 23/27
The values of
(
)
*
,
D
v
Fo s
Bi
f
versus the values of
(
)
*
,
D
v
Fo s
Bi
and Bi are plotted in Figure 13 for
0.5
Bi
=
, s
Bi
=0.3 and
min
5
Bi
=
. For physical consistency, the condition
min
1
Bi
>
ensures in
particular that the mass transfer resistance is higher in P than in F (see Figure 12). The bivariate
probability density function is zero below
min
Bi
and its iso-values exhibit a privileged orientation
along the first bisectrix of axes, which confirms that
*
v values increase with Bi values. The
maximum of probability is obtained close to Fo and Bi .
The combined effects of s
D
and s
Bi
on
(
)
*
0.5,
20,
,
D
h
v
Fo
Bi
s
s
=
=
are compared in Figure 14 by
repeating the analysis performed in Figure 13 for different s
Bi
values. The distributions of Bi
corresponding to the tested s
Bi
values are plotted in Figure 12. Results showed both a small shift
of the maximum of probability on the right and an increasing span of the distribution of *
v . The
first effect is related to the truncation introduced in the distribution of Bi Bi , which moves the
expectation towards values higher than 1 for large s
Bi
values. The second effect is related to the
cumulative effect of uncertainty. For the tested condition
0.5
Fo
=
and
20
Bi
=
, the effect of the
uncertainty on D is higher than the uncertainty of Bi.

5.2.2 Combined effect of s
D
and s
K

The effect of K can be tested similarly by calculating the distribution of
( )
(
)
1
1
1
*
1
*
,
,
,
K
D
K
s
K
L
v
Fo K s
s
K
K
L
-
-
-
-
+
+
, where the prefactor
( )
1
1
1
*
1
K
s
K
L
K
K
L
-
-
-
-
+
+
assess the deviation to
the likely equilibrium concentration in F. It is emphasized that s
K
acts both on the prefactor and
*
v . For the illustration, the distribution of K was chosen as:
(
)
(
)
0,
max
min
,
10
K
Norm
s
K
K
K
(37)
To enforce K values to be lower than 1, K was set to 0.1 and K
max
to 1. Typical values of the
distribution are plotted in Figure 12. As presented in Equation (35), the marginal distribution of
( )
(
)
1
1
1
*
1
*
,
,
,
K
D
K
s
K
L
v
Fo K s
s
K
K
L
-
-
-
-
+
+
was calculated from its conditional distributions for particular
K values and integrated over the whole range of K values.
The results corresponding to
0.5
Fo
=
, L=0.05, Bi=20 and different ranges of s
D
and s
K
values are
plotted in Figure 15. The effect of s
K
is here higher than the effect of s
D
. Increasing s
K
drastic change in K values towards 1 (Figure 12) so that the distributions of
( )
(
)
1
1
1
*
1
*
,
,
,
K
D
K
s
K
L
v
Fo K s
s
K
K
L
-
-
-
-
+
+
obtained for low K values tend to resemble those depicted in
Figure 15 for K=1.