Determination of thermal properties (and their uncertainties) during the cooling of apples (Malus communis)

Abstract

The present study goal was to determine the thermal properties of apples during their cooling. Fuji apple was cooled in a domestic refrigerator by natural convection. Thermal properties were determined assuming the geometry of an equivalent sphere. An optimizer software (LS Optimizer) was used for the inverse problem. A new heat conduction software was developed to solve the direct problem, using the spherical geometry of the diffusion equation with the boundary condition of the third kind. Thus, thermal properties of apples and their uncertainties were calculated during cooling. The developed software for the direct problem was used to simulate the cooling kinetics for any previously specified point within the sphere. The fitting of the simulated curve to the experimental points showed coefficient of determination (R2) greater than 0.99 and low values of the chi‐square function (χ2). Therefore, it can be concluded that the spherical geometry and the boundary condition of the third kind were adequate to describe the process of heat removal for apple. Determined values of thermal diffusivity and convective heat transfer coefficient were α = (1.38 ± 0.07) × 10−7 m2 s−1 and h = (1.360 ± 0.018) × 10−6 m s−1, respectively, with confidence intervals of 95.4%. Another confirmation of the developed model was the fact that the thermal diffusivity was similar to the estimate by Riedel correlation (α = 1.38 × 10−7 m2 s−1). The position of the thermocouple in the equivalent sphere calculated by numerical solution was r = 6.6 mm. Practical Applications One of the main contributions of this paper is the calculation of thermal parameters along cooling with their uncertainties. This will result in very accurate simulation of the pasteurization and freezing processes. Furthermore, the values obtained in the study can be used to predict new cooling curves for the same product, but with different dimensions.

Impact of pretreatments with ethanol and freezing on drying slice papaya: drying performance and kinetic of ultrasound‐assisted extraction of phenolics compounds

“…It is important to determine these thermophysical properties (conductivity and specific heat), as they are essential in studies of modeling, simulation and optimization of industrial processes, especially when operating costs as well as food quality and safety are the main elements to be evaluated 49 …”

“…48 It is important to determine these thermophysical properties (conductivity and specific heat), as they are essential in studies of modeling, simulation and optimization of industrial processes, especially when operating costs as well as food quality and safety are the main elements to be evaluated. 49 Extraction kinetics of total phenolic compound (TPC) Table 2 shows the values obtained for the parameters of the Peleg model fitted to the experimental data of the kinetics of TPC extraction from papaya slices under different conditions and the statistical parameters coefficient of determination (R 2 ) and chisquare function (χ 2 ).…”

Impact of ultrasound pretreatment on banana chip production by convective drying using hot air: Consideration of shrinkage and variable effective mass diffusivity in the process description

“…Classically, the diffusion model based on Fick's second law of diffusion (Crank, 1975) has been applied to explain different types of processes, such as cooling (da Silva et al, 2023; Santos et al, 2022), heating (da Silva et al, 2022), osmotic dehydration (da Silva, de Farias Aires, et al, 2014; da Silva, e Silva, Lins, et al, 2014; Ferreira, Castro, et al, 2020), phytochemical extraction (da Silva et al, 2018), moisture absorption (Pereira et al, 2022), and food drying by moisture gradients (Lima et al, 2022; Pereira et al, 2023; Silva et al, 2008; Srikiatden & Roberts, 2007). Regarding drying, according to the diffusion model, the difference in moisture content within the product is the driving force for moisture transfer (Bird et al, 2001; Crank, 1975; Moran & Higgins, 1970).…”

Thermophysical properties of cassava during its cooling: Experiment, determination by inverse method, and simulation

“…Thus, for small temperature variations, the consideration of constant thermophysical properties, obtained for a given temperature range, usually produces satisfactory results both in the description of slight heating (Ukrainczyk, 2009) and in the cooling of an agricultural product (Erdogdu et al, 2014; da Silva et al, 2010). Thus, an analytical solution of the heat conduction equation can be reliably used to determine the thermophysical properties or even describe the cooling of a product (Dincer, 1995; Santos et al, 2022; da Silva et al, 2018). Thus, considering this literature review and the fact that data on the thermophysical properties of cassava during a transient process were not found in the literature consulted, the objective of this article is defined below.…”