AS  Vol.3 No.4 , July 2012
Diffusion models for the description of seedless grape drying using analytical and numerical solutions
Abstract: This article compares diffusion models used to describe seedless grape drying at low temperature. The models were analyzed, assuming the following characteristics of the drying process: boundary conditions of the first and the third kind; constant and variable volume, V; constant and variable effective mass diffusivity, D; constant convective mass transfer coefficient, h. Solutions of the diffusion equation (analytical and numerical) were used to determine D and h for experimental data of seedless grape drying. Comparison of simulations of drying kinetics indicates that the best model should consider: 1) shrinkage; 2) convective boundary condition; 3) variable effective mass diffusivity. For the analyzed experimental dataset, the best function to represent the effective mass diffusivity is a hyperbolic cosine. In this case, the statistical indicators of the simulation can be considered excellent (the determination coefficient is R2 = 0.9999 and the chi-square is χ2 = 3.241 × 10–4).
Cite this paper: Silva, W. , Silva e Silva, C. , Precker, J. , Gomes, J. , Nascimento, P. and Silva, L. (2012) Diffusion models for the description of seedless grape drying using analytical and numerical solutions. Agricultural Sciences, 3, 545-556. doi: 10.4236/as.2012.34065.

[1]   Margaris, D.P. and Ghiaus, A.G., (2007) Experimental study of hot air dehydration of Sultana grapes. Journal of Food Engineering, 79, 1115-1121. doi:10.1016/j.jfoodeng.2006.03.024

[2]   Pangavhane, D.R., Sawhney, R.L. and Sarsavadia, P.N. (1999) Effect of various dipping pretreatment on drying kinetics of Thompson seedless grapes. Journal of Food Engineering, 39, 211-216. doi:10.1016/S0260-8774(98)00168-X

[3]   Azzouz, S., Guizani, A., Jomaa, W. and Belghith, A. (2002) Moisture diffusivity and drying kinetic equation of convective drying of grapes. Journal of Food Engineering, 55, 323-330. doi:10.1016/S0260-8774(02)00109-7

[4]   Doymaz, I. and Pala, M. (2002) The effects of dipping pretreatments on air-drying rates of the seedless grapes. Journal of Food Engineering, 52, 413-417. doi:10.1016/S0260-8774(01)00133-9

[5]   Doymaz, I. (2006) Drying kinetics of black grapes treated with different solutions. Journal of Food Engineering, 76, 212-217. doi:10.1016/j.jfoodeng.2005.05.009

[6]   Esmaiili, M., Rezazadeh, G., Sotudeh-Gharebagh, R. and Tahmasebi, A. (2007) Modeling of the seedless grape drying process using the generalized differential quadra- ture method. Chemical Engineering and Technology, 30, 168-175. doi:10.1002/ceat.200600151

[7]   Di Matteo, M., Cin-quanta, L., Galiero, G. and Crescitelli, S. (2000) Effect of a novel physical pretreatment process on the drying kinetics of seedless grapes. Journal of Food Engineering, 46, 83-89. doi:10.1016/S0260-8774(00)00071-6

[8]   Ramos, I.N., Miranda, J.M.R., Brand?o, T.R.S. and Silva, C.L.M. (2010) Estimation of water diffusivity parameters on grape dynamic drying. Journal of Food Engineering, 97, 519-525. doi:10.1016/j.jfoodeng.2009.11.011

[9]   Bennamoun, L. and Belhamri, A. (2006) Numerical simulation of drying under variable external conditions: Application to solar drying of seedless grapes. Journal of Food Engineering, 76, 179-187. doi:10.1016/j.jfoodeng.2005.05.005

[10]   Hacihafizoglu, O., Cihan, A., Kahveci, K. and Lima, A.G.B. (2008) A liquid diffusion model for thin-layer drying of rough rice. European Food Research and Technology, 226, 787-793. doi:10.1007/s00217-007-0593-0

