Inverse method for the simultaneous estimation of the thermophysical properties of foods at freezing temperatures

Abstract Because the quality and shelf life of a frozen food greatly depend on the freezing processing time, its accurate estimation is highly relevant. In addition, the estimation of the freezing time is an enormous task due to the difficulty in developing a robust and accurate mathematical model and the need for appropriate thermophysical properties for an immense variety of foods. The objective of this study was to explore, via simulation, the capability of an inverse method to simultaneously determine the thermal conductivity ( k(T) ) and apparent volumetric specific heat ( C(T) ) of foods in the freezing temperature range (i.e., initial freezing point to −40 °C). Experiments and validation experiments were designed with the purpose of a systematic analysis and assessment of the potential capability of an inverse procedure for simultaneously determining the thermophysical properties of foods in the freezing temperature range. Assuming a one-dimensional freezing process and known thermophysical properties of the food material, temperatures were generated at different locations of the food sample by numerically solving the partial differential equation for heat conduction. The inverse method was designed to obtain the unknown parameters for the equations of the thermophysical properties C(T) and k(T) . The ability of the inverse method to simultaneously determine C(T) and k(T) in the freezing temperature range was investigated, and it was determined that the technique is accurate, rapid and robust to typical measurement errors. This fact was supported by a sensitivity coefficient analysis, which compared the direct-adjustment to the inverse method.

[1]  Paulo J.M. Monteiro,et al.  An inverse method to determine the elastic properties of the interphase between the aggregate and the cement paste , 2002 .

[2]  James V. Beck,et al.  Parameter Estimation in Engineering and Science , 1977 .

[3]  C. R. B. Filho,et al.  Transient conduction in spherical fruits: method to estimate the thermal conductivity and volumetric thermal capacity , 2005 .

[4]  Nasser Hamdami,et al.  Thermophysical properties evolution of French partly baked bread during freezing , 2004 .

[5]  Cristina L. M. Silva,et al.  Kinetics of frozen stored green bean (Phaseolus vulgaris L.) quality changes: Texture, vitamin C, reducing sugars, and starch , 2003 .

[6]  Soon-Bok Lee,et al.  Inverse Method to Determine Mechanical Properties of Thin Film by Nanoindentation and Finite Element Analysis , 2006 .

[7]  D. Heldman,et al.  PREDICTION OF FREEZING TIMES FOR FOODS AS INFLUENCED BY PRODUCT PROPERTIES , 1977 .

[8]  Marcel G. Schaap,et al.  Using an inverse method to estimate the hydraulic properties of crusted soils from tension-disc infiltrometer data , 1998 .

[9]  Dennis R. Heldman,et al.  Prediction of Thermal Conductivity in Frozen Foods , 1975 .

[10]  Q. T. Pham,et al.  Effect of biot number and freezing rate on accuracy of some food freezing time prediction methods , 1990 .

[11]  J. Drezet,et al.  Application of Inverse Methods to the Estimation of Boundary Conditions and Properties , 1995 .

[12]  Kan-Ichi Hayakawa,et al.  Parametric Analysis for Predicting Freezing Time of Infinitely Slab-Shaped Food , 1984 .

[13]  Henry G. Schwartzberg,et al.  EFFECTIVE HEAT CAPACITIES FOR THE FREEZING AND THAWING OF FOOD , 1976 .

[14]  V. Li,et al.  Simplified Inverse Method for Determining the Tensile Properties of Strain Hardening Cementitious Composites (SHCC) , 2008 .

[15]  K. Dolan,et al.  Inverse method to sequentially estimate temperature-dependent thermal conductivity of cherry pomace during nonisothermal heating , 2014 .

[16]  Kirk D. Dolan,et al.  Parameter estimation in food science. , 2013, Annual review of food science and technology.

[17]  J. Torres,et al.  An unsteady-state method to determine kinetic parameters for heat inactivation of quality factors: Conduction-heated foods , 1993 .

[18]  O. Fasina.  Thermophysical Properties of SweetPotato Puree at Freezing and Refrigeration Temperatures , 2005 .

[19]  T. Eikevik,et al.  A novel method for simultaneous and continuous determination of thermal properties during phase transition applied to Calanus finmarchicus. , 2010, Journal of food science.

[20]  K. Fikiin,et al.  Predictive equations for thermophysical properties and enthalpy during cooling and freezing of food materials , 1999 .

[21]  Ricardo Simpson,et al.  An inverse method to estimate thermophysical properties of foods at freezing temperatures: apparent volumetric specific heat , 2004 .

[22]  T. Brubaker,et al.  Nonlinear Parameter Estimation , 1979 .

[23]  Edward Kolbe,et al.  Thermal Properties of Surimi Analyzed using DSC , 1991 .

[24]  B. Efron.  Bootstrap Methods: Another Look at the Jackknife , 1979 .

[25]  James K. Carson,et al.  Review of effective thermal conductivity models for foods , 2006 .

[26]  D. R. Heldman,et al.  Predicting the Relationship Between Unfrozen Water Fraction and Temperature During Food Freezing Using Freezing Point Depression , 1974 .

[27]  J. Carson,et al.  Effective thermal conductivity prediction of foods using composition and temperature data , 2016 .

[28]  R. L. Earle,et al.  Assessment of Freezing Time Prediction Methods , 1984 .