Environmental Engineering Reference
In-Depth Information
uur uuur uuur
∂
θ
∂
K
1
⎡
⎤
=∇ ⋅
'
DDT
∇ + ∇ +
θ
⎣
θ
T
⎦
∂
t
∂
z
[10.3]
ur ur
ur
∂
T
∗
⎡
⎤
ρ
c
=∇⋅
λ
∇ +
T
ρ
L D
∇
θ
0
lv
θ
v
⎣
⎦
∂
t
where θ volumetric water content and T temperature are the independent variables,
ρ
0
is the volumetric mass of dry material (i.e. dried in an oven), c is the mass thermal
capacity of the wet material [J/kg.K] and Lv is the latent heat of water vaporization.
Note that if we make the hypothesis of a rock isotherm in space and time, we find
another time (equation [9.28]) in the case of one-dimensional transfer. Nevertheless,
strictly speaking the diffusivity DΘ described the transfer sum in liquid and vapor
phases, transfers that are reduced to the liquid phase as soon as the water contents
reach moderate levels.
Experimental techniques related to water transport in liquid phase and that are
fundamental were described in Chapter 9. Here we propose to briefly describe the
experimental techniques related to thermal and hydric transfers (vapor and liquid
phases) when the simultaneous hypotheses of isothermal and mean to elevated water
content are no longer relevant.
This section aims to present three distinct aspects, taking into account the
specificity of evoked transfers:
- to give bibliographic information related to “the independent variables”;
- to summarize a group of methods and techniques for measuring the values that
appear in [10.3] or close these values and try to classify them;
- to introduce a possible development [CHE 99a] of the association
model/experimentation.
It can be seen that a certain number of references on the metrology of transfer
given later are related to artificial materials (such as concrete), but such information
is applicable to stones. In the end, the only difference in approach is the fact that in
the case of artificial materials it is possible to include sensors when they are flooded
or to leave some
ad hoc
reserved holes.
In a first approach, independent variables (temperature on one hand, water
content, suction or atmospheric relative humidity at the rock-face on the other) and
parameters involved in the expression of physical laws: mass diffusivity, thermal
conductivity, etc., are used.
