Sensitivity coefficients for experimental estimation of interstitial properties during phase change in porous media

Figures & data

Figure 1. Variation of the sensitivity coefficient sq with η and r for Case 1.

Figure 2. Variation of the sensitivity coefficient's sum with η and r for Case 1.

Figure 3. Variation of the sensitivity coefficient st with η and r when (a) τq/τa = 0.5 and (b) τq/τa = 0.8.

Figure 4. Variation of the sensitivity coefficient sq with η and rst + sq for Case 2.

Figure 5. Variation of the sum of sensitivity coefficient's st + sq with η and r for Case 2.

Figure 6. Variation of the sensitivity coefficient st with η and r when (a) τq/τa = 0.5 and (b) τq/τa = 0.8.

Figure 7. Measured phase front location as a function of time for different T0.

Figure 8. Variation of the standard deviation at and near its estimated optimum value of SD = 0.0007474 m as τt or τq changes.

Figure 9. A comparison of the measured and estimated values of dimensionless phase front when (a) T0 = 89.0°C, (b)T0 = 80.3°C, (c) T0 = 71.6°C, and (d) T0 = 64.2°C.

Figure 10. The behavior of experimental data at near LTE condition.

Figure 11. A comparison of the predicted temperature with the experimentally acquired data when T0 = 86°C.

Table

A=	surface area, m^2
A=	correction vector for coefficients
C=	(---595----17) , J m^−3 K^−1
(---595----18) =	mean heat capacitance of materials in pores, J m^−3 K^−1
Cs=	solid heat capacitance, J m^−3 K^−1
D=	deviation vector
ke=	effective thermal conductivity, W m^−1 K^−1
L=	latent heat of fusion, J kg^−1
LTE=	local thermal equilibrium
LTNE=	local thermal non-equilibrium
r=	τ t/τ a
rh=	hydraulic radius
Rc=	contact resistance, m^2 K W^−1
r=	position vector, m
sq=	dimensionless sensitivity coefficient for τq
st=	dimensionless sensitivity coefficient for τt
S=	sensitivity matrix
t=	time, s
Tm=	phase change temperature, K
T0=	surface temperature at x = 0, K
Tp=	mean temperature of pore materials, K
Ts=	solid matrix temperature, K
x, y, z=	coordinates, m
X=	location of the front, m
X*=	(---595----19)
V=	volume, m^3

Table

α=	thermal diffusivity, ke/C, m^2 s^−1
βq=	∂X/∂τq
βt=	∂X/∂τt
ε=	Vf /V
η=	t/τa
θp=	(---595----20)
θs=	(---595----21)
ξ=	(---595----22)
ρ=	density, kg m^−3
τ=	dummy variable
τa=	(---595----23)
τe=	Cs τt /C
τq=	lag time in heat flux, s
τt=	lag time in temperature, s

Table

c=	contact
e=	equivalent
p=	pore
s=	solid