Proceedings e report - Firenze University Press

WOOD SCIENCE FOR CONSERVATION OF CULTURAL HERITAGE
In order to link all these equations, conservation laws can be used. Since phase transitions are
involved, conservation of enthalpy gives
∂H
= −∇
q + Sh
(5).
∂t
Inserting terms results in
∂H
= ∇(
λ ∇ϑ)
+ hv
∇(
δ p∇(
ϕ psat
))
(6),
∂t
dH ∂ϑ
= ∇(
λ ∇ϑ)
+ hv
∇(
δ p∇(
ϕ psat
))
(7),
dϑ
∂t
and
∂ϑ
1
= [ ∇(
λ ∇ϑ)
+ hv
∇(
δ p∇(
ϕ psat
)) ]
(8)
∂t
Cρ
using the definitions of specific heat C [J/kg·K] and density ρ [kg/m 3 ]. On the other hand, using
conservation of mass one can write
∂w
= −∇(
gw
+ gv
) + Sw
(9)
∂t
where Sw [kg/m 3 ·s] describes a possible mass source (e. g., a water leak). Inserting (3) and (4) one
obtains
∂w
= ∇(
Dϕ∇ϕ
+ δ p∇(
ϕ psat
))
(10).
∂t
Observing that dw/dϕ is a material property describing the so-called sorption isothermal lines we
obtain
−1
∂ϕ
⎛ dw ⎞
= ⎜ ⎟ [ ∇(
Dϕ∇ϕ
+ δ p∇(
ϕ psat
)) ]
(11).
∂t
⎝ dϕ
⎠
With equations (8) and (11) we now have two equations for temperature and humidity, respectively,
which are coupled by the last term in (10) and also by the fact that many of the material properties
depend on temperature or moisture. Consequently, the equations have to be solved numerically. The
WKI has developed a software called TUN which can solve the equations in two dimensions by the
finite difference method. Work is under way to include the equations in a commercial finite element
code.
A typical application is the analysis of the moisture behaviour of a wood panel wall with brickwork
curtain as shown in Fig. 6 The question was whether the water repellent layer is really necessary. A
typical summer climate for central Europe was taken as the boundary conditions (Fig. 7 left). The
resulting moistures for selected parts of a construction without water repellent layer are displayed in
the right part of Fig. 7The result is that the moisture at the front side of the first particle board
(approximately. 20%) is too high, and that the moisture gradient over the first particle board is to high
as well leading to the risk of unacceptable distortion. Consequently it is indeed necessary to keep the
water repellent layer or to change the properties of the particle board.
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