Mass transfer inside oblate spheroidal solids: modelling and simulation

Abstract

-A numerical solution of the unsteady diffusion equation describing mass transfer inside oblate spheroids, considering a constant diffusion coefficient and the convective boundary condition, is presented. The diffusion equation written in the oblate spheroidal coordinate system was used for a two-dimensional case. The finite-volume method was employed to discretize the basic equation. The linear equation set was solved iteratively using the Gauss-Seidel method. As applications, the effects of the Fourier number, the Biot number and the aspect ratio of the body on the drying rate and moisture content during the process are presented. To validate the methodology, results obtained in this work are compared with analytical results of the moisture content encountered in the literature and good agreement was obtained. The results show that the model is consistent and it may be used to solve cases such as those that include disks and spheres and/or those with variable properties with small modifications.

Assessment of diffusion models to describe drying of roof tiles using generalized coordinates

“…Several studies have been reported in literature using a diffusion model to describe the physical process, and consider the geometric shape of the bodies as cylinder, sphere, or infinite slab [7][8][9][10][11]. Analytical and numerical solutions to predict heat and mass diffusion in porous bodies are also reported for prolate and oblate spheroids [12,13], as well as parallelepipeds [14][15][16].…”

Analytical Solutions of Mass Transfer around a Prolate or an Oblate Spheroid Immersed in a Packed Bed

“…However, in many situations the shape of the particles immersed in a fluid or porous media is not perfectly spherical, and may be classified as prolate or oblate spheroids. Numerical and analytical solutions of the diffusion equation for prolate spheroids have been reported by Coutelieris et al (2004), Lima et al (2002), Coutelieris et al (1995), etc., and for oblate spheroids by Carmo and Lima (2008), Coutelieris et al (1995), etc. Fluid flow along buried spheroidal surfaces is an important model situation (e.g.…”

Ferramentas Analíticas e Numéricas para a Descrição da Secagem de Sólidos na Forma de Cilindros e de Elipsóides

“…Se uma solução analítica for usada para descrever um processo de secagem, mais hipóteses simplificadoras são requeridas para que tal solução possa ser obtida. Dentre estas hipóteses, pode-se ressaltar volume e difusividade constantes, além de meio homogêneo e isotrópico (OLIVEIRA e LIMA, 2002;LIMA et al, 2004a;AMENDOLA e QUEIROZ, 2007;MELLADO, 2007;OLEK e WERES, 2007;CARMO e LIMA, 2008).…”

“…Entretanto, para uma descrição detalhada do transporte de água, modelos matemáticos devem ser usados. Vários modelos são reportados na literatura e, dentre esses, podem ser citados os modelos empíricos (GOUVEIA et al, 2002;BAINI e LANGRISH, 2007;GOYAL et al, 2007;MARTINAZZO et al, 2007), os modelos de difusão (OLIVEIRA e LIMA, 2002, LIMA et al, 2004aNASCIMENTO et al, 2005;AMENDOLA e QUEIROZ, 2007;CARMO e LIMA, 2008;BAINI e LANGRISH, 2008;SILVA et al, 2009d; SILVA, C., 2010) e o modelo de Darcy (PINHEIRO et al, 1998). O objetivo do uso desses modelos é correlacionar os dados experimentais da secagem a uma equação matemática que vai representar a cinética de secagem do produto.…”

“…Para estas hipóteses, se houver uma distribuição uniforme da grandeza de interesse no início do processo, a equação de difusão pode ser resolvida analiticamente (LIMA, 1999;LIU e SIMPSON, 1999;CARMO, 2004;BAUMER e MARIANI, 2005;LÓPEZ et al, 2005;ABSI et al, 2005;CHEMKHI e ZAGROUBA, 2005 (LIMA, 1999;LIMA et al, 2002;CARMO, 2000;LIMA e NEBRA, 2000;FARIAS, 2002;CARMO, 2004;LIMA et al, 2004a;LI et al, 2004;WU et al, 2004;CARMO e LIMA, 2005;OLIVEIRA, 2006;MELO et al, 2008;CARMO e LIMA, 2008). (SILVA, 2007;SILVA et al, 2009c;SILVA et al, 2009d;SILVA et al, 2009e;SILVA et al, 2010a; FARIAS, V., 2011).…”