2005), apricot (Togrul and Pehlivan, 2002, 2003), plum (Doymaz, 2004), eggplant (Ertekin and Yaldiz, 2004), grape (Yaldiz et al., 2001), green pepper, stuffed pepper, pumpkin, green bean and onion (Yaldiz and Ertekin, 2001). Convection drying as well as other techniques for drying is used in order to preserve the original characteristics of apples. Dried apples could be consumed directly or treated as secondary raw material (Velic et al., 2004). The aim of this work was to study the effect of drying air temperature on the drying characteristics and dehydration ratio for the apple drying process and to select the mostsuitable model (in terms of fitting ability) to describe the thinlayer drying of apple (varietyGolab). Beside, investigate the effects of drying conditions and slices thickness on the coefficients of the selected model. MATERIALS AND METHODS In this study, the apples were selected from a local market and from Golab variety; Iranian variety. The drying experiments were carried out using the laboratory dryer in the Department of Agricultural Machinery, Faculty of Biosystems Engineering, University of Tehran. Figure 1 shows a schematic diagram of the dryer used for experimental work; it consists of an electrical fan, an airflow control unit, heaters, drying chamber and instruments for various measurements (Yadollahinia, 2006). Table 1 shows measurement instruments including their rated accuracy. The airflow control unit regulates the velocity of the drying air through the 30 cm diameter drying chamber. The dryer is capable of providing any desired drying air temperature in the range of 20120^{o}C and velocity in the range of 0.13.0 m/s with high accuracy. Apples were washed, peeled and sliced in thicknesses of 2, 4 and 6 mm using a slicer machine. The uniform thickness of t±0.01 mm was prepared by adjusting the opening of the slicer with a vernier caliper having a least count of 0.01 mm. The product was spread as a thin layer on a screen. The desired drying air temperature was attained by electrical resistance heating elements and controlled by the heating control unit. The air was forced through the heating elements and after reaching the desired temperature was passed through the drying chamber. The drying air temperature and velocity were measured directly in the drying chamber. The air velocity was measured using a hot wire digital anemometer (Testo, 405 V1, Germany) with the accuracy of ±0.1 m/s and the temperature using Ttype thermocouple (Testo 925, Germany) with the accuracy of ±1^{o}C. Weighing of samples inside the drying chamber was carried out manually using an electronic balance with a capacity of 03000 g and accuracy of ±0.01 g. Table 1:  Specifications
of measurement instruments including their rated accuracy 

Thin layers of apples were dried using drying air temperatures from 4080^{o}C at 10^{o}C interval. The drying air velocity was adjusted to 0.5 m/s. The drying samples were cut into 2, 4 and 6 mm slice thicknesses with a slicer (Ertekin, 2002). Moisture content determination was done by drying the samples at 105^{o}C until the weight became constant (Yagcioglu et al., 1999). To determine the initial moisture content, the drying process was continued until the weight became constant. After that the samples were placed in an oven at 105^{o}C for 12 h to find the moisture content according to the following equation: Where M is the apple slice moisture content (g water/ g dry base, d.b.), W_{w} is the wet weight and W_{d} is the dried weight. The initial moisture content of apple was obtained as 5.06.4 (d.b.). The reproducibility of the initial moisture content measurements was within the range of ±5%. The experimental drying data for apple were fitted to the thin layer drying models in Table 2 by using SPSS version 13.0 software and nonlinear regression technique. For mathematical modeling, the thin layer drying equations in Table 2 were tested to select the best model for describing the drying curve of the apple slices. The reduced chisquare (X^{2}), Root Mean Square Error (RMSE) and increased modeling Efficiency (EF) were used as the primary criteria to select the best equation to account for variation in the drying curves of the dried samples (Goyal et al., 2007; Menges and Ertekin, 2006; Yaldiz, 2001). The reduced chisquare is the mean square of the deviations between the experimental and calculated values for the models and was used to determine the goodness of the fit. The RMSE gives the deviation between the predicted and experimental values and it is preferred tending to zero. The EF also gives the ability of the model to predict the drying behavior of the product and its highest value is one. These statistical values were calculated from the following equations: Where MC_{exp,i }is the ith experimental moisture content, MC_{pre,i }is the ith predicted moisture content, N is the number of observations, n is the number of constants in drying model and MC_{expmean} is the mean value of experimental moisture content. RESULTS AND DISCUSSION
The results of the effects of drying air temperature on drying time showed
that, an increase in drying air temperature resulted in a decrease in the drying
time (Fig. 24). The drying rate, DR, is
expressed as the amount of the evaporated moisture over time.
 Fig. 1: 
Schematic diagram of the drying system for measurement of
the thinlayer parameters of apple slices. 1. PC; 2. microcontroller; 3.
digital balance; 4. fan; 5. heating elements; 6. duct and tunnel; 7. trays;
8. temperature sensor; 9. relative humidity sensor 
 Fig. 2:  Experimental
and computed moisture content obtained using the Midilli model for 2mm
thickness 
The drying rates of apple slices were calculated by using Eq.
(5):
Where, M_{t} and M_{t+dt} are the moisture content at t and moisture content at t+dt (kg moisture/kg dry matter), respectively, t is drying time (min).
As shown in Fig. 5, the drying rate increased with increasing
drying air temperature and reached its maximum values at 80^{o}C. Drying
rate decreased continuously with decreasing moisture content or increasing drying
time. Similar results have been reported by Mohammadi et al. (2009) for
kiwifruit, Bala et al. (2003) for pineapple, Prachayawarakorn et al.
(2008) for banana and for different crops by researchers (Kingsly and Singh,
2006; Doymaz, et al., 2005).

