background image
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by
( )
g Fo . It is highlighted that, due mass balance limitations, the transformation that relates Fo
to
*
v
is not affine and, in particular, that an apparent large discrepancy in Fo values (for
significantly large Fo values) does not generate a large dispersion in
*
v
values.
The same approach is applied for different Bi values in Figure 11. It shows that the distribution
of
*
v
is dependent on the slope of
*
v
with Fo. The results cannot however be used to assess the
combined effects on the uncertainty of Fo and Bi. Indeed, in case of doubt on the true Bi value,
Figure 11 generates two distinct distribution of
*
v
, as an example, for a lower value of Bi (e.g.
10
Bi
=
) and an upper value of Bi (e.g.
100
Bi
=
). Since the conditional distributions of
10
*
Bi
v
=
and
100
*
Bi
v
=
have equal weight, the span between extreme predictions are maximized and
no reliable statistics can be derived. This discrepancy is all the higher than the overlapping
regions between conditional distributions are smaller. The next paragraph examines how to
account for both sources of uncertainties in an efficiently manner.
5.2 Estimations of coupled sources of uncertainty in transport
properties

The uncertainty in transport properties D
P
, K, and h
F
is related to experimental errors when their
values are experimentally assessed, to systematic errors when they are predicted by models, to
uncontrolled changes in temperature, to physical simplifications, to other uncontrolled sources of
variation (e.g. process conditions, food properties...). When uncertainty does not seem to exist, it
may be appropriate to include some to improve the robustness of the predictions. This paragraph
analyzes how to combine them.

The examples are based on arbitrary distributions of Fo, Bi and K that are plotted in Figure 12.
5.2.1 Combined effect of s
D
and s
h
5.2.1.1
Interest
Accounting for the uncertainty in h
F
, denoted s
h
, is a particularly interesting feature, since few
values of h
F
values are available in the literature and the physical definition of h
F
may change
according to the simulated conditions. Indeed, from the physical point of view, h
F
as defined in
section 3.2.2 via Equation (10), is a "true" mass transport property only when the food product is
a liquid and stirred. In this situation, the bulk concentration in food as measured, C
F
, is an
appropriate estimate of the concentration far from the interface, and h
F
, which is related to the
mass transfer resistance through the boundary layer, can be assessed independently of the dilution
factor L. When the food is a solid or a semi-liquid or when the volume of the boundary layer is
comparable to the bulk volume, the previous approximation is no more valid and the physical
meaning of h
F
is changed. It is an equivalent transport property, whose value depends on the
considered geometry. Practically, its use is however appropriate the addition of an artificial mass
transport resistance at the interface, R
H
, prevents to simulate the mass transport within the food
product in contact. In other words, when the parameter h
F
or its counterpart, the mass Biot