Influence of the geometry on the numerical simulation of the cooling kinetics of cucumbers

Abstract

In this paper, the effect of the geometric representation of cucumbers on the numerical simulation of its cooling kinetics is studied. It is supposed that the diffusion model with boundary condition of the third kind satisfactorily describes the cooling, and that the thermo-physical parameters are constant during the process. The geometries used to represent the cucumber are: infinite cylinder, finite cylinder, and ellipsoid. The diffusion equation was solved through the finite volume method, with a fully implicit formulation, using cylindrical and generalized coordinates. The convective heat transfer coefficient and the thermal diffusivity were determined through optimization, using the inverse method. The best model in the representation of the cucumber's shape was the ellipsoid, but the time demanded in its optimization was about 66 times greater than the time for the infinite cylinder.Additional key words: convective heat transfer coefficient; Cucumis sativus; cylindrical coordinates; diffusion; finite volume method; generalized coordinates; thermal diffusivity. Resumen Influencia de la geometría en la simulación numérica de la cinética del enfriamiento del pepinoEn este trabajo se ha estudiado el efecto de la representación geométrica de los pepinos en la simulación numérica de su cinética de enfriamiento. Se ha supuesto que el modelo de difusión con la condición de frontera de tercera clase describe satisfactoriamente el enfriamiento y que los parámetros termofísicos son constantes durante el proceso. Las geometrías utilizadas para representar el pepino son cilindro infinito, cilindro finito y elipsoide. La ecuación de difusión se resolvió a través del método de volumen finito, con una formulación totalmente implícita, utilizando coordenadas cilíndricas y generalizadas. El coeficiente de transferencia de calor por convección y la difusividad tér-mica fueron determinados a través de la optimización, utilizando el método inverso. El mejor modelo en la representación de la forma del pepino fue el elipsoide, pero el tiempo exigido para su optimización fue cerca de 66 veces mayor que el tiempo para el cilindro infinito.

Optimal Removal of Experimental Points to Determine Apparent Thermal Diffusivity of Canned Products

“…In order to describe a heat conduction process, depending on the product and/or experimental arrangement, many times the appropriate boundary condition for the heat conduction equation is of the third [18][19][20] or of the first kind [1,15,16,21,22]. On the other hand, if the temperature range is not large, the thermo-physical properties, as well as the dimensions of the product, can be considered constant [1,15,18,21,22].…”

A new exact numerical series for the determination of the Biot number: Application for the inverse estimation of the surface heat transfer coefficient in food processing

“…For more complex geometries (irregular and three-dimensional in general) or for heterogeneous or anisotropic solids, a numerical calculation is required for inverse evaluation of the surface heat transfer coefficient. In this connection, as seen, for example in [13] (time-dependent heat transfer coefficient), [14]- [16], and [17] (who additionally use an iterative process to evaluate the spatial distribution of the surface heat transfer coefficient). This paper presents a new general numerical series for the Biot number, which is mathematically exact in the case of the three elementary geometries, from which it is possible to deduce a first, highly precise approximation by truncating the series at its first partial summation.…”

Calculation of the convective heat transfer coefficient and thermal diffusivity of cucumbers using numerical simulation and the inverse method

“…(19), the chi-square depends on T sim i , which depends on α and h. If the cooling involves an interval of temperature in which the value of h can be considered constant and the thermal diffusivity is given by Eq. (17), the parameters can be determined through the minimization of the objective function, which is accomplished in cycles involving the following steps (Silva et al 2011): Step 1) Inform the initial values for the parameters "a", "b"…”

“…In this article, the authors assumed that the diffusion model with boundary condition of the third kind satisfactorily describes the cooling, and that the thermo-physical parameters are constant during the process. According to Silva et al (2011), the best model in the representation of the cucumber's shape was the ellipsoid, but the time demanded in its optimization was about 66 times greater than the time for the infinite cylinder. As observed by Erdogdu (2008), the simultaneous determination of the thermal diffusivity and convective heat transfer coefficient is difficult to accomplish because there may be several pairs of these parameters for which the solution of the diffusion equation is fitted to a set of experimental data.…”

“…According to the authors, "the instrument used in the experiment had allowed the measurement of the heat transfer coefficient between 400 and 2000 W m −2°C−1 ". On the other hand, Silva et al (2011) studied the effect of the geometric representation of cucumbers on the numerical simulation of its cooling kinetics. The following geometries were used to represent the cucumber: infinite cylinder, finite cylinder, and ellipsoid.…”