Two classes of methods exist to measure the thermal conductivity of a sample: steady-state and non-steady-state methods.

[edit] Steady-state methods

(In Geology/Geophysics) The most common method for consolidated rock samples is the Divided Bar. There are various modifications to these devices depending on the temperatures and pressures needed as well as sample sizes. A sample of unknown conductivity is placed between two samples of known conductivity (usually brass plates). The setup is usually vertical with the hot brass plate at the top, the sample in between then the cold brass plate at the bottom. Heat is supplied at the top and made to move downwards to stop any convection within the sample. Measurements are taken after the sample has attained equilibrium (same heat over entire sample), this usually takes about 10 minutes.

[edit] Transient methods

Non-steady-state methods to measure the thermal conductivity do not require the signal to obtain a constant value. Instead, the signal is studied as a function of time. The advantage of these methods are that they can in general be performed more quickly, since there is no need to wait for a steady-state situation. The disadvantage is that the mathematical analysis of the data is in general more difficult.

[edit] Transient plane source method

Example of probe used for transient plane source measurements. Photo shows a Hotdisk sensor

Transient Plane Source Method is also called the Hot disk method. A plane sensor, a special mathematical model describing the heat conductivity, combined with precise electronics, enables the method to be used to measure Thermal Transport Properties. It covers a thermal conductivity range of 4-5 orders of magnitude and can be used for measuring various kinds of materials, such as solids, powder, liquid, paste and thin films etc. In 2008 it was approved as an ISO-standard for measuring thermal transport properties of polymers (November 2008).

The method was developed by Dr Silas Gustavsson at Chalmers University of technology, Sweden, and is sometimes referred to as ”the Gustavsson Probe”.

The probe is a flat sensor with a continuous double spiral of electrically conducting nickel (Ni) metal etched out of thin foil and clad between two layers of Kapton. The thin Kapton provides electrical insulation and mechanical stability to the sensor. The sensor is placed between the surfaces of two sample pieces of the sample to be measured. During the measurement a current passes through the nickel and creates an increase in temperature. The heat generated dissipates through the sample on either side of the sensor at a rate depending on the thermal transport characteristics of the material. By recording temperature vs. time response in the sensor, the characteristics of the material can be calculated.

[edit] Modified Transient Plane Source (MTPS) Method

A variation of the above method is the Modified Transient Plane Source Method (MTPS) developed by Nancy Mathis of the University of New Brunswick and commercialized through her company Mathis Instruments Ltd (now C-Therm Technologies Ltd.). The device uses a one-sided, interfacial, heat reflectance sensor that applies a momentary, constant heat source to the sample. The difference between this method and traditional transient plane source technique described above is that the heating element is supported on a backing, which provides mechanical support, electrical insulation and thermal insulation. This modification provides a one-sided interfacial measurement in offering maximum flexibility in testing liquids, powders, pastes and solids.

[edit] Transient line source method

Series of needle probes used for transient line source measurements. Photo shows, from left to right, models TP02, TP08, a ballpoint for purposes of size comparison, TP03 and TP09

The physical model behind this method is the infinite line source with constant power per unit length. The temperature profile T(t,r) at a distance r at time t is as follows

where

Q is the power per unit length, in [W·m^-1]

k is the thermal conductivity of the sample, in [W·m^-1·K^-1]

Ei(x) is the exponential integral, a transcendent mathematical function

r is the radial distance to the line source

a is the thermal diffusivity, in [m²·s^-1]

t is the amount of time that has passed since heating has started, in [s]

When performing an experiment, one measures the temperature at a point at fixed distance, and follows that temperature in time. For large times, the exponential integral can be approximated by making use of the following relation

Ei(x) = − γ − ln(x) + O(x)

where

is the Euler gamma constant

This leads to the following expression