Thermal convection coefficient in cooling process of lime fruit: Study through the Galerkin finite element method

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.

Section: Introductionmentioning

confidence: 99%

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

Santos

Silva

Gomes

et al. 2022

“…Most fresh horticultural products required immediate cooling to retain their freshness and to improve their economic benefit due to their characteristics of high moisture content, high sugar content, and large field heat of the horticultural products (Duan et al, 2020; Han, Ji, Zuo, & Yang, 2021; Mercier, Brecht, & Uysal, 2019; Shen, Zhang, Cao, & Jiang, 2018; Valle‐Guadarrama, Cruz‐Pérez, López‐Cruz, & Hahn‐Schlam, 2018). Forced air pre‐cooling (FAC) was acknowledged as the most common and effective pre‐cooling method due to the advantages of adapting to a variety of horticultural products, rapid cooling, and low cost (Cotrim, Coimbra, & Cotrim, 2021; Redding, Yang, Shim, Olatunji, & East, 2016).…”

Section: Introductionmentioning

confidence: 99%

Energy consumption in relation to the number of stacked packages in forced air pre‐cooling of apples

Jia

Yang

Zhang

et al. 2022

To better investigate the effect of the number of stacked packages on the seven‐eights cooling time and the specific fan energy consumption in forced air pre‐cooling (FAC), a three‐dimensional model of FAC in the stacked packages was developed. The predicted total pressure loss was less than the product of the number of stacked packages and the pressure loss of a single package. This was due to the pressure loss of the cold air flowing through the openings in the adjacent packages accounting for the dominant proportion of the stacked packages. The difference was used to prove the overestimation of the specific fan energy consumption calculated in terms of the product of the number of stacked packages and the pressure loss of a single package. In terms of the required parameters in the pre‐cooling industry, the optimal condition of three stacked packages at the air velocity of 1.0 m/s was suggested. Compared with the other complied conditions, the specific fan energy consumption of the optimal condition was reduced by more than 50% and 0.0289–0.975$ t−1, respectively. Practical applications Forced air pre‐cooling was an effective way to retain freshness and to improve the economic benefit of horticultural products. The quantitative relationships among the number of stacked packages, the pressure loss, and the fan energy consumption were obtained by computational fluid dynamics (CFD) simulation. Based on the results, the optimal condition in forced air pre‐cooling of apples was suggested.

“…If the air temperature of FAC was lower than the freezing point temperature of the horticultural products, the chilling injury occurred due to the water freezing in in horticultural products to reduce their economic values (Han, Zhao, Qian, Ruiz‐Garcia, & Zhang, 2018; Hussain, Kamal, & Hafiz, 2021). This meant that it was an effective way to accelerate the cooling rate and prolong the shelf life of horticultural products by increasing the air velocity rather than decreasing the air temperature (Valle‐Guadarrama, Cruz‐Pérez, López‐Cruz, & Hahn‐Schlam, 2018; Wang, Fan, Li, & Liu, 2021). For example, it was found that the pre‐cooling time would be decrease 2 ˜ 3 times with the air velocity from 0.2 to 3.6 m s −1 by Lambrinos, Assimaki, and Manolopoulou (1997).…”

Section: Introductionmentioning

confidence: 99%

General formula of cooling curve for horticultural products on forced air pre‐cooling

Wang

Jia

Lai

et al. 2022

The air velocity played a key role in controlling the cooling process of forced air precooling for horticultural products. However, the present general formula of cooling curve for horticultural products on forced air pre-cooling did not reflect the influence of the air velocity on cooling rate for horticultural products on forced air pre-cooling. This paper aimed to find the relationships among the air velocity, lag factor and cooling coefficient so as to obtain the general formula of the cooling curve for horticultural products on forced air pre-cooling by combining the simulation and the experiment. The results showed that the lag factor had a linear relationship with the air velocity, and the cooling coefficient had a quadratic function or power function relationship with the air velocity. These two kinds of general formulas were verified by experimental data of apples, cherries and blueberries, and were also in agreement with the literature values of apples, grapes and Dutch cucumbers. Based on the accuracy and the predictability of the general formulas, the general formula has higher accuracy and predictability when the cooling coefficient had a power function relationship with the air velocity. Practical ApplicationsThis paper attempted to find a general formula to describe the cooling rates of horticultural products for the different air velocities and temperatures. The general formula was only incident the air velocity and the air temperature while the other factors were considered as the unknown variations which was obtained by the functions fitting. This could contribute to reduce the cost and time of experiments and simulations during the analysis of forced air pre-cooling and to help the operator find the optimal air velocity effectively. To find the suitable general formula, firstly we established the simulated model to find the general formulas by using least square method. Then, the general formulas had been validated by experimental data and literature results. Finally, the predictability of these general formulas had been tested. | INTRODUCTIONPre-cooling was a valid technology that aimed to quickly remove field heat from fresh horticultural products and cool them to get to the appropriate temperature before transportation to cold rooms or refrigerated trucks (Duan