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Influence of temperature in a mass transfer simulation: application to wood

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Abstract

For in situ timber structure applications, heat and mass transfer are strongly dependent on temperature. This work focuses on a parametrical modeling to evaluate and quantify temperature effect at each stage. The model is classically based on a coupling between Fourier's law, which establishes the temporal and spatial distribution of temperature, and Fick's law dealing specifically with the water field distribution. Several hypotheses are proposed and discussed in this work regarding thermal coupling. In particular, it is shown how to integrate temperature into a permeability correction. An interaction between temperature and the sorption isotherm is also proposed herein. The model incorporates partial adsorption and desorption isotherms. Implementation in a finite element software allows highlighting the various couplings, in comparison with more standard calculus approaches.

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Abbreviations

A, B, β :

Fitting parameters of water capacity, dimensionless

A a :

Fitting parameter of ∆Hs in adsorption, in J kg−1

A d :

Fitting parameter of ∆Hs in desorption, in J kg−1

C W :

Heat capacity of water, in J kg−1 K−1

C h :

Homogenized heat capacity, in J kg−1 K−1

C anh :

Dry heat capacity, in J kg−1 K−1

C pv :

Heat capacity of vapor, in J kg−1 K−1

D T :

Heat transfer tensor, in m2 s−1

D W :

Moisture transfer tensor, in m2 s−1

D WT :

Hygrothermal coupling tensor (Soret’s effect), in m2 s−1

D TW :

Thermo-hydric coupling tensor, in m2 s−1

E a :

Activation energy, in J kg−1

h T :

Convective heat transfer coefficient, in W m−2 K−1

h W :

Convective moisture transfer coefficient, in s m−1

H s :

Sorption latent heat, in kJ kg−1

∆Hs :

Latent heat of sorption of bound water, in kJ kg−1

L :

Latent heat of free water vaporization, in kJ kg−1

m W :

Wet mass, in kg

m anh :

Dry mass, in kg

RH:

Relative humidity, dimensionless

∆RH:

Incremental variation of relative humidity, dimensionless

RHamb :

Ambient air relative humidity, dimensionless

RHsurf :

Equivalent surface relative humidity, dimensionless

p v :

Vapor pressure, in Pa

p vs :

Saturated vapor pressure, in Pa

R :

Ideal gas law constant, in J mol−1 K−1

T :

Temperature field, in K

T amb :

Ambient air temperature, in K

T surf :

Surface temperature, in K

W :

Moisture content field, dimensionless

wi, wi+1 :

Incremental moisture content field, dimensionless

w s :

Moisture content at the fiber saturation point, dimensionless

w a :

Moisture content field at the end of adsorption, dimensionless

w d :

Moisture content field at the end of desorption, dimensionless

δ:

Vapor permeability, in kg s−1 m−1 Pa−1

δ* :

Apparent vapor permeability, in kg s−1 m−1 Pa−1

δo :

Vapor permeability fitting parameter, in kg s−1 m−1 Pa−1

λ (w):

Thermal conductivity of the wet material, in W m−1 K−1

ξ:

Water capacity, dimensionless

ξab :

Water envelope capacity in adsorption, dimensionless

ξdb :

Water envelope capacity in desorption, dimensionless

ξa :

Partial water capacity in adsorption, dimensionless

ξd :

Partial water capacity in desorption, dimensionless

ρ h :

Wet density, in kg m−3

ρ anh :

Dry density, in kg m−3

ϕa, αa :

Thermodynamic parameters for adsorption, dimensionless

ϕd, αd :

Thermodynamic parameters for desorption, dimensionless

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Acknowledgements

This work has been funded by the French National Research Agency (ANR) through EFEUR5 project (ANR‐15‐CE08‐0027) concerning Structural behavior of French Hardwood for better optimization with Eurocode 5. The authors would like to express their appreciation towards the ANR financial support.

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Authors and Affiliations

  1. GC2D, EA 3178, Université de Limoges, Egletons, France

    Maximin Varnier, Nicolas Sauvat, Laurent Ulmet & Frédéric Dubois

  2. LMGC, Université de Montpellier, CNRS, Montpellier, France

    Cédric Montero

  3. Université de Clermont-Auvergne, CNRS, Sigma Clermont, Institut Pascal, Clermont-Ferrand, France

    Joseph Gril

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  1. Maximin Varnier
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  2. Nicolas Sauvat
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  3. Laurent Ulmet
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  4. Cédric Montero
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  5. Frédéric Dubois
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  6. Joseph Gril
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Correspondence to Nicolas Sauvat.

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Varnier, M., Sauvat, N., Ulmet, L. et al. Influence of temperature in a mass transfer simulation: application to wood. Wood Sci Technol 54, 943–962 (2020). https://doi.org/10.1007/s00226-020-01197-y

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