Numerical Simulation Of Diffusive Processes In Solids Of Revolution Via The Finite Volume Method And Generalized Coordinates

This article proposes a numerical solution of the diffusion equation for solids obtained by revolution of arbitrarily shaped plane surfaces for the description of heat transfer or mass transport. The diffusion equation is discretized and solved using the finite volume method with fully implicit formulation, generalized coordinates and boundary condition of the first kind. The proposed solution exploits symmetry conditions, which reduces the problem to the two-dimensional case, and it diminishes significantly the computational effort in comparison with the traditional method using three-dimensional grids. Our solution is applied to - and compared with - the drying kinetics of solids with known analytical solutions of the diffusion equation. Both solutions agree well in all analyzed cases. Furthermore, our solution is used to describe the moisture distribution inside solids. © 2009 Elsevier Ltd. All rights reserved.5221-2249764985Crank, J., (1992) The Mathematics of Diffusion, , Clarendon Press, Oxford, UKLima, A.G.B., (1999) Fenômeno de difusão em sólidos esferoidais prolatos. Estudo de caso: secagem de banana, Tese de Doutorado, , Universidade Estadual de Campinas, São Paulo, BrasilJia, C., Yang, W., Siebenmorgen, T.J., Cnossen, A.G., Development of computer simulation software for single grain kernel drying, tempering and stress analysis (2001) Proceedings of the Annual International Meeting, , Sacramento, California, ASAE paper number 01-3010Nascimento, J.J.S., (2002) Fenômenos de difusão transiente em sólidos paralelepípedos. Estudo de caso: secagem de materiais cerâmicos, Tese de Doutorado, , Universidade Federal da Paraíba, João Pessoa, PB, BrasilLima, D.R., N Farias, S., B Lima, A.G., Mass transport in spheroids using the Galerkin method (2004) Braz. J. Chem. Eng., 21 (4), pp. 667-680Carmo, J.E.F., (2004) Fenômeno de difusão transiente em sólidos esferoidais oblatos. Estudo de caso: secagem de lentilhas, Tese de Doutorado, , Universidade Federal de Campina Grande, PB, BrasilLi, Z., Kobayashi, N., Hasatani, M., Modeling of diffusion in ellipsoidal solids: a comparative study (2004) Drying Technol., 22 (4), pp. 649-675Gastón, A.L., Abalone, R.M., Giner, S.A., Bruce, D.M., Geometry effect on water diffusivity estimation in printa-isla verde and broom wheat cultivars (2003) Latin Am. Appl. Res., 33 (1), pp. 327-331. , (Bahía Blanca)Wu, B., Yang, W., Jia, C., A three-dimensional numerical simulation of transient heat and mass transfer inside a single rice kernel during the drying process (2004) Biosyst. Eng., 87 (2), pp. 191-200Tannehill, J.C., Anderson, D.A., Pletcher, R.H., (1997) Computational Fluid Mechanics and Heat Transfer. second ed., , Taylor & Francis, PhiladelphiaMaliska, C.R., (2004) Transferência de calor e mecânica dos fluidos computacional, , LTC Editora S.A., Rio de JaneiroO. Hacihafizoglu, A. Cihan, K. Kahveci, A.G.B. Lima, A liquid diffusion model for thin-layer drying of rough rice, Eur. Food Res. Technol. (2007), doi: 10.1007/s00217-007-0593-0Patankar, S.V., (1980) Numerical Heat Transfer and Fluid Flow, , Hemisphere Publishing Corporation, New YorkSilva, W.P., (2007) Transporte difusivo em sólidos com forma arbitrária usando coordenadas generalizadas, Tese de Doutorado, , Universidade Federal de Campina Grande, PB, BrasilSilva, W.P., Cavalcanti Mata, M.E.R.M., Silva, C.D.P.S.e., Guedes, M.A., Lima, A.G.B., Determination of diffusivity and activation energy for cowpea grains (vigna unguiculata (l.) walp.), always-green variety, based on its drying behavior (2008) Eng. Agríc., 28 (2), pp. 325-333Luikov, A.V., (1968) Analytical Heat Diffusion Theory, , Academic Press, Inc. Ltd, LondonBevington, P.R., Robinson, D.K., (1992) Data Reduction and Error Analysis for the Physical Sciences. second ed., , WCB/McGraw-Hill, BostonTaylor, J.R., (1997) An Introduction to Error Analysis. second ed., , University Science Books, Sausalito, CaliforniaSilva, W.P., C.D.P.S.e Silva, LAB Fit Curve Fitting Software, , www.labfit.net, Available from:, accessed on April 2008Mariani, V.C., Lima, A.G.B., Coelho, L.S., Apparent thermal diffusivity estimation of the banana during drying using inverse method (2008) J. Food Eng., 85 (4), pp. 569-579Kiranoudis, C.T., Maroulis, Z.B., Marinos-Kouris, D., Heat and mass transfer model building in drying with multiresponse data (1995) Int. J. Heat Mass Transfer, 38 (3), pp. 463-480Zogzas, N.P., Maroulis, Z.B., Effective Moisture diffusivity estimation from drying data - a comparison between various methods of analysis (1996) Drying Technol., 14 (7), pp. 1543-1573Hamdami, N., Monteau, J.Y., Le Bail, A., Transport properties of a high porosity model food at above and sub-freezing temperatures. Part 2: evaluation of the effective moisture diffusivity from drying data (2004) J. Food Eng., 62 (4), pp. 385-392Ruiz-López, I.I., García-Alvarado, M.A., Analytical solution for food-drying kinetics considering shrinkage and variable diffusivity (2007) J. Food Eng., 79 (1), pp. 208-21