The main purpose of this paper was to investigate an experimental and theoretical analysis of heat and moisture transport behavior in wood during convective drying process. A convective drying cell was used to follow the measurements of the water content of samples subject to hot air flow in longitudinal and transverse moisture transfer of wood. The effects of drying conditions such as drying air temperature, air velocity and ambient relative humidity on the drying characteristics of wood has been investigated. The constants drying and diffusion coefficients of the drying model, which control the drying rate of wood, were determined from fitting the model against the experimental drying curves. Results showed that, drying kinetic behaviour of the longitudinal diffusion is very significant than the transverse one. The moisture content increased with increase in drying air temperature and air velocity but decreased with time. From the curves of moisture flow evolution versus moisture ratio, convective heat and mass transfer coefficients have been evaluated and compared with values obtained from the literature and existing correlations.

1. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print),
ISSN 0976 – 6499(Online) Volume 5, Issue 5, May (2014), pp. 17-29 © IAEME
17
EXPERIMENTAL AND THEORETICAL ANALYSIS OF HEAT AND
MOISTURE TRANSFER DURING CONVECTIVE DRYING OF WOOD
1
Ahmed Khouya, 2
Abdeslam Draoui
1
Assistant professor, Department of Industrial & Electrical Engineering,
National School of Applied Sciences, Tangier, Morocco
2
Professor, Dept. of physics, Faculty of Science and Technology, Tangier, Morocco
ABSTRACT
The main purpose of this paper was to investigate an experimental and theoretical analysis of
heat and moisture transport behavior in wood during convective drying process. A convective drying
cell was used to follow the measurements of the water content of samples subject to hot air flow in
longitudinal and transverse moisture transfer of wood. The effects of drying conditions such as
drying air temperature, air velocity and ambient relative humidity on the drying characteristics of
wood has been investigated. The constants drying and diffusion coefficients of the drying model,
which control the drying rate of wood, were determined from fitting the model against the
experimental drying curves. Results showed that, drying kinetic behaviour of the longitudinal
diffusion is very significant than the transverse one. The moisture content increased with increase in
drying air temperature and air velocity but decreased with time. From the curves of moisture flow
evolution versus moisture ratio, convective heat and mass transfer coefficients have been evaluated
and compared with values obtained from the literature and existing correlations.
Keywords: Convective Heat Transfer, Diffusion Coefficients, Drying, Mass Transfer Coefficients,
Wood.
I. INTRODUCTION
Convective drying process as well as other drying method is used in order to preserve wood
and food product for longer periods by releasing free water molecular presented in the bound cell of
products. Drying process in term of modelling and simulation are based on the analysis of drying rate
function. This function consists of three drying periods: Constant drying rate period, first period and
second falling rate period. Constant drying rate is defined as the period of drying where moisture
removal occurs at the surface by evaporation and the internal moisture transfer is sufficient enough
to maintain the saturated surface, thus the evaporation rate remains constant. In the first falling-rate
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period, the drying rate decreases as the moisture content decreases due to the additional internal
resistance for moisture transfer. The second falling-rate period begins when the partial pressure of
water throughout the material is below the saturation level.
Experimental and theoretical investigations have been conducted to determine the diffusion
coefficients during drying of wood [1], [2], [3]. Mouchot et al., [1] carried out an experimental study
to estimate the diffusion coefficient of Beech wood in unsteady-state conditions. The diffusion
coefficients of water are deduced from the diffusion coefficients of an inert solute (helium) measured
in a diffusion cell, type Wicke and Kallenbach at temperature of 30 °C. They showed that the
diffusion coefficient in the radial direction is larger than the diffusion coefficient in the tangential
direction. Agoua and al., [2] performed an experimental and theoretical approach to estimate the
diffusion coefficient of wood in unsteady-state conditions. The results found that the analytical
solution of diffusion equation taken into account the resistance to mass transfer at surface give more
satisfactory for determining diffusion coefficients of wood. Joseph and al., [3] Have been performed
an experimental study to determine the diffusion coefficients of wood in the radial, tangential and
longitudinal direction. Results found that the longitudinal diffusion coefficient is larger than the
transversal diffusion coefficient and radial coefficient is larger than the tangential one. Joseph and
al., found that the longitudinal diffusion results in the migration of the water content through fibres,
as for the transverse diffusion, it results in the progressive crossing of vessels cellular cavities.
Many investigations on heat and mass transfer coefficients during drying have been devoted
since several decades [4], [5], [6], [7], [8]. Tremblay and al., [4] performed an experimental and
theoretical investigation to determine heat and mass transfer coefficients of wood during drying.
Experiments were carried out on Red pine at drying air temperature of 56 °C, relative humidity of 52
% and air velocity ranged from 1 to 5 m.s-1
. Heat and mass transfer coefficients were determined
from the constant drying period. They showed that the mass and heat transfer coefficients increase
with increasing air velocity. Nabhani and al., [5] carried out an experimental determination of
convective heat and mass transfer coefficients during drying of Red pine sapwood. They showed that
the heat and mass transfer coefficients are constant until the surface moisture content occurs 60%,
and that these coefficients increase with air temperature and air velocity. Yeo [6] estimated the mass
transfer coefficients of Maple, Oak and pine wood at 30 °C using a colorimetric technique. The mass
transfer coefficient calculated ranges from 1,81 x 10-6
to 5,69 x 10-6
m.s-1
. Comparatively few
investigations have been made to determine heat and mass transfer coefficients from the Nusselt
number and Sherwood formula [7]. Salin [7] mentioned that the use of the Lewis analogy is not
appropriate to estimate heat and mass transfer coefficients. Ananias and al., [8] have been used an
overall mass transfer coefficient to predict the drying curves of wood at low-temperature. They
showed that conventional drying curves of Canelo wood may be modelled by a constant mass
transfer coefficient.
A review of literature reveals very little empirical research about the drying kinetic
behaviours of Red pine. Since, the purpose of this paper is to present an experimental and theoretical
analysis of heat and moisture transfer during drying of wood. We analyse the effect of drying
conditions such as drying air temperature, air velocity and ambient relative humidity on moisture
diffusion, heat and mass transfer coefficients during convective drying process of Red pine.
II. MATE RIAL AND MET HOD
Experimental device
The experimental setup is composed of an electric dryer heating element, humidifier and
probes to control temperature and relative humidity (Figure 1). A Software laboratory controls the air
climate conditions with the thermostat which measures the dry and wet bulb temperature in the drying
cell. Dry and wet bulb temperatures were measured using electrical resistance sensors. The dry bulb

3. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print),
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19
temperature can be controlled between 20 to 70 °C, with a standard deviation of 0,5 °C. Ambient
relative humidity of the drying cell ranged from 20 to 80 %. The average standard deviation of the
relative humidity was 5 %. The climatic cell is equipped with a balance of 0,001 g precision.
The wood material used in this work was cut from Red pine (Pinus resinosa). The samples are
obtained in mixed heartwood/sapwood along the same longitudinal and transverse section. Table 1
provides some physico-mechanical data of Red pine.
Figure 1: Schematic representation of the drying cell
Table 1: Physical and mechanical properties of Red pine [9]
Density 504 kg/m3
Volumic shrinkage 14 %
Total tangential shrinkage 8,5 %
Total radial shrinkage 5 %
Rupture stress 47,5 MPa
Elasticity module 11305 MPa
In order to study both longitudinal moisture transfer and transverse moisture diffusion mode
of wood, a layer of marine varnish has been applied to block the moisture transfer on the other faces
of the sample and the hot air stream was set only along the longitudinal direction of specimen (or the
transverse direction). Table 2 reports the experimental tests performed to determine the effect of
drying conditions such as drying air temperature (T), air velocity (V) and ambient relative humidity
(RH), on the drying kinetic of wood. The samples are put into a drying cell in which the temperature
and relative humidity are controlled respectively by a thermostat and a hygrometer. Several tests of
the moisture diffusion were conducted on the cubic samples of dimensions 20 x 20 x 20 mm (Radial
x Tangential x Longitudinal). A water sorption analysis was used in order to estimate the moisture
migration and moisture flow of wood during drying. The amount of release water was determined by
weighing the sample during the drying process. The moisture content X (%) of the samples
is computed as follows:

