Mathematical modeling for heat conduction in olive fruit

Author
mohsen Dalvi-Isfahan
Assistant professorDepartment of Food Science and Technology, Faculty of Agriculture, Jahrom University, Jahrom, Fars, Iran, P.O. Box 74137-66171
10.22034/FSCT.21.149.159
Abstract
This study aims to develop a numerical model that can simulate the heat transfer in spherical coordinates and predict the temperature of olive fruit during the thermal process. The first step was to measure or estimate the thermophysical properties of olive fruit. The fixed grid finite difference method with an explicit scheme was used to solve the heat transfer equation. The product had an average geometric diameter of 18.18 mm, a bulk density of 556 kg/m3, a porosity of 48% and a specific heat of 3180 kJ/kg. The inverse method was used to determine the thermal conductivity of olive fruit, which was 0.44 W/m°C. The model was validated by comparing the predicted values with the experimental temperature profiles obtained during the thermal process of the fruit (correlation coefficient higher than 0.99 and mean squared error lower than 1.8°C). The sensitivity coefficient results indicated that the surrounding temperature and the diameter of the product were the most influential parameters on the heat transfer of the product. The model was effective in simulating the thermal processing of olive fruit. The research results can be applied to optimize the pasteurization process of olive fruit.
Keywords
Olive fruit
Heat processing
Numerical Modeling

Subjects

[1] Nikzad, N., Sahari, M. A., M, G., Piravi Vanak, Z., Hoseini, S. E., Safafar, H., & Boland Nazar, S. A. (2013). Physico-chemical properties and nutritional indexes of cultivars during table olive processing (in Persian). Journal of food science and technology (Iran), 10(39), 31-41.
[2] Jafarpour, D. (2022). The effect of heat treatment and thermosonication on the microbial and quality properties of green olive. Journal of Food Measurement and Characterization, 16(3), 2172-2180.
[3] Dalvi-Isfahan, M. (2021). Comparison of efficiency between two different numerical modeling methods to predict tomato paste temperature during pasteurization process. Journal of Food Research (Persian), 31(1), 83-94.
[4] Dimou, A., Panagou, E., Stoforos, N. G., & Yanniotis, S. (2013). Analysis of Thermal Processing of Table Olives Using Computational Fluid Dynamics. Journal of Food Science, 78(11), E1695-E1703.
[5] Cuesta, F. J., & Alvarez, M. D. (2017). Mathematical modeling for heat conduction in stone fruits. International Journal of Refrigeration, 80, 120-129.
[6] Dalvi-Isfahan, m., & Hematian-Sourki, A. (2021). Impact of product geometry on accurate heat transfer modelling of irregular shaped fruit during blanching process. Journal of food science and technology (Iran), 18(120), 121-132.
[7] Singh, K. K., & Goswami, T. K. (1996). Physical Properties of Cumin Seed. Journal of Agricultural Engineering Research, 64(2), 93-98.
[8] Singh, R. P., & Heldman, D. R. (2014a). Chapter 1 - Introduction. In R. P. Singh & D. R. Heldman (Eds.), Introduction to Food Engineering (Fifth Edition) (pp. 1-64). San Diego: Academic Press.
[9] Reddy, R. S., Arepally, D., & Datta, A. K. (2022). Inverse problems in food engineering: A review. Journal of Food Engineering, 319, 110909.
[10] Singh, R. P., & Heldman, D. R. (2014b). Chapter 4 - Heat Transfer in Food Processing. In R. P. Singh & D. R. Heldman (Eds.), Introduction to Food Engineering (Fifth Edition) (pp. 265-419). San Diego: Academic Press.
[11] Dalvi, M., & Hamdami, N. (2010). Numerical Heat Transfer Modeling in Ultrafilterated White Cheese. Journal of Food Research (Persian), 20(2), 45-60.
[12] Jalghaf, H. K., Kovács, E., Barna, I. F., & Mátyás, L. (2023). Analytical Solution and Numerical Simulation of Heat Transfer in Cylindrical- and Spherical-Shaped Bodies. In Computation (Vol. 11).
[13] Wang, C., Wang, S., Jin, X., Zhang, T., & Ma, Z. (2021). Analytical solution for the heat and mass transfer of spherical grains during drying. Biosystems Engineering, 212, 399-412.
[14] 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.
[15] Homapour, M., hamedi, M., Moslehishad, M., & Safafar, H. (2014). Physical and chemical properties of olive oil extracted from olive cultivars grown in Shiraz and Kazeroon. Iranian Journal of Nutrition Sciences and Food Technology, 9(1), 121-130.
[16] Simpson, R., & Cortés, C. (2004). An inverse method to estimate thermophysical properties of foods at freezing temperatures: apparent volumetric specific heat. Journal of Food Engineering, 64(1), 89-96.
[17] Monteau, J.-Y. (2008). Estimation of thermal conductivity of sandwich bread using an inverse method. Journal of Food Engineering, 85(1), 132-140.
[18] Hussain, T., Kamal, M. A., Alam, Z., Hafiz, A., & Ahmad, A. (2021). Experimental and numerical investigation of spherical food product during forced convection cooling. Measurement: Food, 3, 100006.
[19] Nicolaï, B. M., & De Baerdemaeker, J. (1996). Sensitivity analysis with respect to the surface heat transfer coefficient as applied to thermal process calculations. Journal of Food Engineering, 28(1), 21-33.
[20] Kızıltaş, S., Erdoğdu, F., & Koray Palazoğlu, T. (2010). Simulation of heat transfer for solid–liquid food mixtures in cans and model validation under pasteurization conditions. Journal of Food Engineering, 97(4), 449-456.
[21] Cordioli, M., Rinaldi, M., Copelli, G., Casoli, P., & Barbanti, D. (2015). Computational fluid dynamics (CFD) modelling and experimental validation of thermal processing of canned fruit salad in glass jar. Journal of Food Engineering, 150, 62-69.