Thermal properties determination of a cylindrical product during its cooling: two-dimensional numerical model and uncertainty

References

• Lemus-Mondaca, R. A.; Zambra, C. E.; Vega-Gálvez, A.; Moraga, N. O. Coupled 3D Heat and Mass Transfer Model for Numerical Analysis of Drying Process in Papaya Slices. J. Food Eng. 2013, 116(1), 109–117. DOI: 10.1016/j.jfoodeng.2012.10.050.
   Web of Science ®Google Scholar
• Perussello, C. A.; Kumar, C.; de Castilhos, F.; Karim, M. A. Heat and Mass Transfer Modeling of the Osmo-Convective Drying of Yacon Roots (Smallanthus Sonchifolius). Appl. Therm. Eng. 2013, 63(1), 23–32. DOI: 10.1016/j.applthermaleng.2013.10.020.
   Web of Science ®Google Scholar
• Silva, W. P.; Silva, C. M. D. P. S.; Gama, F. J. A. Estimation of Thermo-Physical Properties of Products with Cylindrical Shape during Drying: The Coupling between Mass and Heat. J. Food Eng. 2014, 141(1), 65–73. DOI: 10.1016/j.jfoodeng.2014.05.010.
   Google Scholar
• Bhuvaneswari, E.; Anandharamakrishnan, C. Heat Transfer Analysis of Pasteurization of Bottled Beer in a Tunnel Pasteurizer Using Computational Fluid Dynamics. Innovative Food Sci. Emerg. 2014, 23, 156–163. DOI: 10.1016/j.ifset.2014.03.004.
   Web of Science ®Google Scholar
• Ohshima, T.; Tanino, T.; Kameda, T.; Harashima, H. Engineering of Operation Condition in Milk Pasteurization with PEF Treatment. Food Control. 2016, 68(1), 297–302. DOI: 10.1016/j.foodcont.2016.03.047.
   Google Scholar
• Silva, W. P.; Ataíde, J. S. P.; Oliveira, M. E. G.; Silva, C. M. D. P. S.; Nunes, J. S. Heat Transfer during Pasteurization of Fruit Pulps Stored in Containers with Arbitrary Geometries Obtained through Revolution of Flat Areas. J. Food Eng. 2018, 217, 58–67. DOI: 10.1016/j.jfoodeng.2017.08.012.
   Web of Science ®Google Scholar
• Dincer, I. Determination of Thermal Diffusivities of Cylindrical Bodies Being Cooled. Int. Commun. Heat Mass Transfer. 1996, 23(5), 713–720. DOI: 10.1016/0735-1933(96)00054-1.
   Web of Science ®Google Scholar
• Silva, W. P.; Silva, C. M. D. P. S.; Gama, F. J. A. An Improved Technique for Determining Transport Parameters in Cooling Processes. J. Food Eng. 2012, 111, 394–402. DOI: 10.1016/j.jfoodeng.2012.02.003.
   Web of Science ®Google Scholar
• Da Silva, W. P.; Silva, C. M. D. P. S. Calculation of the Convective Heat Transfer Coefficient and Thermal Diffusivity of Cucumbers Using Numerical Simulation and the Inverse Method. J. Food Sci. Technol. 2014, 51(9), 1750–1761. DOI: 10.1007/s13197-012-0738-4.
   PubMed Web of Science ®Google Scholar
• Erdogdu, F.; Linke, M.; Praeger, U.; Geyer, M.; Schlüter, O. Experimental Determination of Thermal Conductivity and Thermal Diffusivity of Whole Green (Unripe) and Yellow (Ripe) Cavendish Bananas under Cooling Conditions. J. Food Eng. 2014, 128, 46–52. DOI: 10.1016/j.jfoodeng.2013.12.010.
   Web of Science ®Google Scholar
• Da Silva, W. P.; Silva, C. M. D. P. S.; Souto, L. M.; Moreira, I. S.; Silva, E. C. O. Mathematical Model for Determining Thermal Properties of Whole Bananas with Peel during the Cooling Process. J. Food Eng. 2018, 227, 11–17. DOI: 10.1016/j.jfoodeng.2018.02.003.
   Web of Science ®Google Scholar
• Mariani, V. C.; Amarante, A. C. C.; Coelho, L. S. Estimation of Apparent Thermal Conductivity of Carrot Purée during Freezing Using Inverse Problem. Int. J. Food Sci. Technol. 2009, 44, 1292–1303. DOI: 10.1111/j.1365-2621.2009.01958.x.
