Mathematical model for estimation of the three-dimensional unsteady temperature variation in chilled packaging units

A mathematical model for heat transfer from surrounding environment to a single food package is developed. A simplified analytical solution for three-dimensional (3D) unsteady temperature distribution in the food package with rectangular geometry taking into account the ambient temperature is obtained. The model is developed to be used as an efficient tool for estimating the effects of temperature abuse on the food product inside a single packaging unit. The food product is considered to be a homogenous solid body. The packaging material and air inside the package are modeled using an effective heat transfer coefficient. The developed model is validated by a comparison with experimental results obtained for fresh haddock fillets in expanded polystyrene (EPS) boxes exposed to temperature abuse and by comparison with numerical results obtained by the commercial software FLUENT. A satisfactory agreement was obtained between the experimental and numerical results.

► Mathematical model for temperature estimation inside food packages was developed.
► The model was validated using experimental results and commercial software FLUENT.
► The mean relative errors, compared with the experiments, were from 2.4% to 8.1%.
► The model was extended for the case of variable environmental temperature.