[11]   Silva, W.P., Precker, J.W., Silva, C.M.D.P.S. and Gomes, J.P. (2010) Determination of effective diffusivity and con- vective mass transfer coefficient for cylindrical solids via analytical solution and inverse method: Application to the drying of rough rice. Journal of Food Engineering, 98, 302-308. doi:10.1016/j.jfoodeng.2009.12.029

[12]   Queiroz, M.R. and Nebra, S.A. (2001) Theoretical and experimental analysis of the drying kinetics of bananas. Journal of Food Engineering, 4, 127-132. doi:10.1016/S0260-8774(00)00108-4

[13]   Zhan, J.-F., Gu, J.-Y. and Cai, Y.-C. (2007) Analysis of moisture diffusivity of larch timber during convective drying condition by using Crank’s method and Dincer’s method. Journal of Forestry Research, 18, 199-203. doi:10.1007/s11676-007-0040-x

[14]   Kaya, A., Ayd?n, O. and Dincer, I. (2010) Comparison of experimental data with results of some drying models for regularly shaped products. Heat Mass Transfer, 46, 555- 562. doi:10.1007/s00231-010-0600-z

[15]   Jia, C., Yang, W., Siebenmorgen, T.J. and Cnossen, A.G. (2001) Development of computer simulation software for single grain kernel drying, tempering and stress analysis. Transactions of the ASAE, 45, 1485-1492.

[16]   Gastón, A.L., Abalone, R.M. and Giner, S.A. (2002) Wheat drying kinetics. Diffusivities for sphere and ellipsoid by finite elements. Journal of Food Engineering, 52, 313-322. doi:10.1016/S0260-8774(01)00121-2

[17]   Li, Z., Ko-bayashi, N. and Hasatani, M. (2004) Modelling of diffu-sion in ellipsoidal solids: A comparative study. Drying Technology, 22, 649-675. doi:10.1081/DRT-120034256

[18]   Wu, B., Yang, W. and Jia, C. (2004) A three-dimensional numerical simulation of transient heat and mass transfer inside a single rice kernel during the drying process. Bio- systems Engineering, 87, 191-200. doi:10.1016/j.biosystemseng.2003.09.004

[19]   Carmo, J.E.F. and Lima, A.G.B. (2005) Drying of lentil including shrinkage: A numerical simulation. Drying Technology, 23, 1977-1992. doi:10.1080/07373930500210424

[20]   Silva, W.P., Silva, C.M.D.P.S., Silva, D.D.P.S. and Silva, C.D.P.S. (2008) Numerical Simulation of the Water Diffusion in Cylin-drical Solids. International Journal of Food Engineering, 4, 1-16. doi:10.2202/1556-3758.1394

[21]   Silva, W.P., Precker, J.W., Silva, C.M.D.P.S. and Silva, D.D.P.S. (2009) Determination of the effective diffusivity via minimization of the objective function by scanning: application to drying of cowpea. Journal of Food Engineering, 95, 298-304. doi:10.1016/j.jfoodeng.2009.05.008

[22]   Silva, W.P., Silva, C.M.D.P.S., Farias, V.S.O. and Silva, D.D.P.S. (2010) Calculation of the convective heat transfer coef-ficient and cooling kinetics of an individual fig fruit. Heat and Mass Transfer, 46, 371-380. doi:10.1007/s00231-010-0577-7

[23]   Luikov, A.V. (1968) Analytical heat diffusion theory. Academic Press Inc. Ltd, London.

[24]   Crank, J. (1992) The mathematics of diffusion. Clarendon Press, Oxford.

[25]   Patankar, S.V. (1980) Numerical heat transfer and fluid flow. Hemisphere Publishing Corporation. New York.

[26]   Bevington, P.R. and Robinson, D.K. (1992) Data reduction and error analysis for the physical sciences. 2nd Edition, WCB/McGraw-Hill, Boston.

[27]   Taylor, J.R. (1997) An introduction to error analysis. 2nd Edition, University Science Books, Sausalito.

[28]   Silva, W.P., Silva, C.M.D.P. S., Farias, V.S.O. and Gomes, J.P. (2012) Diffusion models to describe the drying process of peeled bananas: optimization and simulation. Drying Technology, 30,164-174. doi:10.1080/07373937.2011.628554