Assessment of diffusion models to describe drying of roof tiles using generalized coordinates
Tóm tắt
This article aims to study the mass transient diffusion in solids with an arbitrary shape, highlighting boundary condition of the third kind. To this end, the numerical formalism to discretize the transient 3D diffusion equation written in generalized coordinates is presented. For the discretization, it was used the finite volume method with a fully implicit formulation. An application to drying of roof tiles has been done. Three models were used to describe the drying process: (1) the volume V and the effective mass diffusivity D are considered constant for the boundary condition of the first kind; (2) V and D are considered constant for the boundary condition of the third kind and (3) V and D are considered variable for the boundary condition of the third kind. For all models, the convective mass transfer coefficient h was considered constant. The analyses of the results obtained make it possible to affirm that the model 3 describes the drying process better than the other models.
Tài liệu tham khảo
Elgamalab R, Ronssea F, Radwanb SM, Pietersa JG (2014) Coupling CFD and diffusion models for analyzing the convective drying behavior of a single rice kernel. Dry Technol 32(3):311–320
Olek W, Weres J (2007) Effects of the method of identification of the diffusion coefficient on accuracy of modeling bound water transfer in wood. Transp Porous Media 66(1–2):135–144
Silva WP, Precker JW, Silva CMDPS, Silva DDPS (2009) Determination of the effective diffusivity via minimization of the objective function by scanning: application to drying of cowpea. J Food Eng 95(2):298–304
Silva WP, Silva CMDPS, Lins MAA (2011) Determination of expressions for the thermal diffusivity of canned foodstuffs by the inverse method and numerical simulations of heat penetration. Int J Food Sci Technol 46(4):811–818
Betta G, Rinaldi M, Barbanti D, Massini R (2009) A quick method for thermal diffusivity estimation: application to several foods. J Food Eng 91:34–41
Nguyen MH, Price WE (2007) Air-drying of banana: influence of experimental parameters, slab thickness, banana maturity and harvesting season. J Food Eng 79(1):200–207
Golestania G, Raisiab A, Aroujalianab A (2013) Mathematical modeling on air drying of apples considering shrinkage and variable diffusion coefficient. Dry Technol 31(1):40–51
Saykova I, Cwicklinski G, Castelle P (2009) Analytical approach for predicting effective diffusion coefficients in multidimensional slab geometry. J Univ Chem Technol Metall 44(1):44–49
Ukrainczyk N (2009) Thermal diffusivity estimation using numerical inverse solution for 1D heat conduction. Int J Heat Mass Transf 52:5675–5681
Vasić M, Radojević Z, Grbavčić Ž (2011) Calculation of the effective diffusion coefficient during the drying of clay samples. J Serb Chem Soc 76:1–17
Silva WP, Silva CMDPS, Farias VSO, Gomes JP (2012) Diffusion models to describe the drying process of peeled bananas: optimization and simulation. Dry Technol 30:164–174
Carmo JEF, Lima AGB (2008) Mass transfer inside oblate spheroidal solids: modeling and simulation. Braz J Chem Eng 25(1):19–26
Hacihafizoglu O, Cihan A, Kahveci K, Lima AGB (2008) A liquid diffusion model for thin-layer drying of rough rice. Eur Food Res Technol 226(4):787–793
Nascimento JJS, Mederos BJT, Belo FA, Lima AGB (2005) Trasnporte de materia con reducción de volumen en el interior de sólidos paralelepípedos. Información Tecnológica 16(1):35–41
Silva WP, Silva LD, Farias VSO, Silva CMDPS (2012) Water migration in clay slabs during drying: a three-dimensional numerical approach. Ceram Int. doi:10.1016/j.ceramint.2012.10.252
Silva WP, Farias VSO, Neves GA, Lima AGB (2012) Modeling of water transport in roof tiles by removal of moisture at isothermal conditions. Heat Mass Transf 48:809–821
Silva WP, Silva CMDPS, Silva DDPS, Neves GA, Lima AGB (2010) Mass and heat transfer study in solids of revolution via numerical simulations using finite volume method and generalized coordinates for the Cauchy boundary condition. Int J Heat Mass Transf 53(5–6):1183–1194
Silva WP, Precker JW, Silva DDPS, Silva CDPS, Lima AGB (2009) Numerical simulation of diffusive processes in solids of revolution via finite volume method and generalized coordinates. Int J Heat Mass Transf 52(21–22):4976–4985
Silva WP, Hamawand I, Silva CMDPS (2014) A liquid diffusion model to describe drying of whole bananas using boundary-fitted coordinates. J Food Eng 137:32–38
Wu B, Yang W, Jia C (2004) A three-dimensional numerical simulation of transient heat and mass transfer inside a single rice kernel during the drying process. Biosyst Eng 87(2):191–200
Farias VSO, Silva WP, Silva CMDPS, Lima AGB (2012) Three-dimensional diffusion in arbitrary domain using generalized coordinates for the boundary condition of the first kind: application in drying. Defect Diffus Forum 326–328:120–125
Farias VSO, Silva WP, Silva CMDPS, Delgado JMPQ, Farias Neto SR, Lima AGB (2012) Transient diffusion in arbitrary shape porous bodies: numerical analysis using boundary fitted coordinates. In: Delgado JMPQ, Barbosa de Lima AG, da Silva MZ (eds) Numerical analysis of heat and mass transfer in porous media, Chapter 4. Springer, Berlin, pp 85–119
Farias VSO, Silva WP, Silva CMDPS, Rocha VPT, A.G.B. Lima (2013) Drying of solids with irregular geometry: numerical study and application using a three-dimensional model. Heat Mass Transf 49(5):695–709
Farias VSO, Silva WP, Silva CMDPS, Silva LD, Gama FJA, A.G.B. Lima (2013) Numerical solution of the three-dimensional diffusion equation in solids with arbitrary geometry for the convective boundary condition: application in drying. Defect Diffus Forum 334–335:149–154
Salinas C, Ananias A, Alvear AM (2004) Simulación del secado de la madera: wood drying simulation, Maderas. Ciência e Tecnologia 6(1):3–18
Lakner M, Plazl P (2008) The finite differences method for solving systems on irregular shapes. Comput Chem Eng 32:2891–2896
Musielak G (2001) Possibility of clay damage during drying. Dry Technol 19:1645–1659
Mačiulaitis R, Malaiškien J, Kičait A (2008) The regulation of physical and mechanical parameters of ceramic bricks depending on the drying regime. J Civ Eng Manag 14:263–268
Musielak G, Mierzwa D (2009) Permanent strains in clay-like material during drying. Dry Technol 27:894–902
Mihoubi D, Bellagi A (2012) Modeling of heat and moisture transfers with stress–strain formation during convective air drying of deformable media. Heat Mass Transf 48(10):1697–1705
Patankar SV (1980) Numerical heat transfer and fluid flow. Hemisphere Publishing Coorporation, New York, p 197
Luikov AV (1968) Analytical heat diffusion theory. Academic Press, London
Crank J (1992) The mathematics of diffusion. Clarendon Press, Oxford
Maliska CR (2004) Heat transfer and computational fluid mechanics (In Portuguese), 2nd edn. LTC Editora S. A., Rio de Janeiro
Beer FP, Johnston ERJ (1990) Vector mechanics for engineers: statics and dynamics, 5a edn. McGraw-Hil, Makron
Taylor JR (1997) An introduction to error analysis, 2nd edn. University Science Books, Sausalito