Kayısı meyvesinin dondurarak kurutulmasının sayısal olarak incelenmesi için matematiksel bir model

Year 2022, Volume: 37 Issue: 1, 347 - 360, 10.11.2021

Ebubekir Sıddık Aydın

https://doi.org/10.17341/gazimmfd.791792

Abstract

Bu çalışma, kayısı meyvesinin dondurarak kurutulması sırasında meydana gelen kütle ve sıcaklık değişimlerini ortaya çıkarmak için küresel koordinatlarda oluşturulmuş matematiksel bir model önermektedir. Model denklemlerinin çözümünü bulmak için ortogonal kollokasyon yöntemi olarak bilinen bir tür polinom yaklaşımı uygulanmıştır. Kayısı meyvesinin dondurarak kurutulmasını tanımlayan fiziksel özellikler ve bazı taşınım parametreleri, temeli doğrusal olmayan en küçük kareler yöntemine dayanan Levenberg-Marquardt algoritması kullanılarak tahmin edilmiştir. Modelde belirlenen taşınım parametreleri ile ürün yarıçapı, kurutma sıcaklığı ve ürün şeklinin birincil kurutma aşamasının süresine etkisi araştırılmıştır. Ayrıca dondurarak kurutma işleminin ürün rengi ve toplam fenolik içerik (TFİ) üzerindeki etkisi incelenmiş ve kayısı meyvesinin TFİ değerinin 27,97 ± 1,57'den 525,80 ± 15,48 mg GAE / 100 g dm'ye yükseldiği görülmüştür.

