Mass Transfer in Irregularly-Shaped Solid: An Exact Solution Using the Galerkin-Based Integral Method

Abstract:

This paper presents a theoretical investigation of the mass transfer during the drying of solids of revolution with arbitrary shape. A two-dimensional mathematical model by assuming the liquid diffusion to be the sole mechanism of moisture transport, constant thermophysical properties and convective boundary condition at the surface of the solid is presented. The resulting equation is solved analytically by using the Galerkin-based integral method. Results of the mean moisture content and moisture content distribution within the porous solid are present and analyzed during the process, for different Biot number and aspect ratio. We conclude that solid drying rate is affected by Biot number and area/volume relationships, and which drying process is faster in sharp areas and closed to surface of the solid.

• Periodical: Defect and Diffusion Forum (Volumes 326-328)
• Pages: 199-204
• DOI: https://doi.org/10.4028/www.scientific.net/DDF.326-328.199
• Online since: April 2012
• Authors: I. Batista dos Santos, L.P. de Lucena Silva, Antônio Gilson Barbosa de Lima
• Keywords: Analytical, Drying, Method GBI, Simulation

References

[1] D.R. Lima, S.N. Farias and A.G.B. Lima: Braz. J. Chem. Eng. Vol. 21 (2004), p.667.

[2] A. Haji-Sheikh and E.M. Sparrow: Trans. ASME: J. Heat Transf. Vol. 88 (1966), p.331.

[3] D.B. Brooker, F.W. Bakker-Arkema and C.W. Hall: Drying and storage of grains and oilseeds. (New York: AVI Book, 1992).

[4] J.V. Beck, K.D. Cole, A. Haji-Sheikh and B. Litkouhi: Galerkin-based green's functions and solutions (In: Heat condution using green's functions, Chapter Ten, Hemispheric Publishing Corporation, New York, USA, 1992).

DOI: 10.1201/9781439895214

[5] F.R. Payne, C.C. Corduneanu, A. Haji-Sheikh and T. Huang: On solution of parabolic partial differential equations using Galerkin functions (In: Integral methods in science and engineering, Chapter Hemisphere Publishing Corporation, New York, USA, 1986).

[6] L.V. Kantorovich and V.I. Krylov: Approximate methods of higher analysis. Advanced Calculus (Wiley, New York, USA, 1960).

[7] A. Haji-Sheikh and R. Lakshminarayanan: J. Heat Transf. Vol. 109 (1987), p.557.

[8] A.G.B. Lima: Diffusion phenomenon in prolate spheroidal solids. Case study: drying of banana (PhD Thesis. State University of Campinas, Campinas, Brazil, 1999). (In Portuguese).

[9] J.E.F. Carmo and A.G.B. Lima: Braz. J. Chem. Eng. Vol. 25 (2008), p.19.

[10] J.J.S. Nascimento: Transient diffusion phenomenon in parallelepipeds solids. Case studied: drying of ceramic materials (PhD Thesis, Federal University of Paraiba, João Pessoa, Brazil, 2002). (In Portuguese).

[11] V.A.B. Oliveira and A.G.B. Lima: Braz. J. Agri-ind. Products Vol. 4 (2002), p.41.