A Three Dimensional Model for Heat and Mass Transfer in Convective Wood Drying

Dedić, Aleksandar; Mujumdar, Arun S.; Voronjec, Dimitrije

doi:10.1081/drt-120017280

Cited by 17 publications

(8 citation statements)

References 11 publications

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“…In many papers, one-dimensional diffusion models are used to describe the process (Liu and Simpson 1996;Dincer 1998;Liu et al 2001;Kulasiri and Woohead 2005;Mellado 2007). However, even in the case of lumber, drying physically occurs in three dimensions (Dedic et al 2003;Salin 2008).…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional numerical analysis of water transfer in wood: determination of an expression for the effective mass diffusivity

Silva

Farias

et al. 2013

Wood Sci Technol

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The objective of this article is to determine an expression for the effective mass diffusivity related to the description of wood drying using a diffusion model and experimental data. With this objective, a three-dimensional numerical solution of diffusion equation for the parallelepiped, with convective boundary condition, was used to describe the drying process. For the adopted diffusion model, the convective mass transfer coefficient h was considered constant. The effective mass diffusivity D was considered as a function of the local moisture content, and several expressions were tested to describe the process. To this end, the numerical solution was coupled to an optimizer based on the inverse method, which determines the process parameters D and h using an experimental dataset. For both temperatures of the drying air studied in this article (40 and 80°C), the results obtained by considering the variable effective mass diffusivity are better than those obtained when considering such parameter with a value constant. In addition, with the results for D and h obtained by optimization, the drying kinetics was simulated with success. List of symbols A, BCoefficients of the discretized diffusion equation (dimensionless) DEffective mass diffusivity (m 2 s -1 ) hConvective mass transfer coefficient (m s -1 ) MLocal moisture content at instant t (db, kg kg -1 ) MAverage moisture content at instant t (db, kg kg -1 ) M 0 Initial moisture content (db, kg kg -1 ) M 1 Equilibrium moisture content (db, kg kg -1 )

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Section: Introductionmentioning

confidence: 99%

Three-dimensional numerical analysis of water transfer in wood: determination of an expression for the effective mass diffusivity

Silva

Farias

et al. 2013

Wood Sci Technol

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“…Dedic et al [11] utilized a modified moisture diffusion coefficient in a three-dimensional model to describe drying of beechwood. Their results were satisfactory for the range of air temperatures used in the drying tests.…”

Section: Introductionmentioning

confidence: 99%

A Simulation of Wet Pocket Lumber Drying

Cai

Oliveira

2008

Drying Technology

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In general, wood containing wet pockets is difficult to dry and to ensure uniformity of moisture content at the end of the drying process. Large variations of final moisture content and severe case hardening are common problems associated with the drying of wet wood. In order to devise optimal strategies for drying wood containing wet pockets, it is necessary to understand its complex moisture movement mechanisms and therefore predict drying times and final moisture content. Sub-alpine fir dimension lumber was used in this research because of its inherent issues related to wet pockets.A two-dimensional mathematical drying model for wood containing wet pockets was developed. An effective diffusion coefficient (D eff ) was utilized in the model and heat and mass transfer equations were solved using a control volume approach. The difficulties involved in the simulation of the drying process of wet pocket lumber are due to the differences in moisture content and physical properties between wet and normal wood. Thus, an adjustable D eff based on the moisture content (for both below and above fiber saturation point) was used during the simulation.Four drying runs involving green unsorted sub-alpine fir lumber were carried out in a 3-ft laboratory kiln and in an 8-ft pilot kiln. The results of the simulations were in agreement with the results obtained through the drying experiments. INTRODUCTIONThe difficulty in drying sub-alpine fir (Abies lasiocarpa (Hook) Nutt.) lumber is mainly associated with the occurrence of wet pockets (wet wood) that is characterized by its unusually high moisture content (MC). Higher extractive contents [1] and a larger number of aspirated and encrusted pit membranes on tracheid cell walls are observed in wet wood compared to normal wood. [2] Various drying models reported in the literature propose different mechanisms for moisture movement in wood. Empirical models, such as curve fitting, can be practical and relatively simple. A semi-empirical model proposed by Bramhall [3] can be used to estimate final moisture content and drying times by changing schedule set points. However, this type of model does not predict drying behavior when process conditions (temperature, air velocity, and relative humidity) are outside of the range for which the experiments were carried out.

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“…In [6], a simplified model based on the conservation of mass and energy using constant parameters obtained by comparing experimental data and numerical results for the drying of a block of beech wood was reported. While the model presented in [7] used the full set of conservation equations and experientially determined physical parameters.…”

Section: Introductionmentioning

confidence: 99%

A heterogeneous three-dimensional computational model for wood drying

Truscott

Turner

2005

Applied Mathematical Modelling

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An accurate and efficient heterogenous three-dimensional computational model is developed for simulating the drying of wood. The complex macroscopic drying equations comprise a coupled and highly nonlinear system of partial differential equations. Due to the heterogeneous nature of wood, the physical model parameters strongly depend upon the local pore structure of the medium, the wood density variation within growth rings and the local variations in primary and secondary system variables. In order to provide a realistic representation of this behaviour, previously determined parameters derived using sophisticated image analysis methods and homogenisation techniques are used. Results are presented for a first generation virtual board description, where the board material properties vary along the section according to the pith position that defines the radial and tangential directions. These variations are assumed fixed throughout the longitudinal direction. The development of an accurate and efficient computational model requires the consideration of a number of significant numerical issues, including the virtual board description, the mesh design, the discretisation process, accurate flux approximations, and finally the solution of a large, nonlinear system. Each of these issues will be explored in this paper for the case of low temperature drying of softwood. Nomenclature c molar concentration (mol/m 3 ) D b bound liquid diffusivity (m 2 /s) D v effective vapour diffusivity (m 2 /s) g gravitational acceleration (m/s 2 ) h enthalpy (J/kg) h heat transfer coefficient (W/m 2 /K) h 0 vap latent heat of vaporisation (J/kg) J e energy flux (J/m 2 /s) J w liquid flux (kg/m 2 /s) K eff effective thermal conductivity (W/m/K) k m mass transfer coefficient (m/s) k w relative liquid permeability K w absolute liquid permeability (m 2 ) M v molecular weight of vapour (kg/mol) n normal vector (m) N number of mesh nodes P c capillary pressure (Pa) P w liquid pressure (Pa) r flux limiter sensor S w liquid saturation (m 3 /m 3 ) t time (s) T temperature (°C) V volume (m 3 ) v w liquid phase velocity (m/s) X moisture content (kg/kg) X average moisture content (kg/kg) X fsp fibre saturation point (kg/kg) x v molar fraction of vapour (mol/mol) Greek symbols Dh w differential heat of sorption (J/kg) dt discrete time step (s) dV CV control volume volume (m 3 ) e g gaseous volume fraction (m 3 /m 3 ) k w liquid mobility (m s/kg) l w liquid dynamic viscosity (kg/m/s) q density (kg/m 3 ) q 0 wood density (kg/m 3 ) r flux limiter function / porosity (m 3 /m 3 ) 382 S.L. Truscott, I.W. Turner / Applied Mathematical Modelling 29 (2005) 381-410

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A Three Dimensional Model for Heat and Mass Transfer in Convective Wood Drying

Cited by 17 publications

References 11 publications

Three-dimensional numerical analysis of water transfer in wood: determination of an expression for the effective mass diffusivity

Three-dimensional numerical analysis of water transfer in wood: determination of an expression for the effective mass diffusivity

A Simulation of Wet Pocket Lumber Drying

A heterogeneous three-dimensional computational model for wood drying

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