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A relevant and robust vacuum-drying model applied to hardwoods


A robust mathematical model was developed to simulate the heat and mass transfer process that evolves during vacuum-drying of four commercially important Australian native hardwood species. The hardwood species investigated were spotted gum (Corymbia citriodora), blackbutt (Eucalyptus pilularis), jarrah (Eucalyptus marginata), and messmate (Eucalyptus obliqua). These species provide a good test for the model based on their extreme diversity between wood properties and drying characteristics. The model uses boundary condition data from a series of vacuum-drying trials, which were also used to validate predictions. By using measured diffusion coefficient values to calibrate empirical formula, the accuracy of the model was greatly improved. Results of a sensitivity analysis showed that the model outputs provide excellent agreement with experimental observation despite the large range of species behaviour and variation in wood properties. This study confirms that the drying rate is significantly improved as a direct result of the enhanced convective and diffusive transfer along the board thickness. Contrary to softwood, it appears that longitudinal migration provides only a secondary effect. Not only is the model able to predict the heat and mass transfer behaviour of a range of hardwood species, it is also flexible enough to predict the behaviour for both conventional and vacuum-drying scenarios. The outcomes of this work provide the hardwood industry with a well-calibrated predictive drying tool that can be used to optimise drying schedules.

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c p :

Specific heat (J kg−1 K−1)

c :

Molar concentration (mol m−3)

\(\overline{{{\overline{\mathbf{D}}}}}\) :

Diffusivity tensor (m2 s−1)


Fibre saturation point

g :

Gravitational acceleration (m s−2)

h :

Specific enthalpy (J kg−1)

h :

Heat transfer coefficient (W m−2 K−1)

J :

Flux expression

K :

Intrinsic permeability (m2)

\(\overline{{{\overline{\mathbf{K}}}}}\) :

Absolute permeability tensor (m2)

\(\overline{{{\overline{\mathbf{k}}}}}\) :

Relative permeability tensor

k :

Boltzmann’s constant

k a :

Air permeability (m2)

k m :

Mass transfer coefficient (m s−1)

k r :

Relative permeability

L :

Characteristic length (m)

M :

Molecular weight (kg mol−1)


Moisture content

ΔP :

Pressure difference (Pa)

\(\bar{P}\) :

Average pressure (Pa)

P :

Pressure (Pa)


External heat transfer coefficient (W m−2 °C−1)

R :

Gas constant (J mol−1 K−1)

S :

Volume saturation

t :

Time (s)

T :

Temperature (K)

v :

Mass velocity vector (m s−1)


Poisson’s ratio

V g :

Green volume (m3)

x :

Molar fraction (mol/mol)

X :

Moisture content (dry basis) (kg kg−1)

ε :

Volume fraction


Thermal conductivity (W m−1 K−1)

ρ :

Intrinsic averaged density (kg m−2)

ρ 0 :

Wood density (kg m−2)


Surface tension (N m−1)


Surface tension at temperature T (N m−1)


Dynamic viscosity of air (Pa s)

φ :

Phase potential

ϕ :

Porosity (m3 m−3)

χ :

Depth scalar (m)


Mass fraction

a :


b :


c :


e :



Effective property


Fibre saturation point

g :

Gas phase

l :


s :

Solid phase

v :

Vapour phase

ν :

Vapour phase at boundary

w :

Liquid phase


Value outside the boundary layer in the free stream


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The substantial contributions of CentraleSupelec, Université Paris-Saclay, Queensland University of Technology (QUT), Forest and Wood Products Australia (FWPA) and the Queensland Government Department of Agriculture and Fisheries (DAF), to the undertaking of this collaborative project are gratefully acknowledged. Authors Turner and Carr wish to acknowledge that this research was partially supported by the Australian Research Council (ARC) via the Discovery Project DP150103675 and DECRA project DE150101137, respectively. Thank you to the reviewers for their comments and suggestions that led to an improved final version of the paper.

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Correspondence to Adam L. Redman.

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Redman, A.L., Bailleres, H., Perré, P. et al. A relevant and robust vacuum-drying model applied to hardwoods. Wood Sci Technol 51, 701–719 (2017).

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  • Moisture Content
  • Wood Property
  • Hardwood Species
  • Fibre Saturation Point
  • Average Moisture Content