Optimal Removal of Experimental Points to Determine Apparent Thermal Diffusivity of Canned Products
-
Wilton P. da Silva
,
Cleide M. D. P. S. Silva
Abstract
To describe the transient heat conduction from or to a product, its thermo-physical properties must be known. If the boundary condition of the heat conduction equation is of the first kind, the process is governed by the thermal diffusivity α. Normally this property is determined by fit of the analytical solution with only the first term of the series to an experimental dataset of the temperature versus time, in which the temperature is measured in a known position. In this case, the value obtained for α contains errors due to the consideration of only one term and the inclusion of the first experimental points in the fit. This article presents an algorithm based on optimal removal of experimental points to minimize errors in the determination of α. The algorithm was validated and applied to heating of Agar gel. The precision and accuracy of the obtained result were, respectively, 0.38 and 0.6%.
Acknowledgments
The first author would like to thank CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) for the support given to this research and for his research grant (Process Number 301697/2012-4).
Nomenclature
Coefficients of the infinite series
Specific heat (
Thermal conductivity (
Length of the cylindrical copper container
Number of experimental points
Radial position within the cylinder (
Coefficient of determination
Radius of the cylinder (
Temperature (
Equilibrium and initial temperature (
Measured value of the temperature for the experimental point i (
Simulated temperature for the experimental point i (
Dimensionless temperature
Time (
- Greek symbols
Thermal diffusivity (
Density (
Standard deviation of the experimental point i (K)
Roots of the characteristic equation
Chi-square (objective function, dimensionless)
References
1. UkrainczykN. Thermal diffusivity estimation using numerical inverse solution for 1D heat conduction. Int J Heat Mass Transf2009;52:5675–81.10.1016/j.ijheatmasstransfer.2009.07.029Suche in Google Scholar
2. TocciAM, FloresES, MascheroniRH. Enthalpy, heat capacity and thermal conductivity of boneless mutton between –40 and +40°C. LWT – Food Sci Technol1997;30:184–91.10.1006/fstl.1996.0169Suche in Google Scholar
3. UnklesbayN, UnklesbayK, ClarkeAD. Thermal properties of restructured beef snack sticks throughout smokehouse processing. LWT – Food Sci Technol1999;32:527–34.10.1006/fstl.1999.0591Suche in Google Scholar
4. HuX, MallikarjunanP. Thermal and dielectric properties of shucked oysters. LWT – Food Sci Technol2005;38:489–94.10.1016/j.lwt.2004.07.016Suche in Google Scholar
5. Al-MahasnehMA, AbabnehHA, RababahT. Some engineering and thermal properties of black cumin (Nigella sativa L.) seeds. Int J Food Sci Technol2008;43:1047–52.10.1111/j.1365-2621.2007.01561.xSuche in Google Scholar
6. RinaldiM, ChiavaroE, MassiniR. Apparent thermal diffusivity estimation for the heat transfer modelling of pork loin under air/steam cooking treatments. Int J Food Sci Technol2010;45:1909–17.10.1111/j.1365-2621.2010.02360.xSuche in Google Scholar
7. TogrulIT. Modelling of heat and moisture transport during drying black grapes. Int J Food Sci Technol2010;45:1146–52.10.1111/j.1365-2621.2010.02246.xSuche in Google Scholar
8. ErdogduF. A review on simultaneous determination of thermal diffusivity and heat transfer coefficient. J Food Eng2008;86:453–9.10.1016/j.jfoodeng.2007.10.019Suche in Google Scholar
9. DincerI, DostS. New correlations for heat transfer coefficients during direct cooling of products. Int J Energy Res1996;20:587–94.10.1002/(SICI)1099-114X(199607)20:7<587::AID-ER174>3.0.CO;2-9Suche in Google Scholar
10. DincerI. Determination of thermal diffusivities of cylindrical bodies being cooled. Int Commun Heat Mass Trans1996;23:713–20.10.1016/0735-1933(96)00054-1Suche in Google Scholar
