Doug Cobos and Gaylon Campbell
Decagon Devices and Washington State University
PDF of this Case Study
Outline
 Why measure thermal properties of materials
 Thermal properties definitions
 Ranges and behaviour with density, temperature and moisture
 Measurement methods
 Estimating thermal properties
 Thermal properties on Mars
Why Measure Thermal Properties of Materials?
Thermal Properties of soil impact wind power generation.
Interesting soil and geotechnical applications
 Direct
 Thermal resistivity of building materials
 Surface energy balance
 Geothermal (heat pump) exchangers
 Buried power transmission lines
 Burial of high level radioactive waste
 Indirect
 Water content of soil
 Water content of construction materials (concrete)
Steady State Heat Flow: Fourier’s First Law
Steady State Thermal Properties
 Thermal conductivity (k )
Ratio of heat flux density to temperature gradient – measures the amount of heat a material can transmit for a given temperature gradient
 Thermal resistivity (r )
Reciprocal of thermal conductivity – used mainly in buried power cable applications
For soil, conductivity is almost always preferable to resistivity:
 Better statistical properties
 More correct for averaging
 More linear with water content
 A more correct perception of significance
An extreme example
 Assume two materials of equal area, one with a conductivity of 1 and the other with a conductivity of zero. Resistivities would be 1 and infinity.
 Averaging the conductivities would give ½. Averaging resistivities would give infinity.
Transient Thermal Properties
 Volumetric specific heat (C)
Heat required to raise the temperature of unit volume by 1 K (or C): J m^{3} K^{1}
(product of density and mass specific heat)
 Thermal diffusivity (D)
Ratio of conductivity to heat capacity; measure of propagation rate of thermal disturbances: m^{2} s^{1}
Modeling Soil Thermal Properties
Soil is a mixture of solid, liquid (water) and gas (air and water vapour).
The thermal properties of the soil depend on the thermal properties of the constituents, their volume fractions, and how they are mixed.
Thermal properties of constituents

k
W m^{1} K^{1}

R
m K W^{1}

C
MJ m^{3} K^{1}

D
mm^{2} s^{1}

Soil Minerals 
2.5 
0.40 
2.3 
1.09 
Granite 
3 
0.33 
2.2 
1.36 
Quartz 
8.8 
0.11 
2.1 
4.19 
Organic matter 
0.25 
4.00 
2.5 
0.10 
Water 
0.6 
1.67 
4.18 
0.14 
Ice 
2.2 
0.45 
1.9 
1.16 
Air 
0.025 
40.00 
0.001 
20.83 
Calculating volumetric heat capacity
The heat capacity of a mixture of air, water and solids is the sum of the volume fractions, each multiplied by its heat capacity:
where C is heat capacity.
x – volume fraction of the constituent.
s, w, and a refer to solids, water, and air.
Continued, PDF, 61 pages.