Fig. 3: 
Experimental and computed moisture content obtained using
the Midilli model for 4mm thickness 
 Fig. 4:  Experimental
and computed moisture content obtained using the Midilli model for 6mm
thickness 
Figure 5 shows the drying rate against moisture content of the samples at temperatures of 4080^{o}C of drying air, velocity of 0.5 m/s and thickness of 2 mm and the average initial moisture content of around 5 kg water per kg dry matter was dried to the final moisture content of about 0.1 (d.b.) until no further changes in their mass were observed. The moisture content of apple slices at various drying air temperatures were fitted in twelve models and the results of statistical analysis. In seven cases (Table 3), the value of EF was greater than 0.99 indicating a good fit (Madamba et al., 1996). From the results of RMSE and chisquare values of all thin layer drying models for all drying conditions, the Midilli et al. (2002) model gave the lowest values while the EF showed the highest amount and thus it was chosen to represent the thin layer drying of apple slices (Table 3). The drying constants (k) and (b) and coefficients (a) and (n) values and also statistical parameters RMSE, chisquare and EF for Midilli model are shown in Table 4. Table 2:  Mathematical
models applied to drying curves 

Table 3:  Average
values of the drying constants and coefficients of different models determined
through regression method for apples 

Table 4:  Statistical
results of midilli et al. model and its' constants and coefficients
at different drying conditions 

 Fig. 5:  Influence
of temperature on drying rate of apple slices at five temperatures, air
velocity of 0.5 m/s and slice thickness of 2mm 
It is clear that, in Midilli model, RMSE and chisquare values were very low
and changed between 0.0191570 and 0.0489440 and 0.0003670 and 0.0024010, respectively.
Modeling Efficiency (EF) also ranged from 0.9991930 and 0.9998620. This model
represented the experimental values satisfactorily.
Conclusion: The drying behavior of apple slices in a laboratory dryer was investigated for three thicknesses of apple slices at five different drying air temperatures. The time required to dry apple slices from an initial moisture content of 5.06.4 (d.b.) to the final moisture content of about 0.1 (d.b.) for 2 mm thickness was 320, 220, 150, 100 and 60 min and for thickness of 4 mm, was 600, 400, 320, 320 and 150 min and for thickness of 6mm, was 700, 600, 320 and 300 min, at 40, 50, 60, 70 and 80^{o}C of drying air temperature, respectively.
Drying rate increased with the increase in drying air temperature, thus reducing
the drying time. Results showed that the Midilli et al. model among of
twelve drying models, could be used to describe the drying characteristics of
the apple slices, in the drying conditions and slice thicknesses. This model
had the highest value of EF (0.99961), the lowest RMSE (0.03180) and X^{2}
(0.00109). Determining constants and coefficients of this model is essential
to predict the drying behavior.
ACKNOWLEDGMENT This research was supported by Faculty of Biosystems engineering, University of Tehran, Karaj, Iran.

