Measuring thermal conductivity in freezing and thawing soil using the soil temperature response to heating

TLDR: In this paper, an approximation of heat flow from a heated cylinder with thermal contact resistance between the cylinder and the surrounding medium is compared to the standard line source approximation, and both are applied to data measured over a one-year period in northern Alaska.

About: This article is published in Cold Regions Science and Technology.The article was published on 2006-06-01 and is currently open access. It has received 78 citations till now. The article focuses on the topics: Thermal diffusivity & Thermal contact conductance.

Figures

Figure 5. Freezing characteristic curve generated using a time domain reflectometry volumetric water content sensor and a temperature sensor proximal to the thermal conductivity sensor discussed here. Data are from a three-year period, 2002-2004, and include three freezing and thawing cycles. Least-square linear fits to the to the data are shown on the graph.

Figure 1. Sensitivities of the radial temperature gradient to the parameters for values b = 8 x 10-5 m, S = 131 J m-1 K-1, q = 1.5 W m-1, k = 0.3 W m-1 K-1, and κ = 2.5 x 10-7 m2 s1, as a function of time since the beginning of heating. χi is defined in the text (equation 20). The left hand axis is for k and κ, the right hand axis for H, b and S. H-1 was set to zero for the other five sensitivities, and to 3000 W K-1 for χH. The units of χi depend on i.

Table 1. Calculated thermal conductivities [W m-1 K-1].

Frequently asked questions

Q1. What are the contributions in this paper?

The authors introduce an approximation of heat flow from a heated cylinder with thermal contact resistance between the cylinder and the surrounding medium. 

Q2. How does the thermal gradient change with time?

The thermal gradient falls very rapidly for high k values and slower for low k values within three seconds of the cessation of heating and approaches zero as time increases. 

Q3. What is the effect of hysteresis on the soil?

Hysteresis affects the water content at temperatures above -10 °C and may be result of at least three processes: solute exclusion from the forming ice increases the concentration of solutes in the remaining liquid water, depressing its freezing point; capillarity and the irregularity of the pore space cause hysteresis in a fashion analogous to that of wetting and drying curves and the soil solution may also super-cool before nucleation (Bittelli et al., 2003). 

Q4. What is the type of soil that is classified as a cryaquept?

Landcover type is classified as moist non-acidic tundra, the soil pedon is classified as a cryaquept and the soil horizons are contorted by cryoturbation (Ping, 1998). 

Q5. How does the thermal conductivity of the soil change over time?

Depending on where the induced temperature gradient and the amount of ice accumulated, the thermal conductivity would be increased over the course of multiple measurements. 

Q6. What is the effect of latent heat effects on thermal conductivity measurements?

Using soil composition data to account for latent heat effects on thermal conductivity measurements leads to convergence of the freezing and thawing arms of the thermal conductivity data, suggesting that the values so obtained represent the actual bulk thermal conductivity of the soil. 

Q7. What is the condition for the simultaneous identification of parameter values from a time series of temperature data?

The condition for the simultaneous identification of parameter values from a time series of temperature data is the linear independence of the sensitivities over the time period (Beck and Arnold, 1977). 

Q8. What is the apparent thermal conductivity of the soil?

The apparent thermal conductivity of the soil shows a roughly bimodal seasonal variation, with lower values in thawed soil than in frozen. 

Q9. How is the temperature gradient created during heating?

Moisture is redistributed away from the heating wire radially by the21temperature gradient created during heating (DeVries and Peck, 1958b). 

Q10. What is the effect of heating on the thermal conductivity of frozen soil?

Thermal conductivity measurements in the frozen soil may also be affected by cumulative migration and freezing of water over multiple measurement cycles at the same position. 

Q11. What is the thermal conductivity of the soil near the freezing point?

The thermal conductivity of the soil close to the freezing point is usually assumed to take values close to those that may be interpolated from the frozen and thawed values at the same total water content (Hinzman et al., 1991). 

Q12. What was the power requirement for frequent measurements?

The power requirements for frequent measurements were met by this system (including a meteorological station with TDR unit), with enough reserve power to continue measuring through the winter darkness. 

Q13. What is the difference between the two approximations?

Both approximations result in slight increases in thermal conductivity with decreasing temperature below –10 °C, corresponding to increases in ice content. 

Q14. What is the difference between a frozen and a thawed soil?

Frozen and thawed soil thermal conductivity values are each very weakly dependent on temperature, primarily as a result of the temperature dependence of the thermal conductivity of water and ice.