Development of a mathematical model for predicting moisture changes in pear during convective drying

Author
mohsen Dalvi-Isfahan
Assistant professor, Department of Food Science and Technology, Faculty of Agriculture, Jahrom University, Jahrom, Iran.
10.52547/fsct.18.120.22
Abstract
The efficiency of several theoretical models to predict the moisture content of pear slices during drying were evaluated and compared. Pear slices were dried at 5 different temperatures (30-40-50-60-70‌‌oC) and the moisture diffusivity and convective mass transfer coefficient were estimated. In the next step, mass transfer model was developed by using mathematical solution of Fickchr('39')s second law of diffusion with different numerical and analytical models. The results of the studied models indicated that the both numerical‌ models were substantially more accurate than analytical model in describing the experimental drying curves. However, the best result was obtained with the combined model developed in this study. This model presents the highest coefficient of determination (R2) value (0.999), and the lowest root mean square error (RMSE) value (0.06). The higher accuracy of this model can be attributed to the fact that this model takes into account the term that simulate the convective moisture transport and chooses the appropriate boundary conditions. By applying this model, it is possible to predict moisture variations in pear slices with high accuracy as a function of internal variables (thickness, chemical composition) and external factors (temperature, relative humidity and air velocity).
Keywords
Drying
Numerical solution
analytical solution and pear

Subjects

[1] Guiné, R. P. F., Ferreira, D. M. S., Barroca, M. J., & Gonçalves, F. M. (2007). Study of the drying kinetics of solar-dried pears. Biosystems Engineering, 98(4), 422-429.
[2] Darvishi, H., Asl, A. R., Asghari, A., Azadbakht, M., Najafi, G., & Khodaei, J. (2014). Study of the drying kinetics of pepper. Journal of the Saudi Society of Agricultural Sciences, 13(2), 130-138.
[3] Castro, A. M., Mayorga, E. Y., & Moreno, F. L. (2018). Mathematical modelling of convective drying of fruits: A review. Journal of Food Engineering, 223, 152-167.
[4] Wang, W., Chen, G., & Mujumdar, A. S. (2007). Physical Interpretation of Solids Drying: An Overview on Mathematical Modeling Research. Drying Technology. 4(25), 659-668
[5] Erbay, Z., & Icier, F. (2010). A Review of Thin Layer Drying of Foods: Theory, Modeling, and Experimental Results. Critical Reviews in Food Science and Nutrition, 50(5), 441-464.
[6] Rathnayaka Mudiyanselage, C. M., Karunasena, H. C. P., Gu, Y. T., Guan, L., & Senadeera, W. (2017). Novel trends in numerical modelling of plant food tissues and their morphological changes during drying – A review. Journal of Food Engineering, 194, 24-39
[7] Kulkarni, N., & Rastogi, A. (2014). Comparison of Explicit Finite Difference Model and Galerkin Finite Element Model for Simulation of Groundwater Flow. In).
[8] Agrawal, S. G., & Methekar, R. N. (2017). Mathematical model for heat and mass transfer during convective drying of pumpkin. Food and Bioproducts Processing, 101, 68-73.
[9] Szadzińska, J., & Mierzwa, D. (2021). The influence of hybrid drying (microwave-convective) on drying kinetics and quality of white mushrooms. Chemical Engineering and Processing - Process Intensification, 167, 108532.
[10] Kaya, A., Aydin, O., & Dincer, I. (2007). Numerical Modeling of Forced-Convection Drying of Cylindrical Moist Objects. Numerical Heat Transfer, Part A: Applications, 51(9), 843-854
[11] Crank, J. (1975). The Mathematics of Diffusion (2nd Edition ed.). England: Oxford University Press.
]12[ دلوی، م., همدمی، ن. 1389. مدل سازی عددی انتقال حرارت در پنیر سفید فراپالایش شده. نشریه پژوهش های صنایع غذایی، 3(2).
[13] Mccarthy, M. J., Perez, E., & Özilgen, M. (1991). Model for Transient Moisture Profiles of a Drying Apple Slab Using the Data Obtained with Magnetic Resonance Imaging. Biotechnology Progress, 7(6), 540-543.
[14] Guiné, R. P. F. (2009). Sorption Isotherms of Pears Using Different Models. International Journal of Fruit Science, 9(1), 11-22.
[15] Dalvi-Isfahan, M. (2020). A comparative study on the efficiency of two modeling approaches for predicting moisture content of apple slice during drying. Journal of food process engineering, 43(11), e13527.
[16] Golestani, R., Raisi, A., & Aroujalian, A. (2013). Mathematical Modeling on Air Drying of Apples Considering Shrinkage and Variable Diffusion Coefficient. Drying Technology, 31(1), 40-51.
[17] da Silva, W. P., e Silva, C. M. D. P. S., Farias, V. S. O., & Gomes, J. P. (2012). Diffusion Models to Describe the Drying Process of Peeled Bananas: Optimization and Simulation. Drying Technology, 30(2), 164-174.
[18] Manjunatha, S., & Raju, P. (2019). Mathematical Modelling the Drying Kinetics of Beetroot Strips during Convective Drying at Different Temperatures. Defence Life Science, 4(2), 140-149.
[19] Royen, M. J., Noori, A. W., & Haydary, J. (2020). Experimental Study and Mathematical Modeling of Convective Thin-Layer Drying of Apple Slices. Processes, 8(12), 1562.
[20] Onwude, D. I., Hashim, N., Janius, R. B., Nawi, N. M., & Abdan, K. (2016). Modeling the Thin-Layer Drying of Fruits and Vegetables: A Review. Comprehensive reviews in food science and food safety, 15(3), 599-618.
[21] Yuan, Y., Tan, L., Xu, Y., Yuan, Y., & Dong, J. (2019). Numerical and experimental study on drying shrinkage-deformation of apple slices during process of heat-mass transfer. International Journal of Thermal Sciences, 136, 539-548.
[22] Castro, A. M., Mayorga, E. Y., & Moreno, F. L. (2019). Mathematical modelling of convective drying of feijoa (Acca sellowiana Berg) slices. Journal of Food Engineering, 252, 44-52.
[23] Kaddoura, M. F., Chosa, M., Bhalekar, P., & Wright, N. C. (2021). Mathematical modeling of a modular convection-enhanced evaporation system. Desalination, 510, 115057.
[24] Esfahani, J. A., Majdi, H., & Barati, E. (2014). Analytical two-dimensional analysis of the transport phenomena occurring during convective drying: Apple slices. Journal of Food Engineering, 123, 87-93.
[25] Janjai, S., Lamlert, N., Intawee, P., Mahayothee, B., Haewsungcharern, M., Bala, B. K., & Müller, J. (2008). Finite element simulation of drying of mango. Biosystems Engineering, 99(4), 523-531.
[26] Bourne, M. C. (1986). Effect of water activity on texture profile parameters of apple flesh. Journal of Texture Studies. 17(3), 331-340.