Measuring Thermal Conductivity

Steady state temperature change in methane hydrate at 9.6°C, showing every tenth point of the nearly 900 points used in the linear fit. From this log time plot, thermal conductivity, λ, is calculated from the linear slope, A. The extrapolated linear intercept, B, is used in determining thermal diffusivity (Click for larger image).

If a constant current, I, is supplied to a heater wire with resistance, R, per meter, the heater wire's output per meter, Q, is determined from Q = 2I²R, where the pre-factor 2 accounts for the heater wire being a loop running the length of the needle probe. Following the methodology presented by Blackwell [1954], the heater wire's output causes the temperature change, ΔT, measured within the probe to vary as:

ΔT = A·ln(t) + B,   (1)

where t is the time in seconds since the probe began heating the sample. Eq. 1 is a steady-state relation valid for t»r_p²/κ, where r_p is the probe radius, and κ is the sample's thermal diffusivity. The thermal conductivity, λ, is calculated from the Eq. 1 slope, A:

   (2)

Since λ is determined using a linear fit to several hundred points, the result is fairly stable, with repeat measurements having a scatter of ~1%.