Купить СНПЧ А7 Архангельск, оперативня доставка

crosscheckdeposited

Mass Diffusion Inside Prolate Spherical Solids: An Analytical Solution

DOI: http://dx.doi.org/10.15871/1517-8595/rbpa.v4n1p41-50

http://rbpaonline.com/ 

downloadpdf

Vital A. B. Oliveira1 & Antonio G. B. Lima2

  

Abstract: The analytical solution of the transient mass diffusion equation in prolate spherical coordinates by considering constant transport coefficient and convective boundary conditions is presented. The solution is obtained by the variables separation method. The formal solution is applied to predict the average moisture content and moisture content distribution of a prolate spherical solid (ellipsoid of revolution) during the drying process. Analytical results are compared with numerical results that are reported in the literature and good agreement was obtained.

Key words: drying, formal solution, mass, diffusion, elliptical geometry

 

Resumo: A solução analítica da equação de difusão de massa em coordenadas esferoidais prolata considerando coeficiente de difusão constante e condição de contorno convectiva é apresentada. A solução é obtida usando o método da separação de variáveis. A metodologia é aplicada para predizer o teor de umidade médio e a distribuição do teor de umidade, de um sólido esferoidal prolato (elipsóide de revolução), durante o processo de secagem. Resultados analíticos são comparados com resultados numéricos reportados na literatura e uma boa concordância foi obtida.

Palavras-chave: secagem, solução exata, massa, difusão, geometria elíptica

 

1 Mestre em Engenharia Mecânica, Departamento de Engenharia Mecânica, CCT, Universidade Federal da Paraíba (UFPB), CEP 58109-970, Cx. Postal 10069, Campina Grande-PB, Brasil. Fone (083) 310-1317
2 Professor Doutor do Departamento de Engenharia Mecânica, CCT, Universidade Federal da Paraíba (UFPB), CEP 58109-970, Cx. Postal 10069, Campina Grande-PB, Brasil. Fone (083) 310-1317, e-mail: gilson@dem.ufpb.br

  

Literatura Citada

Alassar, R. S., Heat condution from spheroids. Journal of Heat Transfer, V. 121, n. 2, p.497-499, 1999. https://doi.org/10.1115/1.2826010

Abramowitz, M.; Stegun, I. A., Handbook of mathematical functions, New York: Dover Publications, Inc., p. 752-772, 1972.

Crank, J., The Mathematics of Diffusion, New York: Oxford Science Publications, 1992.414p.

Flammer, C., Spheroidal Wave Functions. Stanford: Stanford University Press, 1957.

Haji-Sheikh, A.; Sparrow, E. M., Transient heat conduction in a prolate spheroidal solid,Transactions of the ASME: Journal of Heat Transfer, v. 88, n. 3, p. 331-333, 1966. https://doi.org/10.1115/1.3691560

Lima, A. G. B., Nebra, S. A., 1999, Analytical solution of the mass diffusion equation applied to ellipsoid of revolution. In: Brazilian Congress of Mechanical Engineering (COBEM). Proceedings… Águas de Lindóia, Brazil, CD-Rom.

Lima, A. G. B., 1999, Diffusion phenomenon in prolate spheroidal solids. Case studied: drying of banana. State University of Campinas (UNICAMP), 1999. 265p. (Doctor Thesis). (In portuguese).

Lima, A. G. B.; Nebra, S. A., Theoretical analysis of the diffusion process inside prolate spheroidal solids. Drying Technology, v. 18, n. 1-2, p. 21-48. 2000. https://doi.org/10.1080/07373930008917691

Luikov, A. V., Analytical heat diffusion theory, London: Academic Press, Inc. Ltd, 1968. 685p.

Morse, P. M.; Feshbach, H., Methods of Theoretical Physics, Part II, New York: McGraw-Hill Book Company, Inc., p. 1502- 1513, 1956.

Norminton, E. J., Blackwell, J. H. Transient heat flow from constant temperature spheroids andthe thin circular disk. The Quarterly Jour. of Mech. and Applied Mathematics, v. XVII, Part 1, p. 65-72, 1964. https://doi.org/10.1093/qjmam/17.1.65

Robin, L. Fonctions Sphériques de Legendre etFonctions Sphéroidales, Tome III, Paris: Gauthier-Villares, p. 212-262. 1959.

Skelland, A. H. P., Diffusional mass transfer,New York: John Wiley & Sons, 1974.

Stratton, J. A.; Morse, P. M.; Chu, L. J.; Little, J.D. C.; Corbató, F. J., Spheroidal wave functions, New York: The Tech. Press of M. I. T. and John Wiley & Sons, Inc., 1956.

Stratton, J. A.; Morse, P. M.; Chu, L. J.; Little, J. D. C.; Huntner, R. A. Elliptic cylinder and spheroidal wave functions, New York: The Tech. Press of M. I. T. and John Wiley & Sons, Inc., 1941.