The transfer of heat energy is defined as heat flux, Q. By definition, this is the flow of heat energy through a defined area over a defined time. So, the units for Q are Joules (energy) divided by area (square meters) and time (seconds). Joules/(m^2∙sec). Since power is defined as energy divided by time and 1 Watt is equal to 1 Joule/second, Q can also be expressed as Watts/m^2 .
Fourier’s Law defines the ability of a specific material to transfer heat. It defines the heat flux, Q, through a material in terms of the cross-sectional area through which the heat energy transfer occurs, A, and the temperature gradient over which the transfer occurs, ∆T/∆x:
Q=-κA ∆T/∆x (1)
k is the proportionality constant for this relationship, known as the thermal conductivity. It is a characteristic property of a material. The units of the individual components of Equation (1) can be written out (with Q defined in terms of power):
Watts =κ∙m^2∙K/m (2)
When the units of length are cancelled out, Equation (2) becomes:
Solving for the thermal conductivity, k:
How is Thermal Conductivity Measured?
Unlike other physical properties, thermal conductivity is dependent on many different properties; therefore, the thermal conductivity of the same material can vary under different conditions. This includes the temperature, pressure, humidity, and phase of the material. Therefore, there are many flexible methods to measure thermal conductivity.
The Modified Transient Plane Source (MTPS) technique is a very quick and versatile method. Using MTPS, the thermal conductivity of solids, liquids, and powders can be measured in about 3 seconds. A single sided sensor, the MTPS works by simply placing sample on the sensor, where a small amount of heat is induced. Then, based on correlations, the voltage drop across the sensor is measured and correlated to thermal conductivity.
The Transient Plane Source (TPS) is similar to the MTPS, but offers much more configuration. The TPS allows the user to configure the power level and test times, and boasts a thermal conductivity range from 0.03 to 2000 W/mK. The TPS sensor is ideal for anisotropic materials and thin films, and is available in multiple sizes.
The Transient Line Source (TLS) sensor is a needle probe style sensor. This sensor works by applying being fully submerged in a sample, and applying heat radially into the sample. The temperature is measured at the centre and the end of the needle, and this rate of change is correlated to thermal conductivity. This method is ideal for large powders, soil, gravel, and highly viscous or sticky materials like polymer melts.
For more information on the different ways to measure thermal conductivity, see the additional resources below.
Method selection guide – Ideal for understanding the differences between sensors and their applications
Trident brochure – The Trident Thermal Conductivity Instrument combines all three methods listed to provide the greatest flexibility and configuration to the user
Request a quote – If you believe that thermal conductivity is a necessary property for your work, request a quote and talk with a technical expert on how we can help.