سینتیک خشک کردن و شبیه‌سازی ریاضی برش های پرتقال در خشک کن رفرکتنس ویندو

In this study, the drying parameters and kinetics of sliced orange (Thomson variety) were investigated in a refractance window dryer at temperatures (60, 75, and 90 degrees Celsius) and slice thicknesses (4, 6, and 8 mm). Analysis of variance was used to determine the effects of temperature and thickness on the parameters of color change, shrinkage, and resorption intensity. Five mathematical models were selected to describe and compare the drying kinetics of orange slices, and the coefficient of determination (R2), chi-square (χ2), and root mean square error (RMSE) were used for evaluation. Also, the moisture transfer from orange slices was described by fitting the Fick diffusion model. The results showed that drying temperature and slice thickness had a significant effect on the drying behavior of orange slices. Drying time decreased with increasing temperature and decreasing thickness. Temperature and thickness had little effect on the total color changes, shrinkage rate, and resorption intensity of dried orange slices. Among the mathematical models, the modified Page model had the best fit with the lowest error and the highest coefficient of determination. The effective diffusion coefficient (Deff) increased with increasing drying temperature and was found to be in the range of 39.6× 10-10 - 42.5× 10-10 m2/s. The temperature dependence of the effective diffusion was described by the Arrhenius equation and the activation energy for moisture diffusion in orange slices was determined to be 27.5 kJ/mol.

Introduction
Iran ranks seventh in the world in terms of citrus production. The country's annual citrus production is about six million tons, of which three million tons are oranges. A significant portion of the oranges produced, after consumption as fresh fruit and export, can be used in various processing and complementary industries, including fruit juice and dried fruit. Since fruit drying can be done on a small and home scale, the development of suitable dryers with high energy efficiency is very important. Refractance Window, known as the fourth generation of dryers, is a moisture removal system for producing high-quality dried or concentrated foods. Refractance window dryers can produce dried products with relatively low energy consumption, in a short time, and with minimal thermal damage. In the refracting system, the thermal energy of hot water is transferred to the fruit slices placed on the film through a polymer film. The moisture removal process in this system is fast, under atmospheric pressure, self-regulating, and at a temperature lower than the temperature of the hot water used, so thermal damage to the material being dried is minimized. The resulting water vapor is removed from the dryer chamber by a fan (Ortez-Jeres, 2015). Researchers have used various methods in the field of drying agricultural products and cut fruits. Given the extensive research conducted on these methods, this study attempts to address the research conducted on the refractivity window dryer system.

Materials and Methods
Thomson variety of oranges were obtained from orchards in the city of Jooybar, Mazandaran province. First, the oranges were washed in water and after drying, they were sliced into 4, 6, and 8 mm thick slices using a slicer. All samples were weighed before drying. The weight of the samples was measured using a digital scale (AND-EK-600G) with an accuracy of ±0.01. A refractance window dryer was used to dry the samples. The refractance window device used in the experiments is located at the Mashhad Agricultural Jihad Research and Development Center, which uses hot water circulation as a heat source with a boiling temperature at atmospheric pressure, which can be changed with the water temperature controller due to the elements inside the tank. Hot water in the hot water bath is circulated through a heating unit to maintain a constant water temperature and increase thermal efficiency. A valve is installed between the hot water bath and the water heating tank to pump water until the water temperature is lower than the desired value. A pump is provided to pump hot water from the hot water tank to the bath. The heat energy from heating the water is transferred to the product through a Mylar polyester plastic sheet. For drying, the predetermined samples are spread on a transparent plastic sheet (Mylar) and its bottom is placed in contact with hot water from a shallow container. The Mylar sheets pass the pure energy from the hot water through conduction and radiation, causing the product to dry. Also, two fans are located at the top of the Mylar sheet to remove the moisture created in the chamber. Orange slices with a thickness of 4 mm were placed in a single layer on the drying chamber tray, and experimental treatments for drying thin slices of apple were performed, including drying temperatures from 30 to 70 degrees Celsius, with an increase of 10 degrees Celsius, and air speeds from 1 to 2 meters per second, with an increase of 0.5 meters per second. After turning on the heat pump dryer, the temperature and air speed were adjusted to the desired treatment, and then the drying process began. Drying continued until the weight of the thin slices of apple was approximately constant, and the collected data were recorded every ten minutes. A factorial experimental design based on a completely randomized design with three replications was used for data analysis.

Results and Discussion
The drying intensity decreased continuously with drying time. As can be seen, increasing the drying temperature resulted in an increase in the drying rate and consequently a decrease in the drying time. With increasing drying temperature and due to the intensification of the heat transfer rate, water molecules moved faster and accelerated the water transfer from the product. The higher drying rate occurred during the initial drying period, which was due to lower external resistance and greater water migration into the product. As the thickness of the samples decreased, the time to reach the end point decreased from 190 minutes for 8 mm thickness to 140 minutes for 4 mm thickness. Also, the moisture removal rate was higher in the initial stage of drying, which then decreased. It is obvious that the time to reach the end point of drying of orange slices changes with the thickness of the sample. This indicates that the thickness of the sample affects the drying time. It can be seen that among these equations, the three mathematical models of modified Page, logarithmic and Medley et al. with a coefficient of determination higher than 0.99 can well describe the law of moisture change. Among them, the modified Page model has the highest R2 and the lowest χ2 and RMSE. It can be concluded that the modified Page model is the best model for describing the drying of sliced orange slices in a refractance window dryer. It was found that its range of variation changed from 39.6× 10-10 to 42.5× 10-10 m2/s. As expected, the Deff values increased with increasing air temperature during the drying process, which was due to the increase in vapor pressure inside the samples, which led to molecular motion and rapid movement of water at high temperatures. Also, with increasing thickness, the mass transfer rate increased, which led to an increase in the effective diffusion coefficient. The highest and lowest activation energies were 28.38 and 21.94 kJ/mol, respectively, for treatments at 90°C and 8 mm thickness and 60°C and 4 mm thickness.

Conclusion
The use of refractivity window for drying orange slices was tested and the best model was presented using mathematical models to fit the experimental data and predict the drying behavior. Increasing the temperature and decreasing the thickness of the orange slices both accelerate the drying process. Among them, the modified Page model has the highest R2 and the lowest χ2 and RMSE. It can be concluded that the modified Page model is the best model to describe the drying of orange slices in the refractivity window dryer. The Deff values increased with increasing drying temperature, which is due to the increase in vapor pressure inside the samples, which leads to rapid movement of water at high temperatures. The activation energy for moisture diffusion was obtained from the Arrhenius equation as 27.5 kJ/mol.