11. HeSY, LiYF. Theoretical simulation of vacuum cooling of spherical foods. Appl Therm Eng2003;23:1489–501.10.1016/S1359-4311(03)00085-1Suche in Google Scholar
12. MorawickiRO, SchmalkoME. Prediction of out-of-container pasteurization of pickled cucumbers using the finite-difference method. J Food Eng2011. DOI: 10.1016/j.jfoodeng.2011.07.020.Suche in Google Scholar
13. BaïriA, LaraqiN, García de MaríaJM. Determination of thermal diffusivity of foods using 1D Fourier cylindrical solution. J Food Eng2007;78:669–75.10.1016/j.jfoodeng.2005.11.004Suche in Google Scholar
14. KumarR, KumarA, MurthyUN. Heat transfer during forced air precooling of perishable food products. Biosyst Eng2008;99:228–33.10.1016/j.biosystemseng.2007.10.012Suche in Google Scholar
15. MercaliGD, SarkisJR, JaeschkeDP, TessaroIC, MarczakLD. Physical properties of acerola and blueberry pulps. J Food Eng2011. DOI: 10.1016/j.jfoodeng.2011.05.010.Suche in Google Scholar
16. SilvaWP, SilvaCM, LinsMA. Determination of expressions for the thermal diffusivity of canned foodstuffs by the inverse method and numerical simulations of heat penetration. Int J Food Sci Technol2011;46:811–18.10.1111/j.1365-2621.2011.02552.xSuche in Google Scholar
17. PanasAJ, SypekJ. Validation of the thermal diffusivity from modified monotonic heating regime procedure. Int J Thermophys2006;27:1844–58.10.1007/s10765-006-0129-zSuche in Google Scholar
18. SilvaWP, SilvaCM, FariasVS, SilvaDD. Calculationof the convective heat transfer coefficient and coolingkinetics of an individual fig fruit. Heat Mass Transf2010;46:371–80.10.1007/s00231-010-0577-7Suche in Google Scholar
19. SilvaWP, SilvaCM, NascimentoPL, CarmoJE, SilvaDD. Influence of the geometry on the numerical simulation of the cooling kinetics of cucumbers. Spanish J Agric Res2011;9:242–51.10.5424/sjar/20110901-055-10Suche in Google Scholar
20. SilvaWP, SilvaCM, GamaFJ. An improved technique for determining transport parameters in cooling processes. J Food Eng2012;111:394–402.10.1016/j.jfoodeng.2012.02.003Suche in Google Scholar
21. MarkowskiM, BialobrzewskiI, CierachM, PauloA. Determination of thermal diffusivity of Lyoner type sausages during water bath cooking and cooling. J Food Eng2004;65:591–8.10.1016/j.jfoodeng.2004.02.025Suche in Google Scholar
22. GlavinaMY, Di ScalaKC, AnsorenaR, Del ValleCE. Estimation of thermal diffusivity of foods using transfer functions. LWT – Food Sci Technol2006;39:455–9.10.1016/j.lwt.2005.03.010Suche in Google Scholar
23. LuikovAV. Analytical heat diffusion theory. London: Academic Press, 1968.Suche in Google Scholar
24. CrankJ. The mathematics of diffusion. Oxford, UK: Clarendon Press, 1975.Suche in Google Scholar
25. SilvaWP, CarmoJE, SilvaCM, AragãoRF. Determination of convective heat transfer coefficient during cooling of an individual strawberry fruit using different methods. Int Rev Chem Eng2011;3:233–40.Suche in Google Scholar
26. BevingtonPR, RobinsonDK, ReductionD. Error analysis for the physical sciences, 2nd ed. Boston, MA: WCB/McGraw-Hill, 1992.Suche in Google Scholar
27. TaylorJR. An introduction to error analysis, 2nd ed. Sausalito, CA: University Science Books, 1997.Suche in Google Scholar
28. SilvaWP, SilvaCM, SilvaDD, SilvaCD. Numerical simulation of the water heat conduction in cylindrical solids. Int J Food Eng2008;4:1–16.Suche in Google Scholar
29. BettaG, RinaldiM, BarbantiD, MassiniR. A quick method for thermal diffusivity estimation: application to several foods. J Food Eng2009;91:34–41.10.1016/j.jfoodeng.2008.08.003Suche in Google Scholar
30. MarianiVC, AmaranteAC, CoelhoLS. Estimation ofapparent thermal conductivity of carrot purée duringfreezing using inverse problem. Int J Food Sci Technol2009;44:1292–303.10.1111/j.1365-2621.2009.01958.xSuche in Google Scholar
