A mathematical solution for food thermal process design

A new mathematical procedure was developed to correlate g (the difference between the retort and the coldest point temperatures in 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) and Jcc (the cooling lag factor). These are the four heat penetration parameters of 57 Stumbo's tables (18,513 datasets) in canned food. The quantities fh/U, z and Jcc are input variables to determine the g values, which is used in Ball's formula to calculate the heating process time B at constant retort temperature. The new procedure was based on three equations; the first was obtained by the inversion of the function that expresses the process lethality, F, and hence the fh/U parameter. However, the inversion was possible for a sub-domain of the function. The inverse function g = g(fh/U, z, Jcc ) was then extended to the entire domain (10°C ≤ z ≤111°C , fh/U ≥ 0.3 and 0.4 ≤ Jcc ≤ 2 ) using two polynomials (second and third equation) obtained with articulated multiple regressions starting from the Stumbo's datasets. A comparison between the calculated value of g and desired Stumbo's values of g provided the following values: a determination coefficient R2=0.9999, a mean relative error MRE=0.85±0.91% and a mean absolute error MAE=0.06°±0.09°C (0.11°±0.16°F). The results obtained by applying the mathematical procedure of this work, namely the g values using the three equations and the process time B using Ball's formula, closely followed the process time calculated from tabulated Stumbo's g values (root mean square of absolute errors RMS=0.393 min, average absolute error=0.259 min with a standard deviation SD=0.296 min). The high accuracy and simplicity of the procedure proposed here, make it useful in the development of mathematical algorithms for calculating and controlling, by computer, of food thermal processes. These algorithms replace the 57 look-up tables and 18,513 data sets needed in the Stumbo formula method. As such, this work offers a computerized formula method as an alternative to existing computerized numerical methods for this purpose.