   Web of Science ®Google Scholar
• Kiani, H.; Sun, D.-W. Numerical Simulation of Heat Transfer and Phase Change during Freezing of Potatoes with Different Shapes at the Presence or Absence of Ultrasound Irradiation. Heat Mass Transfer. 2018, 54(3), 885–894. DOI: 10.1007/s00231-017-2190-5.
   Web of Science ®Google Scholar
• Le Niliot, C.; Lefèvre, F. A Parameter Estimation Approach to Solve the Inverse Problem of Point Heat Sources Identification. Int. J. Heat Mass Transfer. 2004, 47(4), 827–841. DOI: 10.1016/j.ijheatmasstransfer.2003.08.011.
   Web of Science ®Google Scholar
• Mariani, V. C.; Lima, A. G. B.; Coelho, L. S. Apparent Thermal Diffusivity Estimation of the Banana during Drying Using Inverse Method. J. Food Eng. 2008, 85, 569–579. DOI: 10.1016/j.jfoodeng.2007.08.018.
   Web of Science ®Google Scholar
• Ukrainczyk, N. Thermal Diffusivity Estimation Using Numerical Inverse Solution for 1D Heat Conduction. Int. J. Heat Mass Transf. 2009, 52(25–26), 5675–5681. DOI: 10.1016/j.ijheatmasstransfer.2009.07.029.
   Web of Science ®Google Scholar
• Muramatsu, Y.; Greiby, I.; Mishra, D. K.; Dolan, K. D. Rapid Inverse Method to Measure Thermal Diffusivity of Low-Moisture Foods. J. Food Sci. 2017, 82(2), 420–428. DOI: 10.1111/1750-3841.13563.
   PubMed Web of Science ®Google Scholar
• Levenberg, K. A Method for the Solution of Certain Problems in Least Squares. Q. Appl. Math. 1944, 2(2), 164–168. DOI: 10.1090/qam/10666.
   Google Scholar
• Marquardt, D. W. An Algorithm for Least-Squares Estimation of Nonlinear Parameters. J. Soc. Ind. Appl. Math. 1963, 11(2), 431–441. DOI: 10.1137/0111030.
   Google Scholar
• Da Silva, W. P.; Silva, C. M. D. P. S.; Silva, D. D. P. S.; Silva, C. D. P. S.; Lima, A. G. B. Determination of Approximate Functions for the Numerical Solution of an Ordinary Differential Equation (In Portuguese: Determinação de funções Aproximadas para a solução numérica de uma equação diferencial ordinária). Revista De La Faculdad De Ingeniería UCV. 2006, 21(2), 29–37.
   Google Scholar
• Patankar, S. V. Numerical Heat Transfer and Fluid Flow; Hemisphere Publishing Corporation: New York, NY, 1980.
   Google Scholar
• Press, W. H.; Teukolsky, S. A.; Vetterling, W. T.; Flannery, B. P. Numerical Recipes in Fortran 77. The Art of Scientific Computing; Cambridge University Press: New York, 1996; Vol. 1.
   Google Scholar
• ASHRAE. Handbook of Fundamentals; American Society of Heating, Refrigerating and Air Conditioning Engineers: Atlanta, 1993.
   Google Scholar
• Sweat, V. E. Thermal Properties of Foods. In Engineering Properties of Foods; Rao, M. A., Rizvi, S. S. H., Eds.; Marcel Dekker: New York, 1986; pp 49–87.
   Google Scholar
• Fasina, O. O.; Fleming, H. P. Heat Transfer Characteristics of Cucumbers during Blanching. J. Food Eng. 2001, 47(3), 203–210. DOI: 10.1016/S0260-8774(00)00117-5.
   Web of Science ®Google Scholar
• Campanõne, L. A.; Giner, S. A.; Mascheroni, R. H. Generalized Model for the Simulation of Food Refrigeration. Development and Validation of the Predictive Numerical Method. Int. J. Refrig. 2002, 25(7), 975–984. DOI: 10.1016/S0140-7007(01)00058-5.
   Web of Science ®Google Scholar
• Pirozzi, D. C. Z.; Amendola, M. Mathematical Model and Numerical Simulation of Strawberry Fast Cooling with Forced Air. Eng. Agr. 2005, 25(1), 222–230. DOI: 10.1590/S0100-69162005000100025.
   Google Scholar
• Amendola, M.; Dussán-Sarria, S.; Rabello, A. A. Determination of the Convective Heat Transfer Coefficient of Fig Fruits Submitted to Forced Air Precooling. Rev. Bras. Eng. Agric. Ambient. 2009, 13, 176–182. DOI: 10.1590/S1415-43662009000200011.
   Google Scholar
• Taylor, J. R. An Introduction to Error Analysis, 2nd ed.; University Science Books: California, Sausalito, 1997.
   Google Scholar