Thermal Conductivity Measurement
by the Line Heat Source Method

(Technical Note #74)

The constant heat production by a line source of heat enclosed in an infinite volume of material produces a cylindrical temperature field. The temperature rise at any point within the material is:

Initially (i.e. t = 0), the material is supposed to be at a uniform temperature T(0) = 0.
For small values of (i.e. r -> 0), the exponential integral can be approximated as:

The temperature rise becomes:

This is the basic equation of the line heat source method. The temperature of the line heat source is recorded, and the thermal conductivity is obtained from the slope of the plot of temperature rise vs. logarithmic of time:

The experimental plot of T(t) vs. is curved at the upper and lower limits with a linear portion in between. The equation is only valid for points on this linear portion. The lowest curved portion of the graph controls the earliest possible time when the thermal conductivity can be measured. It is due to the heat transfer between heater and test material. The upper curved portion is the result of the heat front reaching the boundaries of the material since the test piece is of finite size. The maximum possible time for the thermal conductivity measurement is therefore dependent on the test-piece geometry and thermal diffusivity.

The temperature variations T(t) are measured with a pure platinum wire, which also acts as the line heat source. The rate of temperature increase of the platinum wire is accurately determined by measuring its increase in resistance R(T) in the same way a platinum resistance thermometer is used:

The thermal conductivity is finally expressed as:

dR(T) / dlnt is the slope of the linear portion of the plot of the resistance of the platinum wire vs. the logarithm of the time.