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20
s
st
M
MM
X
−
= (1)
Where Mt is the weight of sample at time t, and Ms is the dry solid weight.
The dry solid weight is obtained by drying the sample in a heated oven at temperature of 103
°C until constant weight. The equilibrium moisture content of the sample is occurs when the
moisture content of samples does not vary for a constant drying air temperature and relative
humidity.
Table 2: Experimental data conducted to determine the effect of drying conditions on heat and mass
transfer in longitudinal and transverse diffusion of Red pine
Test V (m.s-1
) T(°C) RH (%)
n° 1 1 30 50
n° 2 1 45 70
n° 3 1 60 50
n° 4 1 45 70
n° 5 1 45 35
n° 6 2 45 50
n° 7 0,5 45 50
II.2. Estimation of longitudinal and transverse diffusion coefficients of wood
The mathematical model of moisture diffusion is based on the following assumptions:
- The moisture transfer is in one dimensional;
- The problem considers a sample wood exposed to longitudinal (or transversal) hot flow during
convective drying;
- Moisture transfer is by diffusion only;
- The flow air is laminar;
- The initial moisture content of the sample is uniform,
- The shape of the materiel remains constant and shrinkage is negligible;
- There is a thermal equilibrium between the wood surface and air.
Moisture diffusion, in a slap of thickness e is written in the (ox) referential:






∂
∂
∂
∂
=
∂
∂
x
X
D
xt
X
m (2)
where X is the moisture content (kg water.kg dry solid-1
), t is the drying time, and Dm is the
longitudinal diffusion coefficient (m2
/s) (or transversal diffusion coefficient).
The analytical solution of the equation (2) using appropriate boundary conditions [10]:
∑
∞
=






−−
−
=
−
−
=
1
2
2
2
22
..
.)12(exp.
)12(
18)(
n
m
ei
e
e
tD
n
nXX
XtX
MR
π
π
(3)
where X(t) is the average moisture content, Xe is the equilibrium moisture content and Xi the
initial moisture content of the sample (kg water.kg dry solid-1
).
In many cases the diffusion coefficients of wood estimated by using only the first term (n=1)
of the general solution. Thus (1) can be written as:

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21
).exp(.
.
.exp.
8
2
2
2
tAK
e
tD
MR m
=





−= π
π
(4)
where: 2
8
π
=K ; 2
2
.
e
D
A m
π−= (5)
In order to apply the diffusion equation in our study, we assumed that the measurements of moisture
content X of the sample verified the following expression:
BAtMRLny ii +== )( (6)
where i is the numerous of moisture ratio measurement at time t.
The coefficients A and B are obtained using the simple linear regression method as follow:
∑ ∑
∑ ∑ ∑
= =
= = =
−
−
= N
i
N
i
ii
N
i
N
i
N
i
iiii
ttN
ytytN
A
1 1
22
1 1 1
)(
;
∑ ∑
∑ ∑ ∑∑
= =
= = ==
−
−
= N
i
N
i
ii
N
i
N
i
N
i
iiii
N
i
i
ttN
yttyt
B
1 1
22
1 1 11
2
)(
(7)
where N is the number of measurements during test.
The slope A provides measurement of diffusion coefficient for each experiment and is
calculated by substituting the experimental data into equation (5). The root mean square error
between the experimental and fitting results with the model is as follows:
∑ −×=
N
cal XX
N
RMSE
1
2
exp
1
(8)
where Xcal and Xexp are respectively the theoretical and experimental moisture ratio of wood during
convective drying process.
II.2. Determination of heat and mass transfer coefficients
The moisture content of Red pine is measured by using the gravimetric method. This method
allows recording the mass M of the sample versus drying time. These data are converted to draw the
curve of the drying rate. The moisture flow F is calculated thanks to the experimental data obtained
from the drying rate evolution versus time and the transfer surface S between the steam water and
wood [9]:






−=
dt
dM
S
F
1
(kg.m-2
.s-1
) (9)
where
dt
dM
is the drying rate (kg.s-1
) and S is the transfer surface (m2
)
The moisture ratio is:
ei
e
XX
XX
MR
−
−
= (10)
Xe is the equilibrium moisture content and Xi is the initial moisture content.

