پیش بینی زمان انجماد و مدل سازی عددی انتقال حرارت در حین فرآیند انجماد

نویسنده
محسن دلوی اصفهان
استادیار گروه علوم و صنایع غذایی دانشگاه جهرم
10.52547/fsct.18.116.171
چکیده
در این مطالعه، از سه مدل ریاضی (پلانک، فام و مدل عددی (اجزاء محدود)) برای پیش بینی زمان انجماد نمونه‌های سیب زمینی استفاده شد. به منظور توسعه مدل عددی، خصوصیات ترموفیزیکی (چگالی، هدایت حرارتی و گرمای ویژه) به عنوان تابعی از ترکیب نمونه و دما پیش بینی شد. ضریب انتقال حرارت همرفتی نیز با استفاده از روش مسئله معکوس و اعداد بدون بعد برآورد شد. نتایج نشان داد که زمان محاسبه شده توسط مدل عددی از بین سه مدل دیگر، دقیق‌ترین بوده و در مرحله بعدی بهترین مدل، مدل پیشنهادی فام است. علاوه بر این، تطابق خوبی بین دمای مشاهده شده و دمای پیش بینی شده توسط روش عددی در روش‌های مختلف انجماد مشاهده شد. به عنوان نتیجه گیری کلی، مدل عددی توسعه یافته، دمای نمونه‌های سیب زمینی را به درستی در حین انجماد پیش بینی می‌کند و می‌تواند برای شبیه سازی انجماد مواد غذایی معلق در هوا مورد استفاده قرار گیرد. علاوه بر این، روش مسأله معکوس توسعه داده شده برای پیش بینی ضریب انتقال حرارت همرفتی می‌تواند در سیستم‌های مختلف انجماد به منظور انتخاب بهترین سیستم یا بهینه سازی روند انجماد مواد غذایی بکارگرفته شود.
کلیدواژه‌ها
اجزاء محدود
انجماد
زمان انجماد
مدل عددی

موضوعات

عنوان مقاله English

Prediction of Freezing Time and Numerical Model of Heat Transfer during Freezing Process

نویسنده English

mohsen Dalvi-Isfahan
Mohsen Dalvi Assistant professor Department of Food Science and Technology, Faculty of Agriculture, Jahrom University, Jahrom, Fars, Iran, P.O. Box 74137-66171Email: Mohsen.Dalvi@gmail.com, Dalvi@jahromu.ac.ir
چکیده English

In this study, three mathematical models (Plank, Pham and numerical model (finite element)) were used to predict the freezing time of potato samples. In order to develop the numerical model, thermophysical properties (density, thermal conductivity and specific heat) were predicted as a function of sample composition and temperature. Convective heat transfer coefficient was also estimated using the inverse problem method and dimensionless numbers. The results showed that the time calculated by the numerical model was the most accurate among three models and in the next step the best model was Pham model. In addition, an excellent agreement was obtained between observed temperature and temperature predicted by the numerical method in different freezing methods. In conclusion, the developed numerical model predicts the freezing temperature of potato samples correctly and can be used to simulate the freezing of suspended food in the air. In addition, the inverse problem method developed to predict convective heat transfer coefficient can be used in different freezing systems in order to choose the best system or optimize the process of food freezing.

