Evaluation of Methodologies for Mathematical Modeling of Packaged Conductive Foods Heat Process

Abstract

The heat process is a safe method of food preservation. The use of mathematical modeling for heat transfer by finite elements analysis (FEA) makes it possible to determine the cold spot of conventional and non conventional packages, evaluate their thermal history, microbial and enzyme inactivation and nutrients retention for an optimum process design. Several works use simplifications during mathematical modeling, such as adiabatic headspace, considering the thermal resistance of package negligible. The impact of these simplifications is rarely evaluated. The aim of the present work was to evaluate the effect of these simplifications on sterilization value (Fp) for a conductive food. Two commercial glass bottles (G1 and G2) were selected for the assays. FEA model was built using the bottles' real geometries. Three methodologies were evaluated, considering (i) the four components of the system, i.e., product, glass wall, headspace and metal cap, and uniform heating (PGHM); (ii) adiabatic headspace, i.e., a model considering product and glass wall, with its upper side adiabatic (PG); and (iii) only product, with adiabatic upper side (P). A tomato concentrate industrial pasteurizator profile was used as boundary condition. The Fp was determined by using two values of thermal coefficient (z), 5.5ºC and 12.5ºC, representing a possible range of contaminant’s z-value. The cold spot of the two packages was located at 32% (G1) and 46% (G2) of the product height. For the same process, the differences of Fp for the two packages ranged between 62 and 320%. Comparing the Fp by PGHM and PG models, differences were observed between 4 and 13%. These differences were over 45% when comparing PGHM with P models, even with similar thermal history. The results indicated the importance of the previous evaluation of the impact of each simplification on the accuracy of the model. Due to exponential relationship between temperature and reactions during the heat process, the need for Fp evaluation instead of thermal history in conductive food was confirmed.