REFERENCES 
1: Agricultural Statistical Bulletin (ASB), 2005. Crop year 20042005. Ministry of JihadAgriculture of Iran.
2: Atungulu, G., Y. Nishiyama and S. Koide, 2004. Electrode configuration and polarity effects on physiochemical properties of electric field treated apples post harvest. Biosyst. Eng., 87: 313323. Direct Link 
3: Bala, B.K., M.R.A. Mondol, B.K. Biswas, B.L. Chowdury and S. Janjai, 2003. Das solar drying of pineapple using solar tunnel drier. Renewable Energy, 28: 183190.
4: Cihan, A., K. Kahveci and O. Hacihafizoglu, 2007. Modelling of intermittent drying of thin layer rough rice. J. Food Eng., 79: 293298.
5: Cohen, J.S. and T.C.S. Yang, 1995. Progress in food dehydration. Trends Food Sci. Technol., 6: 2025. Direct Link 
6: Doymaz, I., 2004. Convective air drying characteristics of thin layer carrots. J. Food Eng., 61: 359364. CrossRef 
7: Doymaz, I., N. Tugrul and M. Pala, 2005. . Drying characteristics of dill and parsley leaves. J. Food Eng., 65: 421428.
8: Ertekin, C. and O. Yaldiz, 2004. Drying of eggplant and selection of a suitable thin layer drying model. J. Food 63: 349359. CrossRef  Direct Link 
9: Goyal, R.K., A.R.P. Kingsly, M.R. Manikantan and S.M. Ilyas, 2007. Mathematical modelling of thin layer drying kinetics of plum in a tunnel dryer. J. Food Eng., 79: 176180. CrossRef 
10: Kaleemullah, S. and R. Kailappan, 2006. Modelling of thinlayer drying kinetics of red chillies. J. Food Eng., 76: 531537. Direct Link 
11: Karathanos, V.T., 1999. Determination of water content of dried fruits by drying kinetics. J. Food Eng., 39: 337344. CrossRef  Direct Link 
12: Karathanos, V.T. and V.G. Belessiotis, 1999. Application of a thinlayer equation to drying data of fresh and semidried fruits. J. Agric. Eng. Res., 74: 355361. CrossRef  Direct Link 
13: Kingsly, A.R.P. and D.B. Singh, 2006. Drying kinetics of pomegranate arils. J. Food Eng., 80: 123130.
14: Menges, H.O. and C. Ertekin, 2005. Mathematical modeling of thin layer drying of golden apples. J. Food Eng., 77: 119125.
15: Menges, H.O. and C. Ertekin, 2006. Thin layer drying model for treated and untreated Stanley plums. Energy Convers. Manage., 47: 23372348.
16: Midilli, A., H. Kucuk and Z. Yapar, 2002. A new model for singlelayer drying. Drying Technol.: Int. J., 20: 15031513. CrossRef  Direct Link 
17: Mohammadi, A., S. Rafiee, A. Keyhani and Z. EmamDjomeh, 2009. Moisture content modeling of sliced kiwifruit (cv. Hayward) during drying. Pak. J. Nutr., 8: 7882. CrossRef  Direct Link 
18: Ozdemir, M. and Y.O. Devres, 1999. The thin layer drying characteristics of hazelnuts during roasting. J. Food Eng., 42: 225233. CrossRef 
19: Page, G., 1949. Factors influencing the maximum rates of airdrying shelled corn in thin layers. M.Sc. Thesis, Purdue University, Lafayette, IN., Illinois, USA.
20: Prachayawarakorn, S., W. Tia, N. Plyto and S. Soponronnarit, 2008. Drying kinetics and quality attributes of lowfat banana slices dried at high temperature. J. Food Eng., 85: 509517. CrossRef 
21: Rahman, M.S., C.O. Perera and C. Thebaud, 1998. Desorption isotherm and heat pump drying kinetics of peas. Food Res. Int., 30: 485491. CrossRef  Direct Link 
22: Sacilik, K. and A.K. Elicin, 2006. The thin layer drying characteristics of organic apple slices. J. Food Eng., 73: 281289. CrossRef  Direct Link 
23: Simal, S., C. Rossello, A. Berna and A. Mulet, 1994. Heat and mass transfer model for potato drying. Chem. Eng. Sci., 22: 37393744.
24: Togrul, I.T. and D. Pehlivan, 2002. Mathematical modeling of solar drying of apricots in thin layers. J. Food Eng., 55: 209216.
25: Togrul, I.T. and D. Pehlivan, 2003. Modeling of drying kinetics of single apricot. J. Food Eng., 58: 2332. CrossRef  Direct Link 
26: Velic, D., M. Planinic, S. Tomas and M. Bilic, 2004. Influence of airflow velocity on kinetics of convection apple drying. J. Food Eng., 64: 97102. Direct Link 
27: Verma, L.R., R.A. Bucklin, J.B. Endan and F.T. Wratten, 1985. Effects of drying air parameters on rice drying models. Trans. ASAE, 28: 296301. CrossRef  Direct Link 
28: Wang, N. and J.G. Brennan, 1992. Effect of water binding on the drying behavior of potato. Sci. Publi., 92: 13501359.
29: Wang, Z., J. Sun, X. Liao, F. Chen, G. Zhao, J. Wu and X. Hu, 2007. Mathematical modeling on hot air drying of thin layer apple pomace. Food Res. Int., 40: 3946. CrossRef 
30: Westerman, P.W., G.M. White and I.J. Ross, 1973. Relative humidity effect on the high temperature drying of shelled corn. Trans. ASAE., 16: 11361139.
31: Yadollahinia, A.A., 2006. Thin layer drying model for paddy dryer. M.Sc. Thesis, Faculty of Biosystems Engineering, University of Tehran.
32: Yagcioglu, A., A. Degirmencioglu and F. Cagatay, 1999. Drying characteristics of laurel leaves under different drying conditions. Proceedings of the 7th International Congress on Agricultural Mechanization and Energy, May 2627, 1999, Adana, Turkey, pp: 565569
33: Yaldiz, O. and C. Ertekin, 2001. Thin layer solar drying of some different vegetables. Dry. Technol., 19: 583596.
34: Yaldiz, O., C. Ertekin and H.I. Uzun, 2001. Mathematical modeling of thin layer solar drying of sultana grapes. Energy, 26: 457465. CrossRef  Direct Link 
35: Madamba, P.S., R.H. Driscoll and K.A. Buckle, 1996. The thinlayer drying characteristics of garlic slices J. Food Eng., 29: 7597. CrossRef  Direct Link 



