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# Measuring and Modelling Thermal Properties of Porous Materials

Doug Cobos and Gaylon Campbell

Decagon Devices and Washington State University

Outline

• Why measure thermal properties of materials
• Thermal properties definitions
• Ranges and behaviour with density, temperature and moisture
• Measurement methods
• Estimating thermal properties
• Modeling
• Interpolation
• 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 • 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: m2 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 mm2 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.