Relationship between Force and Heat Flux in the Electric Pulse Heating of a Metal Conductor
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Relationship between Force and Heat Flux in the Electric Pulse Heating of a Metal Conductor A. V. Kostanovskiya, * and M. E. Kostanovskayaa aJoint
Institute for High Temperatures, Russian Academy of Sciences, Moscow, 125412 Russia *e-mail: [email protected] Received March 19, 2020; revised August 5, 2020; accepted September 11, 2020
Abstract—Using experimental data on the electric pulse heating of a niobium wire, we showed for the first time that a linear relationship between the flux and force—the fundamental assumption of the linear regime in thermodynamics—is fulfilled at a rate of temperature change of dT/dτ ≈ 5 × 107 K/s. DOI: 10.1134/S0018151X20050119
INTRODUCTION
the conductor were presented simultaneously in the microsecond range in the only study [4].
The linear regime in thermodynamics has been actively studied from the beginning of the last century to the present, because stationary and nonstationary problems that include a temperature gradient grad(T) or nonstationary problems in the absence of grad(T) are being increasingly implemented in modern technological processes. In theory, the linear regime is defined ambiguously: it is assumed that the hypothesis of local thermodynamic equilibrium is correct; Onsager’s reciprocity relations must be met; the local production of entropy p = F J linearly depends k k k on forces Fk and fluxes Jk; and the linear phenomenological laws in which fluxes linearly depend on the corresponding forces J k = L F (Lkj are phenomj kj j enological coefficients) are fulfilled [1, 2]. Experimental confirmation of the theoretical laws of the linear regime is of fundamental significance. We showed earlier that the linearity between the flux and force in the experiment of electrostatic levitation, in which the spontaneous cooling of a spherical sample of molybdenum in the solid phase occurs (the maximum rate of temperature change in time is dT/dτ ≈ 2 × 103 K/s), is not strictly fulfilled [3].
The goal of this work is to verify that the linear relationship between the flux and force is satisfied at higher values of dT/dτ. To solve this problem, we selected an experiment with electric pulse heating of a niobium sample in which the maximum rate of temperature change is dT/dτ ≈ 5 × 107 K/s [4]. For a long time, the time dependences of the supplied electric power IU = f(τ) (where I is the current and U is the voltage drop between the probes) and the brightness temperature Tbr(τ) of the sample (a multichannel loop oscilloscope was used) upon electric pulse heating of
EXPERIMENTAL The 99.9%-pure niobium sample was a wire with a radius of r = 0.8 mm and a total length of 63.5 mm. The voltage drop U was determined in the central portion of a sample with a length L = 25 mm. The brightness temperature Tbr(τ) of the sample surface was measured with a pyrometer at a wavelength of 0.65 μm; the diameter of the sighting spot was 0.5 mm; and the speed performance of the pyrometer was 1 μs. Using Wien’s displacement law, data on the temperature dependence (linear fun
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