Modelling turbulent flow and heat transfer using macro-porous media approach used to predict cooling kinetics of stack of food products

A semi-empirical model was established in order to predict two-dimensional turbulent flow and temperature evolution of each product through stacked spherical food during cooling or heating by forced convection. The model compares the products to a macro-porous medium. It uses the Darcy–Forchheimer momentum equation to predict the average superficial velocity. Turbulence intensity inside the porous medium, is obtained from an original transport equation for turbulent kinetic energy in which generation and dissipation are explicitly related to superficial velocity. The energy equation for fluid and solid phases is considered taking into account one-dimensional heat conduction inside the spherical products and heat transfer between air and product surface depending on local velocity and turbulence intensity.Few parameters of the model have to be experimentally determined for arranged spherical products. The same approach can be used for other shapes and arrangements. The experimental thermal heterogeneity, characterised by half-cooling time dispersion, was in agreement with predicted values in the case of a two-dimensional pattern with two baffles.