31. LemmonEW, McLindenMO, FriendDG. Thermophysical properties of fluid systems. In: LinstromPJ, MallardWG, editors. NIST chemistry WebBOOK, NIST standard reference database number 69. Gaithersburg, MD: National Institute of Standards and Technology, 2005. Available at: http://webbook.nist.gov.Suche in Google Scholar
32. FariasVS, SilvaWP, SilvaCMD, DelgadoJM, NetoSR, LimaAG. Transient diffusion in arbitrary shape porous bodies: numerical analysis using boundary-fitted coordinates. Numerical Anal Heat Mass Transf Porous Media – Adv Structured Mater2012;27:85–119.10.1007/978-3-642-30532-0_4Suche in Google Scholar
©2014 by Walter de Gruyter Berlin / Boston
Artikel in diesem Heft
- Frontmatter
- Review Article
- The Effect of Lactic Acid Bacteria in Food and Feed and Their Impact on Food Safety
- Research Articles
- Milk-Coagulating Extract Produced from Solanum aethiopicum Shum Fruits: Multivariate Techniques of Preparation, Thermal Stability and Effect on Milk Solids Recovery in Curd
- Optimal Removal of Experimental Points to Determine Apparent Thermal Diffusivity of Canned Products
- Mathematical Modelling of Heat Transfer in Mortadella Bologna PGI during Evaporative Pre-Cooling
- Preparation of Oxidized Starch Using Environment Friendly Chlorine Dioxide as Oxidant
- Assessment of Quality Attributes of Banana Slices Dried by Different Drying Methods
- Effects of High Hydrostatic Pressure Treated Mung Bean Starch on Characteristics of Batters and Crusts from Deep-Fried Pork Nuggets
- Exergy and Energy Analysis, Drying Kinetics and Mathematical Modeling of White Mulberry Drying Process
- Convective Drying of Apples: Kinetic Study, Evaluation of Mass Transfer Properties and Data Analysis using Artificial Neural Networks
- Identification of Eggshell Crack using BPNN and GANN in Dynamic Frequency Analysis
- Optimization of Osmotic Dehydration of Seedless Guava (Psidium guajava L.) in Sucrose Solution using Response Surface Methodology
- Effects of Screw Speed and Sesame Cake Level on Optimal Operation Conditions of Expanded Corn Grits Extrudates
- Evaluation and Optimization of Steam and Lye Peeling Processes of Sweet Potato (Ipomea batatas) using Response Surface Methodology (RSM)
- Physical Properties of Naked Oat Seeds (Avena nuda L.)
Artikel in diesem Heft
- Frontmatter
- Review Article
- The Effect of Lactic Acid Bacteria in Food and Feed and Their Impact on Food Safety
- Research Articles
- Milk-Coagulating Extract Produced from Solanum aethiopicum Shum Fruits: Multivariate Techniques of Preparation, Thermal Stability and Effect on Milk Solids Recovery in Curd
- Optimal Removal of Experimental Points to Determine Apparent Thermal Diffusivity of Canned Products
- Mathematical Modelling of Heat Transfer in Mortadella Bologna PGI during Evaporative Pre-Cooling
- Preparation of Oxidized Starch Using Environment Friendly Chlorine Dioxide as Oxidant
- Assessment of Quality Attributes of Banana Slices Dried by Different Drying Methods
- Effects of High Hydrostatic Pressure Treated Mung Bean Starch on Characteristics of Batters and Crusts from Deep-Fried Pork Nuggets
- Exergy and Energy Analysis, Drying Kinetics and Mathematical Modeling of White Mulberry Drying Process
- Convective Drying of Apples: Kinetic Study, Evaluation of Mass Transfer Properties and Data Analysis using Artificial Neural Networks
- Identification of Eggshell Crack using BPNN and GANN in Dynamic Frequency Analysis
- Optimization of Osmotic Dehydration of Seedless Guava (Psidium guajava L.) in Sucrose Solution using Response Surface Methodology
- Effects of Screw Speed and Sesame Cake Level on Optimal Operation Conditions of Expanded Corn Grits Extrudates
- Evaluation and Optimization of Steam and Lye Peeling Processes of Sweet Potato (Ipomea batatas) using Response Surface Methodology (RSM)
- Physical Properties of Naked Oat Seeds (Avena nuda L.)
