A New Mathematical Model for Food Thermal Process Prediction

Dario Friso

doi:10.1155/2013/569473

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 mathematical model can be used to predict the intermediate values of any combination of inputs, avoiding the storage requirements and the interpolation of 57 Stumbo’s tables, it allows a quick and easy automation of thermal process calculations and to perform these calculations using a spreadsheet.

Highlights

Featherstone [1] indicated that the nutritional value of properly processed canned food is as good as that of fresh or frozen food
The same mathematical model made of the ten equations (26), (27), (8), (7), (13), (14), (16), (19), (21), and (28) was implemented in the spreadsheet, to calculate g values for various fh/U values obtained from Stumbo’s tables
The system of equations is implicit in the g value; g can be rapidly calculated using the spreadsheet by putting Stumbo’s fh/U values into (28) and searching for the corresponding g value that ensures the validity of the ten equations

Summary

Introduction

Featherstone [1] indicated that the nutritional value of properly processed canned food is as good as that of fresh or frozen food. To assure a safe canned product with minimal damage to organoleptic quality and nutritional value, it needs to optimize the thermal processing of the product through rigorous calculations [2]. The general method was the first method developed for thermal process calculations [3]. The fundamental concepts on which it was based served as foundation for the development of the more sophisticated procedures [4]. Because the general method lacks the predictive power needed for design purpose, the difficulties associated with this procedure inspired interest in the formula method first proposed by Ball [5]. Ball’s formula method passed through rigorous evaluations, simplifications, and improvements [6, 7]

Objectives

Results

Conclusion