No abstract

This paper deals with the determination of expressions to estimate the thermal diffusivity of foodstuffs placed in cans during their pasteurisation. To this end, experimental data of the temperature in the geometric centre of the can were compared with data obtained by simulations of heat penetration. For these simulations, the diffusion equation was numerically solved by using the finite volume method, with fully implicit formulation. The numerical solution was coupled to an optimiser based on the inverse method, in order to fit this solution to the experimental data obtained during the pasteurisation of tomato puree and custard cream placed within sealed cans. In the literature, the assumption of constant thermal diffusivity during the pasteurisation is common but for the analysed cases such hypothesis resulted in biased fits. Better results were obtained supposing an increasing expression for the thermal diffusivity, as function of the local temperature. In this case, the errors of the experimental data about of the numerical solution can be considered randomly distributed.

An important property of composite material is related with its water absorption characteristic. Several articles present studies about this property and, in general, in these articles an analytical solution of the diffusion equation is used to describe the process. In this case, the effective water diffusivity is considered with a constant value. However, the water penetration modifies the internal structure of the material and this can modify the effective mass diffusivity of the product. In this article, a one‐dimensional numerical solution of the diffusion equation in Cartesian coordinates is presented, enabling to consider a constant value or a variable expression for the effective water diffusivity. A comparison between the models with constant and variable diffusivity was performed and the results indicate that the model with variable diffusivity as a decreasing function of the local moisture content describes better the process than the model with constant diffusivity.

To describe the transient heat conduction from or to a product, its thermo-physical properties must be known. If the boundary condition of the heat conduction equation is of the first kind, the process is governed by the thermal diffusivity α. Normally this property is determined by fit of the analytical solution with only the first term of the series to an experimental dataset of the temperature versus time, in which the temperature is measured in a known position. In this case, the value obtained for α contains errors due to the consideration of only one term and the inclusion of the first experimental points in the fit. This article presents an algorithm based on optimal removal of experimental points to minimize errors in the determination of α. The algorithm was validated and applied to heating of Agar gel. The precision and accuracy of the obtained result were, respectively, 0.38 and 0.6%.

Lima bean is a legume produced and consumed in various countries. To reduce post harvest losses and to enable the storage for long periods, an alternative is to dry the product. To describe the drying process, a mathematical model is usually required. In this article, four empirical equations available in the literature were used to simulate thin layer drying kinetics of lima bean at temperatures of 40, 50 and 60°C. The four empirical equations were chosen based on their simplicity, involving only one or two fitting parameters. The statistical indicators showed that the Page and Silva et al. models were the best ones to describe the process. These two empirical equations has helped to deduce an analytical expression for the drying rate and these expressions produce results which can be considered equivalent.