Theoretical Study Of Intermittent Drying (tempering) In Prolate Spheroidal Bodies

The process of intermittent drying in prolate spheroidal bodies was simulated assuming liquid diffusion to be the sole mass transport process, a constant diffusion coefficient and equilibrium conditions at the surface. The mass diffusion equation in a prolate spheroidal coordinate system was used for a two-dimensional case. Due to the use of a dimensionless coordinate system, a Fourier number for tempering is defined, in order to determine the dimensionless time required to achieve a flat moisture content profile. Assuming that the drying process is stopped only once at a fixed point, the tempering Fourier number was determined for aspect ratios of 1.1, 2.0 and 5.0. Many cases were studied, changing the tempering Fourier and aspect ratio of the body. Focusing on the drying rate, the effect of one, two and four drying passes was studied for different interruption points in the process and aspect ratios of 1.1, 2.0 and 5.0, in all cases using the continuous process as a comparison. From the numerical results it was found that during the tempering process, the drying rate and the final mean moisture content are affected by the tempering Fourier number, multipass drying and geometrical dimensions of the body.19815691589Brooker, D.B., Bakker-Arkema, F.W., Hall, C.W., (1978) Drying Cereal Grains, , AVI Publishing Company, Inc., Connecticut, 265 pElbert, G., Tolaba, M.P., Surez, C., Effects of drying and tempering on head parboiled rice yield (1997) IADC - Inter-American Drying Conference, B, pp. 502-507. , Itu, BrazilFioreze, R., (1986) The Intermittent Drying Agricultural Crops With Particular Reference to Energy Requirements, , Ph.D. Thesis. Granfield Institute of Technology, Silsoe College, 153 pFranca, A.S., Fortes, M., Haghighi, K., Numerical simulation of intermittent and continuous deep-bed drying of biological materials (1994) Drying Technology, 12 (7), pp. 1537-1560Hall, C.W., (1980) Drying, and Storage of Agricultural Crops, , AVI Publishing Company, Inc., Connecticut, 381 pLima, A.G.B., Nebra, S.A., Altemani, C.A.C., Simulation of the drying kinetics of the silkworm cocoon considering diffusive mechanism in elliptical coordinate (1997) IADC - Proceedings of the Inter-American Drying Conference, B, pp. 317-324. , Itu, BrazilLima, A.G.B., Diffusion phenomenon in prolate spheroidal solids (1999) Case Studies: Drying of Banana, , Doctor Thesis, State University of Campinas, Campinas, Brazil, 265p., (In portuguese)Lima, A.G.B., Nebra, S.A., Theoretical analysis of the diffusion process inside prolate spheroidal solids (2000) Drying Technology, 18 (1-2), pp. 21-48Maliska, C.R., (1995) Computational Heat Transfer and Fluid Mechanics, , LTC, Rio de Janeiro, 424 p., (In portuguese)Pakowski, Z., Mujumdar, A.S., (1987) Handbook of Industrial Drying. Chapter 3: Basic Process Calculations in Drying, pp. 83-129. , Marcel Dekker, IncPatankar, S.V., (1980) Numerical Heat Transfer and Fluid Flow, , Hemisphere Publishing Corporation, New York, 197 pSabbah, M.A., Foster, G.H., Haugh, C.G., Peart, R.M., Effect of tempering after drying on cooling shelled corn Transaction of the ASAE, 15 (4), pp. 763-765Singh, R.P., Wang, C.Y., Zuritz, C., A numerical approach to simulate rice drying (1980) Proceeding of the Second International Drying Symposium (IDS'80), 1, pp. 227-232. , MontrealSteffe, J.F., Singh, R.P., Theoretical and practical aspects of rough rice tempering (1980) Transaction of the ASAE, pp. 775-782Steffe, J.F., Singh, R.P., Bakshi, A.S., Influence of tempering time and cooling on rice milling yields and moisture removal (1979) Transactions of the ASAE, 22, pp. 1214-1218. , and 1224Strumillo, C., Kudra, T., (1986) Drying: Principles, Science and Design, , Gordon and Breach Science Publishers, New York, 448 pTolaba, M.P., Aguerre, R.J., Suárez, C., Drying of corn with tempering: Simulation and experimental verification (1997) IADC - Inter-American Drying Conference, B, pp. 516-523. , ItuWalker, L.P., Bakker-Arkema, F.W., Energy efficiency in concurrent rice drying (1981) Transactions of the ASAE, 24, pp. 1352-1356Zhang, D., Mujumdar, A.S., Deformation and stress analysis of porous capillary bodies during intermittent volumetric thermal drying (1992) Drying Technology, 10 (2), pp. 421-443Zhang, Q., Litchfield, J.B., An optimization of intermittent corn drying in a laboratory scale thin layer dryer (1991) Drying Technology, 9 (2), pp. 383-39

Transporte de Materia con Reducción de Volumen en el Interior de Sólidos Paralelepípedos

Se describe un modelo matemático tridimensional transitorio aplicado al fenómeno de difusión de agua en el interior de sólidos paralelepípedos. Se utilizó el método de los volúmenes finitos considerando propiedades térmica y mecánicas constantes, equilibrio en la superficie y reducción de volumen del material. El modelo fue utilizado para estudiar el proceso de secado de un ladrillo de cerámica. Se muestran los resultados de la cinética de secado y la distribución del contenido de humedad en varios planos, para un determinado tiempo y para dos coeficientes de encogimiento. Los resultados muestran que el fenómeno de reducción de volumen afecta considerablemente la tasa de secado del sólido, así como la distribución del contenido de humedad en el interior del mismo. Se encuentra también que los gradientes más altos del contenido de humedad se sitúan en las proximidades del vértice del sólido, en cualquier instante de tiempo. El conocimiento de las diferencias de humedad y la cinética de secado permiten optimizar este proceso y aumentar la calidad del producto final

Mass transfer inside oblate spheroidal solids: modelling and simulation

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

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