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An analytical solution for the coupled heat and mass transfer during the freezing of high-water content materials. (English) Zbl 1144.80343

Summary: The coupled problem of heat and mass transfer during the solidification of high-water content materials like soils, foods, tissues and phase-change materials is developed. Assuming quasi-steady heat conduction in the frozen region, the system leads to a set of coupled ordinary differential equations. The model takes into account the influence of material characteristics and process variables on the advance of the freezing and sublimation fronts, temperature and water vapour profiles and weight loss. It was validated against the analytical solution of the freezing (without surface ice sublimation) of a semi-infinite medium and was extensively used to perform a parametric study.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
80A22 Stefan problems, phase changes, etc.
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[1] , Analysis, design and simulation, 95-136 (1990)
[2] , Heat transfer with freezing and thawing, 1-167 (1991)
[3] Luikov, A. V.: Systems of differential equations of heat and mass transfer in capillary porous bodies (review), Int. J. Heat mass transfer 18, 1-14 (1975) · Zbl 0291.76037 · doi:10.1016/0017-9310(75)90002-2
[4] D.A. Tarzia, A bibliography on moving-free boundary problems for the heat diffusion equation. The Stefan and related problems, MAT – Serie A, # 2, Rosario, 2000, 297 pages. See <www.austral.edu.ar/MAT-SerieA/2>. · Zbl 0963.35207
[5] Marcus, E. A. Santillan; Tarzia, D. A.: Explicit solution for freezing of humid porous half-space with heat flux condition, Int. J. Eng. sci. 38, 1651-1665 (2000) · Zbl 1210.80017 · doi:10.1016/S0020-7225(00)00009-4
[6] Mascheroni, R. H.; Calvelo, A.: Relationship between heat transfer parameters and the characteristic damage variables for the freezing of beef, Meat sci. 4, 267-285 (1980)
[7] Delgado, A. E.; Sun, D. -W.: Heat and mass transfer models for predicting freezing processes review, J. food eng. 47, 157-174 (2001)
[8] Plank, R.: Beitrage zur berechnung und bewertung der gefriergeschwindigkeit von lebensmitteln, Beiheft zur zeitschrit fur die gesamte kalte-industrie 3, 1-17 (1941)
[9] Salvadori, V. O.; Mascheroni, R. H.: Prediction of freezing and thawing times by means of a simplified analytical method, J. food eng. 13, 67-78 (1991)
[10] , Fundamentals of freeze drying, 16-125 (1978)
[11] Farid, M.: The moving boundary problems from melting and freezing to drying and frying of food, Chem. eng. Process. 41, 1-10 (2002)
[12] Kochs, M.; Körber, Ch.; Nunner, B.; Heschel, I.: The influence of the freezing process on vapour transport during sublimation in vacuum-freeze-drying, Int. J. Heat mass transfer 34, 2395-2408 (1991)
[13] Puente, J. Aguirre; Frémond, M.; Comini, G.: Freezing of soils – physical study and mathematical models, Int. J. Refrig. 1, 99-106 (1978)
[14] Pham, Q. T.; Willix, J.: A model for food desiccation in frozen storage, J. food sci. 49, 1275-1281 (1984)
[15] Sukhwal, R. N.; Puente, J. Aguirre: Sublimation des milieux dispersés. Considerations theoriques et experimentation, Rev. gen. Therm. 262, 663-673 (1983)
[16] G.P. Lambrinos, J. Aguirre Puente, Deshydratation des milieux dispersés congelés. Influence des conditions d’entreposage sur les pertes de masse, in: Proceedings of the XVI International Congress of Refrigeration, Paris, France, August 31 – September 7, vol. 2, 1983, pp. 567 – 573.
[17] Campañone, L. A.; Roche, L. A.; Salvadori, V. O.; Mascheroni, R. H.: Monitoring of weight losses in meat products during freezing and frozen storage, Food sci. Technol. int. 8, 229-238 (2002)
[18] Campañone, L. A.; Roche, L. A.; Salvadori, V. O.; Mascheroni, R. H.: Structural studies on unpackaged foods during their freezing and storage, J. food sci. 71, E218-E226 (2006)
[19] J. Aguirre Puente, R.N. Sukhwal, Sublimation of ice in frozen dispersed media, in: Proceedings of the Third International Offshore Mechanics and Arctic Engineering Symposium, New Orleans, USA, February 12 – 16, 1983, pp. 38 – 44.
[20] L.A. Campañone, Transferencia de calor en congelación y almacenamiento de alimentos. Sublimación de hielo, calidad, optimización de condiciones de proceso, Doctor in Engineering Thesis, Universidad Nacional de La Plata, Argentina, 2001.
[21] Campañone, L. A.; Salvadori, V. O.; Mascheroni, R. H.: Weight loss during freezing and storage of unpackaged foods, J. food eng. 47, 69-79 (2001)
[22] Campañone, L. A.; Salvadori, V. O.; Mascheroni, R. H.: Food freezing with simultaneous surface dehydration. Approximate prediction of freezing time, Int. J. Heat mass transfer 48, No. 6, 1205-1213 (2005) · Zbl 1189.76692 · doi:10.1016/j.ijheatmasstransfer.2004.09.030
[23] Campañone, L. A.; Salvadori, V. O.; Mascheroni, R. H.: Food freezing with simultaneous surface dehydration. Approximate prediction of weight loss during freezing and storage, Int. J. Heat mass transfer 48, No. 6, 1195-1204 (2005) · Zbl 1189.76691 · doi:10.1016/j.ijheatmasstransfer.2004.09.031
[24] O. Fennema, L.A. Berny, Equilibrium vapour pressure and water activity of food at subfreezing temperature, in: Proceedings of IV International Congress of Food Science and Technology, vol. 2, 1974, pp. 27 – 35.
[25] London, A. L.; Seban, R. A.: Rate of ice formation, Trans. ASME 65, 711-779 (1943)
[26] Lamé, G.; Clapeyron, B. P.: Memoire sur la solidification par refroidissement d’un globe liquide, Annal. chim. Phys. 47, 250-256 (1831) · ERAM 007.0280cj
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