Keywords

Dondurarak kurutma, Matematiksel model, Kayısı meyvesi, Ortogonal kollokasyon

References

• 1. Ö.A. Gümüşay, A.A. Borazan, N. Ercal, O. Demirkol, Drying effects on the antioxidant properties of tomatoes and ginger, Food Chemistry, 173, 156–162, 2015.
• 2. C.H. Chang, H.Y. Lin, C.Y. Chang, Y.C. Liu, Comparisons on the antioxidant properties of fresh, freeze-dried and hot-air-dried tomatoes, Journal of Food Engineering, 77, 478–485, 2006.
• 3. H. Essalhi, M. Benchrifa, R. Tadili, M.N. Bargach, Experimental and theoretical analysis of drying grapes under an indirect solar dryer and in open sun, Innovative Food Science and Emerging Technologies, 49, 58–64, 2018.
• 4. D. Fissore, M. Harguindeguy, D.V. Ramirez, T.N. Thompson, Development of freeze-drying cycles for pharmaceutical products using a micro freeze-dryer, Journal of Pharmaceutical Sciences, 109, 797–806, 2020.
• 5. H. Sadikoglu, A.I. Liapis, Mathematical Modelling of the Primary and Secondary Drying Stages of Bulk Solution Freeze-Drying in Trays: Parameter Estimation and Model Discrimination by Comparison of Theoretical Results With Experimental Data, Drying Technology, 15, 791–810, 1997.
• 6. S.M. Patel, T. Doen, M.J. Pikal, Determination of end point of primary drying in freeze-drying process control, AAPS PharmSciTech, 11, 73–84, 2010.
• 7. W.M. El-Maghlany, A.E.-R. Bedir, M. Elhelw, A. Attia, Freeze-drying modeling via multi-phase porous media transport model, International Journal of Thermal Sciences, 135, 509–522, 2019.
• 8. S. Bobba, M. Harguindeguy, D. Colucci, D. Fissore, Diffuse interface model of the freeze-drying process of individually frozen products, Drying Technology, 38, 758–774, 2020.
• 9. A. Tarafdar, N.C. Shahi, A. Singh, Freeze-drying behaviour prediction of button mushrooms using artificial neural network and comparison with semi-empirical models, Neural Computing and Applications, 31, 7257–7268, 2019.
• 10. P.J. Gloor, O.K. Crosser, A.I. Liapis, Dusty-Gas parameters of activated carbon absorbent particles, Chemical Engineering Communications, 59, 95–105, 1987.
• 11. M.J. Millman, A.I. Liapis, J.M. Marchello, An analysis of the lyophilization process using a sorption‐sublimation model and various operational policies, AIChE Journal, 31, 1594–1604, 1985.
• 12. C. Hammami, F. René, Determination of Freeze-drying Process Variables for Strawberries, Journal of Food Engineering, 32, 133–154, 1997.
• 13. K. Nakagawa, T. Ochiai, A mathematical model of multi-dimensional freeze-drying for food products, Journal of Food Engineering, 161, 55–67, 2015.
• 14. W.J. Ferguson, R.W. Lewis, L. Tömösy, A finite element analysis of freeze-drying of a coffee sample, Computer Methods in Applied Mechanics and Engineering, 108, 341–352, 1993.
• 15. W.J. Mascarenhas, H.U. Akay, M.J. Pikal, A computational model for finite element analysis of the freeze-drying process, Computer Methods in Applied Mechanics and Engineering, 148, 105–124, 1997.
• 16. A.I. Liapis, R. Bruttini, A mathematical model for the spray freeze drying process: The drying of frozen particles in trays and in vials on trays, International Journal of Heat and Mass Transfer, 52, 100–111, 2009.
• 17. C.S. Song, J.H. Nam, C.J. Kim, S.T. Ro, A finite volume analysis of vacuum freeze drying processes of skim milk solution in trays and vials, Drying Technology, 20, 283–305, 2002.
• 18. H. Sadikoglu, a. I. Liapis, O.K. Crosser, Optimal Control of the Primary and Secondary Drying Stages of Bulk Solution Freeze Drying in Trays, Drying Technology, 16, 399–431, 1998.
• 19. E.S. Aydin, O. Yucel, H. Sadikoglu, Modelling and simulation of a moving interface problem: freeze drying of black tea extract, Heat and Mass Transfer, 53, 2143–2154, 2017.
• 20. S. Whitaker, Simultaneous Heat, Mass, and Momentum Transfer in Porous Media: A Theory of Drying, Advances in Heat Transfer, 13, 119–203, 1977.
• 21. P. Sheehan, A.I. Liapis, Modeling of the primary and secondary drying stages of the freeze drying of pharmaceutical products in vials: Numerical results obtained from the solution of a dynamic and spatially multi‐dimensional lyophilization model for different operational policies, Biotechnology and Bioengineering, 60, 712–728, 1998.
• 22. A. Wojdyło, J. Oszmiański, R. Czemerys, Antioxidant activity and phenolic compounds in 32 selected herbs, Food Chemistry, 105, 940–949, 2007.
• 23. O.M. Hernández-Calderón, E. Rubio-Castro, E.Y. Rios-Iribe, Solving the heat and mass transfer equations for an evaporative cooling tower through an orthogonal collocation method, Computers and Chemical Engineering, 71, 24–38, 2014.
• 24. A Review of: “SOLUTION OF DIFFERENTIAL EQUATION MODELS BY POLYNOMIAL APPROXIMATION”, by J. Villadsen and M. L. Michelsen. Prentice-Hall, 1978. 446 pp., Chemical Engineering Communications, 2, 275–275, 1978.
• 25. J. Solsvik, H.A. Jakobsen, Effects of Jacobi polynomials on the numerical solution of the pellet equation using the orthogonal collocation, Galerkin, tau and least squares methods, Computers and Chemical Engineering, 39, 1–21, 2012.
• 26. Ö.A. Gümüşay, M.Y. Yalçın, Effects of Freeze-Drying Process on Antioxidant and Some Physical Properties of Cherry Laurel and Kiwi Fruits, Akademik Gıda, 17, 9–15, 2019.
• 27. R. Ihns, L.M. Diamante, G.P. Savage, L. Vanhanen, Effect of temperature on the drying characteristics, colour, antioxidant and beta‐carotene contents of two apricot varieties, International Journal of Food Science & Technology, 46, 275–283, 2011.
• 28. A. Leccese, S. Bartolini, R. Viti, Total antioxidant capacity and phenolics content in apricot fruits, International Journal of Fruit Science, 7, 3–16, 2007.