A New Mathematical Model for Food Thermal Process Prediction

Abstract

A mathematical model was developed to correlate the four heat penetration parameters of 57 Stumbo's tables (18,513 datasets) in canned food: (the difference between the retort and the coldest point temperatures in the canned food at the end of the heating process), ℎ / (the ratio of the heating rate index to the sterilizing value), (the temperature change required for the thermal destruction curve to traverse one log cycle), and , (the cooling lag factor). The quantities , , and , are input variables for predicting ℎ / , while , and ℎ / are input variables for predicting the value of , which is necessary to calculate the heating process time , at constant retort temperature, using Ball's formula. The process time calculated using the value obtained from the mathematical model closely followed the time calculated from the tabulated values (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.

The check problem of food thermal processes: a mathematical solution

“…The process lethality F and, hence, the sterilizing values U and, finally, the fh/U values, which could be called number of Ball, calculated by applying the mathematical approach of this work, were closer to the Stumbo fh/U values, compared to those obtained by a previous mathematical model [22] and by ANN models [20 and 21].…”

“…It consists in a high number of algebraic equations solved by an information processing system (black box) that learns from 18,513 Stumbo's datasets. In a previous work [22], the 18,513 Stumbo's datasets, were also transformed into a mathematical model, based on ten equations for the computerized solution of check problem, that is the verification of desired microbial lethality F. Instead for the design problem, i.e. the calculation of the g value, necessary to compute directly the thermal process time B with Ball's formula, known a priori the process lethality F, a mathematical approach, which consisted of only three equations, was proposed [23].…”

“…, it was observed that is continuous and monotonically increasing. Therefore, to extend the use of equation 15for Jcc>0.4, it's necessary to modify the g value, obtained from equation 13, before introducing it in equation (15) (22) By developing the product of two polynomials, the previous equation symbolically becomes:…”

“…Considering the need to simplify and to improve the previous mathematical model of ten equations [22], proposed for the solution of the check food thermal process problem and considering the new type of mathematical solution found for the design problem [23], the overall objective of this paper was to develop a new mathematical procedure, that solves the check problem i.e. to furnish more quickly and precisely the microbial lethality F for a given heating time (B) of the canned food.…”

Study of thermal stability of ascospores Aspergillus (Neosartorya) fischeri depending on the concentration of soluble solids in apple juice

“…Гибель популяции клеток и спор микроорганизмов в продукте при нагревании происходит не мгновенно, и если в полулогарифмической системе координат изобразить этот процесс (продолжительность нагрева -число оставшихся жизнеспособных спор), то на определенном участке он может быть аппроксимирован линейной функцией [18]. В этом случае скорость отмирания клеток или спор (K) определяется уравнением Аррениуса, используемого для расчета скорости химических реакций [19]:…”