Determinação da difusividade e da energia de ativação para feijão macassar (Vigna unguiculata (L.) Walp.), variedade sempre-verde, com base no comportamento da secagem

Abstract

RESUMO:Neste artigo, teve-se o objetivo de determinar curvas de secagem em camada fina para grãos de feijão macassar, variedade sempre-verde. Visou-se, também, à determinação da difusividade efetiva da água no interior do produto, bem como a energia de ativação. Para tal, foram utilizadas amostras com 150 g de feijão com teor inicial de água de 37% (bu), nas temperaturas de 40; 50 e 60 o C. A velocidade do ar do secador convectivo foi mantida em 1,0 m s -1 e, durante todo o processo, os valores médios da temperatura e da umidade relativa do ar ambiente foram, respectivamente, 29 o C e 58%. A difusividade efetiva da água no produto foi determinada, em cada temperatura, por meio da lei de Fick, pressupondo um modelo esférico para os grãos. Uma expressão para a difusividade efetiva da água em função da temperatura foi determinada por meio do ajuste da equação de Arrhenius aos dados obtidos. A análise dos resultados possibilita concluir que a equação de Page representa, de forma satisfatória, o processo de secagem em todas as condições estudadas. O modelo esférico estabelecido para os grãos é satisfatório, resultando em difusividade efetiva que variou de 7,13x10 -11 até 14,0x10 -11 m 2 s -1 , e em energia de ativação igual a 26,9 kJ mol -1 . Foi observado que, para a temperatura do ar de secagem mantida em 60 o C, houve a formação de fissuras em quantidade significativa de grãos.PALAVRAS-CHAVE: modelo de Page, segunda lei de Fick, teor de água, grãos esféricos. DETERMINATION OF DIFFUSIVITY AND ACTIVATION ENERGY FOR COWPEA GRAINS (Vigna unguiculata (L.) Walp.), ALWAYS-GREEN VARIETY, BASED ON ITS DRYING BEHAVIORABSTRACT: In this paper it was determined the thin layer drying curves for cowpea grains, always-green variety. It was also determined the effective water diffusivity inside the product and its activation energy. For these purposes, 150 g samples of cowpea grains dried at temperatures of 40; 50 and 60 °C were used. The drying air velocity was maintained constantly at 1.0 m s -1 during the drying process. The drying air temperature and relative humidity were 29 °C and 58%, respectively. The effective water diffusivity inside the product was determined, for each drying temperature, by using Fick's equation assuming a spherical shape for the grains. A mathematical expression for the effective water diffusivity inside the product as a function of temperature was determined by fitting Arrhenius's equation to the observed data. According to the analysis of the results, it is possible to conclude that the Page equation can be used to satisfactorily represent the cowpea grains drying process for the conditions of this research. The assumption of a spherical shape for the grains was satisfactory, resulting in a water effective diffusivity varying from 7.13x10 -11 to 14.00x10 -11 m 2 s -1 and activation energy equal to 26.9 kJ mol -1 . It was also observed that for a drying air temperature of 60 °C a significant amount of grains presented fissures.

Modeling of water transport in roof tiles by removal of moisture at isothermal conditions

“…This model is widely accepted in the literature [10,12,13,[16][17][18][19][20][21][22], both to describe the water transport with boundary condition of the first kind, and with boundary condition of the third kind.…”

“…The coefficient of determination R 2 and Chi-square v 2 were used as statistical indicators for the analysis of the results. On the other hand, an Arrhenius type equation [21,26,35,36] was used to determine the diffusivity as function of the temperature:…”

Determination of the effective diffusivity via minimization of the objective function by scanning: Application to drying of cowpea

“…For many processes of adsorption and desorption of water in agricultural products, particularly for grains, the diffusion equation can be solved for boundary condition of the first kind under the assumption of simplifying hypotheses (Azzouz et al, 2002;Doymaz and Pala, 2003;Iguaz et al, 2003;Lima et al, 2004;Bello et al, 2004;Hacihafizoglu et al, 2008;Silva et al, 2008). In this case, the solutions for various simple geometries are given by an infinite series which depends only on the initial moisture content (assumed to be uniform), the equilibrium moisture content and the effective diffusivity.…”

Mathematical models to describe the volumetric shrinkage rate of red beans during drying

“…However, when the air temperature raises (Table 3) the coefficient "b" decreases. Its influence on the volumetric shrinkage rate of the bean during the drying process could be described through the Arrhenius representation, as indicated in 26.9 kJ mol -1 (SILVA et al, 2008). However, ZOGZAS et al (1996 pointed out that the activation energy of agricultural products ranges between 12.7 and 110.0 kJ mol -1 .…”