Extension of the hot wire method to the characterization of stratified soils with multiple temperature analysis

Figures & data

Figure 1 Two-dimensional conduction in an heterogeneous medium with one-dimensional varying thermal properties.

Figure 2 Schematic diagram of the heat transfer system and boundary conditions.

Figure 3 Schematic diagram of the sensitivity analysis problem.

Table I Parameters of the sensitivity problem

Thermal properties	Heat flux	Geometry
k1 = 0.16 W m^−1 K^−1	ϕ = 0.3 W	e = 0.1 m
ρC1 = 1.46 MJ m^−3 K^−1		rc = 1.5 × 10^−3 m
k2 = 0.6 W m^−1 K^−1		rr = 2.1 × 10^−3 m
ρC2 = 4.18 MJ m^−3 K^−1
λc = 0.12 W m^−1 K^−1
ρCc = 1.25 MJ m^−3 K^1
λr = 0.2 W m^1 K^−1
ρCr = 1.6 MJ m^−3 K^−1

Figure 4 Sensitivity of temperatures T_i, i = 1, N to the thermal conductivity of layer i = 6.

Figure 5 Sensitivity of temperatures T_i, i = 1, N to the specific heat of layer i = 6.

Table II Thermophysical properties of the media

Medium 1 (CMC-gel)	Medium 2 (semolina)
k = 593 mW m^−1 K^−1	k = 130 mW m^−1 K^−1
ρC = 4 × 10^6 J m^−3 K^−1	ρC = 1.05 × 10^6 J m^−3 K^−1

Figure 6 Experimental temperature history vs. natural logarithm of time.

Figure 7 Thermal conductivity profile (real and estimated).

Table

a	thermal diffusivity
A, B, C, D	generalized quadripole matrices
e	sample thickness
I0, I1	modified Bessel functions of first kind of order 0 and 1 respectively
K0, K1	modified Bessel functions of second kind of order 0 and 1 respectively
k	thermal conductivity
l	length of probe
N	number of mesh
P, P^−1	eigenvectors matrix
rc	radius of central cylinder
rr	global radius of probe
R	contact resistance
R	contact resistance matrix
s	laplace variable
t	time
T	temperature
ρC	specific heat
(---485----9)	laplace temperature
(---485----10)	laplace temperature vector
Δz	distance between nodes
ϕ	heat flux in the r direction
ϕ	heat flux density in the z direction
(---485----11)	laplace heat flux
(---485----12)	laplace heat flux vector
Ω	diagonal eigenvalues matrix