Mass transport in spheroids using the Galerkin method

Abstract

-This work presents an analytical modelling of mass transfer in spheroidal solids using a liquid diffusion model. The diffusion equation, written in cylindrical coordinates, is solved using the Galerkin method with a constant diffusion coefficient and an equilibrium boundary condition at the surface of the solid. Results on the drying kinetics, and moisture content distribution in the solids are presented and analysed. The iso-concentration lines for moisture content show that the drying process is faster in sharp areas,. It was verified that solids with a larger area/volume ratio dry faster. The results obtained are consistent so the model presented can be used to solve diffusion problems such as drying, wetting, heating and cooling of solids with a shape that varies from a circular disk to an infinite cylinder, including a sphere and ellipsoids.

Determination of effective diffusivity and convective mass transfer coefficient for cylindrical solids via analytical solution and inverse method: Application to the drying of rough rice

“…Under certain conditions (spherical or cylindrical geometries, infinite slabs, and constant thermo-physical parameters and volume), the diffusion equation has an analytical solution (Luikov, 1968;Crank, 1992). These solutions are used for the description of thin-layer drying for various agricultural products (Lima et al, 2004;Cunningham et al, 2007;Ruiz-López and García-Alvarado, 2007;Hacihafizoglu et al, 2008).…”

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

“…For simple geometries with constant volume and diffusivity, the diffusion equation has analytical solutions, assuming initially uniform moisture distribution (Luikov, 1968;Crank, 1992). These solutions are frequently used to describe the moisture content of a body as a function of time (Lima et al, 2004;Bello et al, 2004;Amendola and Queiroz, 2007;Cunningham et al, 2007;Hacihafizoglu et al, 2008).…”

“…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.…”

Mass transfer inside oblate spheroidal solids: modelling and simulation

“…may be classified as prolate spheroids and lentils as oblate spheroids. Numerical and analytical solutions of the diffusion equation for prolate spheroids have been reported by Payne et al (1986), Oliveira (2001), , Teruel et al (2002) and Oliveira and Lima (2002), and for oblate spheroids Brazilian Journal of Chemical Engineering Payne et al (1986), Farias (2002), Carmo (2004), Lima et al (2004) and Carmo and Lima (2005).…”