Numerical simulation of diffusive processes in solids of revolution via the finite volume method and generalized coordinates

Silva, Wilton Pereira da; Precker, Jürgen W.; Silva, Diogo D. P. S. e; Silva, Cleiton D. P. S. e; Lima, Antônio Gilson Barbosa de

doi:10.1016/j.ijheatmasstransfer.2009.05.008

Cited by 32 publications

(25 citation statements)

References 11 publications

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“…Another example of the use of this method can be found in Lima et al [8] These authors used a finite volume method to describe the drying process of peeled bananas considering shrinkage and an ellipsoidal configuration for the product. Several numerical solutions of the diffusion equation using finite volume for various geometries are available in the literature; for example, the solutions proposed by Silva et al [22][23][24] (arbitrary geometry, boundary condition of the first kind; arbitrary geometry, boundary condition of the third kind; and sphere, boundary condition of the third kind, respectively).…”

Section: Introductionmentioning

confidence: 99%

Diffusion Models to Describe the Drying Process of Peeled Bananas: Optimization and Simulation

Silva

Farias

2011

Drying Technology

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This article aims to study the mass transient diffusion in solids with a cylindrical shape. To this end, the one-dimensional diffusion equation was discretized using the finite volume method with a fully implicit formulation. The solution can be used to simulate diffusive processes and to determine thermophysical parameters via optimization techniques. The computational package developed was applied to study the thin-layer drying of peeled bananas. Three models were used to describe the drying process: (1) the volume V and the effective mass diffusivity D are considered constant; (2) variable V and constant D; (3) V and D are considered variable. For all models, the convective mass transfer coefficient h is considered constant. The statistical indicators show that for the two cases analyzed (low and high temperature), model 3 describes the drying process better than the other models.

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Section: Introductionmentioning

confidence: 99%

Diffusion Models to Describe the Drying Process of Peeled Bananas: Optimization and Simulation

Silva

Farias

2011

Drying Technology

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“…In the case of a variable transport coefficient C U , a harmonic mean will be used for its estimation at the interfaces of each control volume [17,18]. At the nodal points, C U must be calculated by an appropriate function that relates C U with the value of U at each nodal point.…”

Section: Average Value Of U and Variable Coefficient C Umentioning

confidence: 99%

“…In many areas of production involving heat and mass transfer, there are many situations in which the solids under study do not present regular geometry [17][18][19][20][21][22][23][24][25][26]. Some examples can be cited: sanitary ware, some types of coating, tile, rice, wheat, lentil, pumpkin and cashew.…”

Section: Introductionmentioning

confidence: 99%

“…It is possible to find in the literature some solutions applied to solids with irregular shape, using generalized coordinates by means of 2D models [17][18][19], 3D model with orthogonal mesh [20] and 3D model for the equilibrium boundary condition [21][22][23]. However, there is a lack of studies that take into account the arbitrary geometry of bodies through 3D models using convective boundary condition [24], which is necessary in order to describe more precisely the process.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of diffusion models to describe drying of roof tiles using generalized coordinates

Farias

Silva

et al. 2015

Heat Mass Transfer

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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. List of symbols Latin symbols A, BCoefficients of algebraic equation of the discretized equation A 1 , B 1 , C 1 , Constants obtained by non-linear regression for dimensions of the tiles a, bFitting parameters obtained by optimization D efEffective water diffusivity (m 2 s -1 ) E, L, C Dimensions of the roof tiles (m) hConvective mass transfer coefficient (m s -1 ) J Jacobian of the transformation (m -3 )

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“…They concluded that numerical simulation provided an accurate prediction of heat and mass diffusion inside spherical foods with variable properties that were almost impossible to obtain with analytical solutions. Da Silva et al [78] proposed the use of the FVM to investigate the two-dimensional heat and mass diffusion for cowpea grain during drying. The diffusion equations were discretized with a fully implicit formulation, generalized coordinates, and boundary condition of the first kind.…”

Section: Nonconjugated Casesmentioning

confidence: 99%

Computational Simulation and Developments Applied to Food Thermal Processing

2011

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New challenges to improve food processing have created an incentive in the potential use of computeraided engineering for simulating thermal processes in foods as a viable technique to provide effective and efficient design solutions. Mathematical conjugated and nonconjugated models used along suitable numerical methods such as finite differences, finite elements, and finite volumes in predicting food freezing, dehydration, and sterilization are discussed in this review. The application of computational simulation should be used in combination with conventional techniques such as physical experiments and analytical solutions in order to enhance the knowledge of fluid mechanics, heat and mass transfer in foods.

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Numerical simulation of diffusive processes in solids of revolution via the finite volume method and generalized coordinates

Cited by 32 publications

References 11 publications

Diffusion Models to Describe the Drying Process of Peeled Bananas: Optimization and Simulation

Diffusion Models to Describe the Drying Process of Peeled Bananas: Optimization and Simulation

Assessment of diffusion models to describe drying of roof tiles using generalized coordinates

Computational Simulation and Developments Applied to Food Thermal Processing

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