Abstract
Preliminary investigations have been conducted to discuss the possibility of measuring the thermal conductivity of hydrogen gas by the three-omega method. A one-dimensional analytical solution for the 3ω component is derived which includes the effect of the wire heat capacity. It is shown that it is very important to take into account the wire heat capacity in the calculation to measure the thermal conductivity of gas by the three-omega method. In contrast, the wire heat capacity is less important for the thermal conductivity of the liquid or solid phase. The importance of the wire heat capacity is found to increase with increasing frequency and decrease if the sample thermal conductivity is high. In order to measure the thermal conductivity of hydrogen gas at atmospheric pressure, a wire of diameter less than 1μm is necessary if the properties of the wire are to be neglected.
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Abbreviations
- A j :
-
Empirically determined accommodation coefficient
- C p :
-
Heat capacity at constant pressure
- f :
-
Frequency
- I o :
-
Magnitude of the oscillating current
- I 0 :
-
Modified Bessel function of 0th order
- k :
-
Boltzmann’s constant
- K 0 :
-
Modified Bessel function of 0th order
- K j :
-
The temperature-jump coefficient
- K v :
-
Modified Bessel function of v-th order
- l :
-
Length of the wire
- l mfp :
-
Mean free path
- P :
-
Pressure
- Pr :
-
Prandtl number for the gas
- r o :
-
Radius of the wire
- r :
-
r-axis
- R T :
-
Resistance of the wire at temperature T
- R T0 :
-
Resistance of the wire at temperature T at zero heating
- R 0C :
-
Resistance of wire at 0 °C
- t :
-
Time
- T :
-
Temperature
- T 0 :
-
Initial temperature of the bath ( °C)
- V :
-
Voltage
- W :
-
Power
- X :
-
Magnitude of 3ω voltage of in-phase component
- Y :
-
Magnitude of 3ω voltage of out-of-phase component
- z :
-
z-axis
- α :
-
Thermal diffusivity
- σ :
-
Effective collision cross section
- β :
-
Temperature coefficient
- γ c :
-
The ratio of the constant-pressure specific heat to the constant-volume specific heat
- λ :
-
Thermal conductivity
- ρ :
-
Density
- ω :
-
Phase frequency (2π f )
- fg:
-
Function generator
- j:
-
Temperature jump effect
- ref:
-
Reference
- w:
-
Properties of the wire
- s:
-
Sample
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Yusibani, E., Woodfield, P.L., Fujii, M. et al. Application of the Three-Omega Method to Measurement of Thermal Conductivity and Thermal Diffusivity of Hydrogen Gas. Int J Thermophys 30, 397–415 (2009). https://doi.org/10.1007/s10765-009-0563-9
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DOI: https://doi.org/10.1007/s10765-009-0563-9