کلیدواژه‌ها English

Finite element
Freezing
Freezing Time
Numerical model
[1] Delgado, A. E., and Sun, D. 2001. Heat and mass transfer models for predicting freezing processes-A review. Journal of Food Engineering, 47(3): 157–174.
[2] López-Leiva, M., and Hallström, B. 2003. The original Plank equation and its use in the development of food freezing rate predictions. Journal of Food Engineering, 58(3): 267–275.
[3] Cleland, A. C., and Earle, R. L. 1977. A comparison of analytical and numerical methods of predicting the freezing times of foods. Journal of Food Science, 42(5): 1390–1395.
[4] Mannapperuma, J. D., and Singh, R. P. 1988. Prediction of freezing and thawing times of foods using a numerical method based on enthalpy formulation. Journal of Food Science, 53(2): 626–630.
[5] Pham, Q. T. 1985. A fast, unconditionally stable finite-difference scheme for heat conduction with phase change, International Journal of Heat and Mass Transfer, 28(11): 2079–2084.
[6] Erdoğdu, F. 2000. Optimization in Food Engineering, CRC Press - Taylor & Francis Group, Boca Raton, FL, USA.
[7] Ebrahimnia-Bajestan, E., Niazmand, H., Etminan-Farooji, V., and Ebrahimnia, E. 2012. Numerical modeling of the freezing of a porous humid food inside a cavity due to natural convection. Numerical Heat Transfer; Part A: Applications, 62(3): 250–269.
[8] Fricke, B. A., and Becker, B. R. 2006. Sensitivity of freezing time estimation methods to heat transfer coefficient error. Applied Thermal Engineering, 26(4): 350–362.
[9] Carson, J. K., Willix, J., and North, M. F. 2006. Measurements of heat transfer coefficients within convection ovens. Journal of Food Engineering, 72(3): 293-301.
[10] Dima, J. B., Santos, M. V., Baron, P. J., Califano, A., and Zaritzky, N. E. 2014. Experimental study and numerical modeling of the freezing process of marine products. Food and Bioproducts Processing, 92(1): 54–66.
[11] Cornejo, I., Cornejo, G., Ramírez, C., Almonacid, S., and Simpson, R. 2016. Inverse method for the simultaneous estimation of the Thermophysical properties of foods at freezing temperatures. Journal of Food Engineering, 191: 37–47.
[12] Salas-Valerio, W., Solano-Cornejo, M., Zelada-Bazán, M., and Vidaurre-Ruiz, J. 2019. Three-dimensional modeling of heat transfer during freezing of suspended and in-contact-with-a-surface yellow potatoes and ullucus. Journal of Food Process Engineering, 42(6): e13174.
[13] Rahman, M. S., Machado-Velasco, K., Sosa-Morales, M., and Velez-Ruiz, J. F. 2009. Freezing point: Measurement, data, and prediction. In M. S. Rahman (Ed.), Food properties handbook (2nd ed., p. 838). Boca Raton, FL: Taylor & Francis Group, LLC.
[14] Boonsupthip, W., Sajjaanantakul, T., and Heldman, D. R. 2009. Use of average molecular weights for product categories to predict freezing characteristics of foods. Journal of Food Science, 74(8): E417–E425.
[15] Hamdami, N., Monteau, J.Y., and Le-Bail, A. 2004. Heat and mass transfer in par-baked bread during freezing. Food Research International, 37(5): 477-488.
[16] Valentas, K. J., Rotstein, E., and Singh, R.P. 1997. Handbook of food engineering practice. Boca Raton, Fla., CRC Press.
[17] Murray, G. P.E., and Saunders, M. A. 2002. SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization. SIAM Journal on Optimization, 12 (4): 979-1006.
[18] Pham, Q.T. 2001. Prediction of cooling/freezing/thawing time and heat load. In: D.-W. Sun, ed. Advances
in Food Refrigeration. Leatherhead: Leatherhead Food RA, pp. 110–152.
[19] Pham, Q.T. 1984. An extension to Plank’s equation for predicting freezing times of foodstuffs of simple shapes. International Journal of Refrigeration, 7: 377–383.
[20] Pham, Q. T. 2006. Modelling heat and mass transfer in frozen foods: A review. International Journal of Refrigeration, 29 (6): 876–888.
[21] COMSOL. 2007. Multiphysics Modelling by COMSOL, http://www.comsol.com.
[22] Uyar, R., and Erdogdu, F. 2012. Numerical Evaluation of Spherical Geometry Approximation for Heating and Cooling of Irregular Shaped Food Products. Journal of Food Science, 77(7): E166-E175.
[23] Zhao, Y., and Takhar, P. S. 2017. Freezing of foods: Mathematical and experimental aspects. Food Engineering Reviews, 9(1): 1–12.
[24] James, C., Purnell, G., and James, S. J. 2015. A review of novel and innovative food freezing technologies. Food and Bioprocess Technology, 8(8): 1616–1634.