6. International Journal of Advanced Research in Engineering and Technology (IJARET), ISSN 0976 – 6480(Print),
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22
Convective heat and mass transfer coefficients are required in any heat and moisture transfer
calculations. Convective heat transfer coefficient is often determined using empirical correlations
based on the measurements of different geometry and flows. Convective heat transfer between a
moving fluid and a surface transfer of materiel can be defined by the following relationship:
vst HFTThQ ∆=−= ∞ .)( (11)
where F is the mass flow (kg.m-2
.s-1
), Q is the heat flow (W.m-2
), ht is the convective heat transfer
coefficient (W.m-2
.°C-1
), Ts is the temperature at surface (°C), T_ is ambient air temperature (°C) and
∆Hv is the differential heat of sorption (J.kg-1
).
Similarly, mass transfer coefficient hm (kg2
.m-2
.s-1
.J-1
) can be described by the following equation:
)( ∞−= ψψ smhF (12)
where ψs is the surface water potential (J.kg-1
) and ψ is the water potential of air-water vapour
mixture (J.kg-1
).
III. RESULTS AND DISCUSSION
Figure 2 shows the effect of drying air temperature on wood behaviour during convective
drying in longitudinal and transverse diffusion. The initial moisture content is equal to 0,7 kg
water.kg dry solid-1
. The ambient relative humidity of drying cell during this test has 50 % with an
air velocity of 1 m.s-1
. The wood samples subjected to drying process are small, mainly, to reduce the
drying time and to reaches rapidly the equilibrium moisture content. The convective hot air caused
evaporation of water in the surface of wood, leads to decreases moisture content and drying time, till
it reached equilibrium water content with the surrounding air. Results showed that the longitudinal
diffusion is larger than transverse one, probably because of the longitudinal contribution of the fibres
in the transport of water [3]. The sample micro-topography obtained with the scanning electron
microscope (figure 3); explain the difference between the longitudinal and the transverse diffusion of
water. The drying kinetic curves show the falling drying rate period controlled by diffusion process
that governs the moisture movement in the bound wood cell. This results show that the drying time
decreased with air temperature, because the drying force between the vapour pressure of air and
surface saturated pressure increased as the drying air temperature increased. In fact, the increase of
the energy supply rate to the product and moisture migration throughout the wood is accelerated. The
drying time was reduced substantially with an increase of drying air temperature from 30 °C to 60
°C. For drying air temperature of 60 °C, only 8 hours were needed to reach the equilibrium moisture
content. For 45 °C, the equilibrium moisture content moisture was obtained after 24 hours of drying.
However, for an air temperature of 30 °C, 24 hours were still sufficient and the drying is completed
when the thermal equilibrium between wood surface and surrounding air is established.
The effect of ambient relative humidity on drying kinetic of Red pine is shown in Figure 4. It
can be noticed that the drying rate decreased as the ambient relative humidity increased from 50 to
70 %. This effect is considered less important than that of the drying air temperature. Figure 5 shows
that the air velocity, affects the drying rate of wood because the surface water potential depend on
the convective heat and mass transfer coefficients which decreased as the air velocity decreased [4].
It is showed that there is an acceleration of the drying process due to the increase of the air velocity
from 0,5 to 2 m.s-1
. This effect is considered, in general, lower than the influence of drying air
temperature.

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Figure 2: Average moisture content versus time: effect of drying air temperature
a) b)
Figure 3: Longitudinal a) and transverse b) micro-topography of Red pine
Figure 4: Average moisture content versus time: effect of ambient relative humidity.

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Figure 5: Average moisture content versus time: effect of air velocities.
Fitting the moisture ratio model has been done with the experimental data of drying at 30, 45
and 60 °C, ambient relative humidity of 35, 50 and 70 % and three level air velocities 0,5, 1 and 2
m.s-1
. Several experiments fitted the drying model in the form of changes in water content versus
time. From equation 6, a plot of ln(MR) versus drying time for various drying air temperature gives a
straight line with intercept =B, and slope =A (Figure 6). It is noted that the slope of straight line
increased as the air temperature increased and the drying times also become shorter as the drying air
temperature is increased.
Table 3 show the diffusion coefficients, drying constants A and B which are deduced after
fitting our model with the experimental results with a root mean square error (RMSE) not exceeding
0,2. The drying constant A was evaluated to estimate the diffusion coefficients using the equation
(5). The drying constant A of the moisture ratio model was calculated from the slopes of drying
curves as shown in figure 6. The drying constant A ranged from – 0,129 to – 0,65 h-1
. Air velocity
and ambient relative humidity also affected the slope of ln(MR) versus drying time; the slop A was
found higher in the high values of air velocity and relative humidity is low. As discussed previously,
the drying times also become shorter as the air flow rate is increased.
Figure 6: ln(MR) versus drying time: effect of drying air temperature

