Environmental Engineering Reference
In-Depth Information
∂
T
λ
∗
ρ
c
=∆
T
[10.5]
0
∂
t
which is a heat equation. If we include the geometry of the problem and time
scale considered, it is possible to deduce, from analysis of the response to a
perturbation of rung or slot type, one or other of the following thermophysic
properties: conductivity λ*, volumetric heat ρ
0c
, diffusivity α = λ*/ ρ
0c
, or effusivity
b = (λ* ρ
0c
)
1/2
.
Here are a few possible techniques by which to induce perturbation:
- metallic thread stuck on the surface of the material and used as a sensor and
generator of thermal flux by the Joule effect [PRE 84];
- the same as above, but with ribbons [GUS 82] or planar heating films applied
to the surface of the plate [BAS 87];
- use of heating tubes, whether associated with other heating tubes or not [LAU
89].
Dealing briefly with the planar film method, if we heat one face of a plate of
rock of thickness
e
with a film delivering power
J
q
(in W/cm
2
) from time
t
= 0. The
unity film-plate is put between two thick isolating plates. Thermocouples enable us
to measure the temperatures of both rock plate faces (heated and not heated).
Resolution of [10.5] applied to this configuration provides the theoretical evolutions
of temperatures
T
h
and
T
nh
of both faces.
2
2
J
3
e
q
t
< ⇒ =
T
[10.6]
c
2
b
π
a
⎧
⎡
⎤
t
e
TJ
=
−
⎪
⎢
⎥
c
q
2
∗
ρ
ce
3
e
3
λ
⎪
⎣
⎦
0
t
> ⇒
⎨
[10.7]
2
a
π
⎡
t
e
⎤
⎪
TJ
=
−
⎢
⎥
⎪
nc
q
∗
ρ
ce
6
λ
⎩
⎣
⎦
0
As the experimental temperature changes are in accordance with theoretical
forecasts, it is possible to deduce the values of λ*, ρ
0c
, α and
b
(the study by
“anamorphosis”, for example, of
T
c
as a function of
t
1/2 leads to the value of
effusivity
b
[J/s
1/2
.m
2
.K]).
It has to be noted that such a method of the hot thread is adaptable to an
anisotropic rock [SU 91].
