Journal Article

Replacing Stumbo’s Tables with Simple and Accurate Mathematical Modelling for Food Thermal Process Calculations

Friso, Dario

2026

Overview

The practical use of computational thermo-fluid dynamics (CFD) for food thermal process calculations still appears very premature due to both the high costs and the inhomogeneity and anisotropy of foods. Therefore, the traditional formula method with both Ball and Stumbo’s tables is still widely used due to its accuracy and safety. In both cases, the calculations require consulting and interpolating data from the respective tables, making the procedure slow and prone to human errors. The computerization of Ball’s tables to speed up and automate the calculations with a new mathematical approach based on the substitution of the integral exponential function and the initial cooling hyperbola has already been developed. The high accuracy obtained, superior to the direct regression of the table data, suggested adopting it also in the computerization of Stumbo’s tables. However, the latter are 14 times larger than those of Ball due to the extension of the thermo-bacteriological parameter z up to over 100 °C and the variability of the cooling lag factor Jcc. Therefore, the mathematical modelling was modified using an additional function, dependent on z and Jcc. The results obtained with the mathematical modelling showed a mean relative error and the standard deviation with respect to the Stumbo’s tables equal to MRE ± SD = 0.62% ± 1.29%. Further validation was obtained by calculating the thermal process time for different lethalities and thermo-bacteriological parameters with MRE ± SD compared to the Stumbo tables equal to 1.04% ± 0.82%.

• Publisher: MDPI AG
• Subject: Accuracy / Anisotropy / Cooling / Exponential functions / Fluid dynamics / Food / Food processing / Heat transfer / Hyperbolas / Inhomogeneity / Mathematical models / Modelling / Parameters