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The longitudinal diffusion coefficient is larger than the transverse diffusion coefficient. The
diffusion coefficients was found higher in the high drying air temperature, because the heat sorption
of bound cell increased as the drying air temperature increased. It was also observed that the
diffusion coefficients range from 1,44 x 10-9
to 7,2 x 10-9
m2
.s-1
under the above drying conditions.
The result has shown that the logarithmic of drying model has strong linear relationship with drying
time. This study confirms the reliability of the simple regression linear method used to estimate the
diffusion coefficient because the values of these coefficients are in good agreement with results
given by Mouchot [1] and Agoua [2] for wood.
Table 3: Constants drying fitting of moisture ratio model and diffusion coefficients of Red pine
Transfer mode T (°C)
RH
(%)
V
(m.s-1
)
A (h-1
) B
Dm x 10-9
(m2
.s-1
)
RMSE
Longitudinal
diffusion
30 50 1 – 0,165 0,14 1,84 0,052
45 50 1 – 0,21 0,02 2,35 0,065
60 50 1 – 0,65 0,1 7,2 0,15
45 70 1 – 0,137 – 0,009 1,53 0,024
45 35 1 – 0,284 – 0,394 3,18 0,17
45 50 0,5 – 0,138 – 0,087 1,54 0,035
45 50 2 – 0,357 – 0,436 4 0,065
Transverse
diffusion
30 50 1 – 0,146 0,22 1,63 0,081
45 50 1 – 0,182 0,164 2,03 0,053
60 50 1 – 0,45 0,45 5,04 0,083
45 70 1 – 0,129 0,08 1,44 0,057
45 35 1 – 0,258 – 0,167 2,88 0,18
45 50 0,5 – 0,13 0,003 1,45 0,028
45 50 2 – 0,344 – 0,082 3,85 0,02
Figures 7 and 8 show the profile of moisture flow versus drying time in longitudinal and
transverse moisture diffusion of Red pine. The moisture flow is calculated from the experimental
data of water content using the equation (9). For each sample the transfer surface is S = 400 mm².
The moisture flow curves were found higher in the high drying air temperature and low ambient
relative humidity. In fact, high drying air temperature and low relative humidity allowing to favorite
the driving force for the water evaporates into the air and get more power for drying.

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Figure 7: Moisture flow versus moisture ratio of longitudinal diffusion
Figure 8: Moisture flow versus moisture ratio of transversal diffusion
When the air velocity was increased, the moisture flow and water evaporation inside the
materiel were considerable. This phenomenon is because of applying more flow rate to the wood
product and increasing in moisture migration and reduces the drying time. These results provide that
the drying air temperature is the main factor affecting the drying rate and reduce the drying time
during the convective drying process of wood.
Table 4 indicates heat and mass transfer coefficients deduced from the maximum moisture
flow data. The difference in water potential between the surface and the surrounding air is used to
determine the convective heat and mass transfer coefficients by substituting the experimental data of
moisture flow into equations (11) and (12).

