Propagation properties of thermal waves and thermal diffusivity in metals

Abstract

By means of an experimental technique which makes use of the so-called modified Angstrom method, the thermal diffusivityD of some noninsulated tantalum, niobium and copper wires has been measured over a certain range of thermal-oscillation frequency, together with the thermal-loss coefficient which takes into account the heat losses through the lateral surface of the specimen by radiation, conduction and convection. The results give for the thermal diffusivity of the three metals values which are independent of frequency and in good agreement with the literature; on the other hand, the thermal-loss coefficient μ has been found to depend upon frequency. The same measurements led to the evaluation of the characteristic propagation parameters of thesethermal waves, such as the phase velocityv, the wave number β and the attenuation coefficient α. The quantityμ0 = 1/2αν, which is also related to the thermal losses, was found to depend on the oscillation frequency according to the linear relationshipμ0 =a +bω; the values of the parametera depend essentially on the physical condition of the surrounding medium, while the parameterb appears as a property of the surface of the specimen itself. For a frequency of 0.01 Hz the phase velocity at room temperature was about 0.22 cm·s−1 for tantalum, 0.18 cm·s−1 for niobium and 0.40 cm·s−1 for copper. By lowering the temperature, the phase velocity increases, its value being proportional to the square root of thermal diffusivity, which seems to play here a role similar to that of an elastic modulus in elastic-wave propagation. The phase velocity depends also upon frequency and the corresponding group velocity is always larger than the former, approaching the limiting value 2v in the high-frequency range. The experimental method appears very reliable and suitable for determining the thermal diffusivity and then the thermal conductivity of solids on a wide range of temperature independently of the thermal losses of the specimen; on the other hand, it gives at the same time the values of the surface thermal conductance, which are rather important in connection with the physical properties of the surface of the specimen. In addition, the measurements carried out at different frequencies may provide interesting and stimulating information about the propagation properties of these thermal waves, behind the particular boundary conditions of the experiment.