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Title
Abstract
Figures
Introduction
Review of Canned Food Thermal Process Calculations
Results and Discussion
Conclusions
References
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Mathematics
Applied Mathematics

A New Mathematical Model for Food Thermal Process Prediction

Profile image of Dario FrisoDario Friso

2013, Modelling and Simulation in Engineering

https://doi.org/10.1155/2013/569473
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Abstract

A mathematical model was developed to correlate the four heat penetration parameters of 57 Stumbo’s tables (18,513 datasets) in canned food:g(the difference between the retort and the coldest point temperatures in the canned food at the end of the heating process),fh/U(the ratio of the heating rate index to the sterilizing value),z(the temperature change required for the thermal destruction curve to traverse one log cycle), andJcc, (the cooling lag factor). The quantitiesg,z, andJcc, are input variables for predictingfh/U, whilez,Jccandfh/Uare input variables for predicting the value ofg, which is necessary to calculate the heating process timeB, at constant retort temperature, using Ball’s formula. The process time calculated using thegvalue obtained from the mathematical model closely followed the time calculated from the tabulatedgvalues (root mean square of absolute errors RMS = 0.567 min, average absolute error = 0.421 min with a standard deviation SD = 0.380 min). Because the ...

Figures (8)
By combining (10) with (3) and with integration, the cooling process lethality F. is achieved as follows: As can be seen later, for convergence of results of the mathematical model to data of Stumbo’s tables showing the f,/U : g relationship, it is necessary to introduce a correction factor.
By combining (10) with (3) and with integration, the cooling process lethality F. is achieved as follows: As can be seen later, for convergence of results of the mathematical model to data of Stumbo’s tables showing the f,/U : g relationship, it is necessary to introduce a correction factor.
Figure 1: When J,, is less than 1, the time of lag becomes virtually negative in the cooling time scale t,,. The dashed line shows the intersection of the cooling exponential curve with the time axis at the negative virtual time: f, - log(J,,).
Figure 1: When J,, is less than 1, the time of lag becomes virtually negative in the cooling time scale t,,. The dashed line shows the intersection of the cooling exponential curve with the time axis at the negative virtual time: f, - log(J,,).
Ficure 3: Predicted f,,/U values using the mathematical model versus desired Stumbo’ values of f),/U. Figure 2: Correction function M’ versus cooling rate lag factor at the coldest point J,. and versus z (°C) value. The solid lines are power functions obtained by nonlinear regression.
Ficure 3: Predicted f,,/U values using the mathematical model versus desired Stumbo’ values of f),/U. Figure 2: Correction function M’ versus cooling rate lag factor at the coldest point J,. and versus z (°C) value. The solid lines are power functions obtained by nonlinear regression.
RMS: root mean square of deviations; SD: standard deviations. TABLE 1: Comparison of process time calculated using g values from the Stumbo [7] tables, ANN model of Sablani and Shayya [21], ANN model of Mittal and Zhang [22], and mathematical model of this work.
RMS: root mean square of deviations; SD: standard deviations. TABLE 1: Comparison of process time calculated using g values from the Stumbo [7] tables, ANN model of Sablani and Shayya [21], ANN model of Mittal and Zhang [22], and mathematical model of this work.
Ficure 4: Values of g predicted using the mathematical model versus desired Stumbos values of g.
Ficure 4: Values of g predicted using the mathematical model versus desired Stumbos values of g.
Ficure 5: Comparison of the process time, calculated using g values from Stumbo’s tables [7], and the mathematical model of this work.
Ficure 5: Comparison of the process time, calculated using g values from Stumbo’s tables [7], and the mathematical model of this work.

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