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Table 4: Heat and mass transfer coefficients calculated on the basis of the moisture flow
Transfer mode T (°C) RH (%)
V
(m.s-1
)
ht
(W.m-2
.°C-1
)
hm x 10-10
(kg2
.m-2
.s-1
.J-1
)
Longitudinal diffusion
30 50 1 4,59 1,83
45 50 1 10,52 5,18
60 50 1 18,06 10,48
45 70 1 10,19 4,35
45 35 1 11,35 8,2
45 50 0,5 6,82 2,86
45 50 2 17,59 8,66
Transverse diffusion
30 50 1 4,45 1,78
45 50 1 7,03 3,46
60 50 1 13,2 7,66
45 70 1 8,38 2,78
45 35 1 9,26 4,77
45 50 0,5 5,35 2,63
45 50 2 10,79 5,31
For similar operating conditions, these values are different and depend on the longitudinal
and transverse moisture diffusion of wood. These values range from 4,45 to 18,04 W.m-2
.°C- 1
for
heat transfer coefficient and from 1,78 x 10-10
to 10,48 x 10-10
Kg2
.m-2
.s-1
.J-1
for mass transfer
coefficient. Both coefficients increase as drying air temperature and air velocity increased.
As discussed previously, several types of researches have been conducted in order to determine heat
and mass transfer coefficients during drying of wood, the difference between these works is the main
driving force used in different version of diffusion models such as moisture potential, water potential
or pressure vapour. The main driving force used in different version of diffusion model is reported in
table 5. Our results are in good agreement with results of Tremblay [4], and Nabhani [5], using the
water potential as driving force. These results demonstrate the feasibility and accuracy of the
approach using the water potential to estimate convective heat and mass transfer coefficients during
drying of wood.
Table 5: Heat and mass transfer coefficients given by some authors for wood
Authors Method Air conditions hm ht
Tremblay [4]
Water potential
T =56 °C,
V =1 to 5 m.s-1
1 to 14 x 10-10
Kg2
.m-2
.s-1
.J-1
5 to 45
W.m-2
.°C-1
Dimensionless
parameters
T =56 °C,
V=1 to 5 m.s-1
8,6 to 13,8 x 10-10
Kg2
.m-2
.s-1
.J-1
23 to 34
W.m-2
.°C-1
Nabhani [5]
Water potential
T =30 to 90 C,
V =2 to 5 m.s-1
7 to 20 x 10-10
Kg2
.m-2
.s-1
.J-1
13 to 25
W.m-2
.°C-1
Dimensionless
parameters
T =30 to 90 °C,
V =2 to 5 m.s-1 0,008 to 0,025 m.s-1 4 to 18
W.m-2
.°C-1
Ananias [8]
Moisture
content
T =40 to 70 °C,
V =2,5 m.s-1 0,012 to 0,021 m.s-1 26 to 44
W.m-2
.°C-1
Thomas [11]
Moisture
potential
T =110 °C
2,5 x 10-6
kg2
.m-2
.s-1
.°M-1 22,5 W.m-2
.°C-1
Sutherland [12] Vapour density
T =90 °C,
V =3 m.s-1 0,02 m.s-1
20,9 W.m-2
.°C-1

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IV. CONCLUSIONS
Experimental and theoretical analysis of heat and moisture transfer during convective drying
of Red pine has been investigated. The curves of moisture content versus drying time shows only the
falling drying rate period and that the longitudinal moisture transfer removes water faster than the
transverse mode. The results has shown that drying time is affected by drying air temperature, air
velocity and ambient relative humidity and that the drying air temperature is the main factor in
controlling the product drying rate. The plot of ln (MR) versus drying time for various drying
conditions gives a straight line relationship with time. The diffusion coefficients have been
determined from the values of the slop A and the longitudinal moisture diffusion coefficient is larger
than the transverse one. From the measurements of moisture flow evolution during drying, heat and
mass transfer coefficients have been determined and compared to results from the literature to
demonstrate the efficiency analysis of the method used to estimate heat and moisture movement
during convective drying of Red pine. However, this method for the estimation of the diffusion
coefficient only assumes a constant diffusion coefficient in longitudinal and transverse direction
throughout the whole drying process. For this further reason, more comprehensive drying conditions,
energy efficiency and design of drying model should be considered to determine the need
for further diagnostic research on drying efficiency of Red pine. Moreover, the influence of drying
method and various sizes of specimen can be studied using this theoretical approach.
REFERENCES
[1] N. Mouchot, A. Wehrer, V. Bucur, A. Zoulalian, Détermination indirecte des coefficients de
diffusion de la vapeur d’eau dans les directions tangentielle et radiale du bois de hêtre, Ann.
For. Sci. 57, 2000, 793 – 801.
[2] E. Agoua, S. Zohoun, P. Perré, A double climatic chamber used to measure the diffusion
coefficient of water in wood in unsteady-state conditions: determination of the best fitting
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