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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