Simple finite volumes and finite elements procedures for food quality and safety simulations

This research paper presents simple, but extremely useful, finite volumes method (FVM) and finite elements method (FEM) procedures that can be applied to calculate food quality and safety losses during processing, storage and distribution. FVM and FEM schemes are presented for the following reaction kinetic models: (i) zero-order reaction kinetics; (ii) first-order reaction kinetics; (iii) fractional conversion model; (iv) the Bigelow model of thermal inactivation (D − z) and (v) non-linear microbiological death model with lag and shoulder phases.Reaction rates, specimens concentrations, quality loss factors and microbiological population were assumed to vary consistently with the element shape function inside the finite element. Furthermore, no mass transfer was assumed between element nodes, and only reaction models were derived. These can thereafter be used in conjuction with other FVM and FEM schemes during ‘multi-physics’ simulations.Statistical functions are presented for both FVM and FEM to make easier the evaluation of food quality and safety. The average and standard deviation is evaluated inside all physical domain, but is also derived for the foods surface. Finally, considerations on the presented FVM and FEM procedures are discussed.