Shock waves and second sound in a rigid heat conductor: A critical temperature for NaF and Bi

Abstract

We study shock waves propagating in a rigid heat conductor at low temperature using a generalized Maxwell-Cattaneo equation. The existence of a critical temperature 6, characteristic of the material, for which the structure of the shock changes is proved. When the unperturbed temperature ^o is less than 9 the temperature ^i behind the shock wave front is such that 9\ > 6o (hot shock), and, vice versa, if ao> ^then Oi < OQ {cold shock). We find ^=15.36 K for NaF and (9 = 3.38 K.for Bi. These temperatures are very close to the values at which the second sound was identified experimentally in pure NaF and Bi crystals.

Mixtures of Euler’s fluids and second sound propagation in superfluid helium

“…In [17], [18] it was proved that these functions are determined by where c v (θ) = ε (θ) is the specific heat at constant volume and U E (θ) represents the velocity of small perturbations propagating in an equilibrium state (i.e. with q = 0).…”

“…Using the universal principles of the Extended Thermodynamics [16], Ruggeri and co-workers [17], [18], [19], [20] studied the second sound propagation in crystals introducing a thermal inertia factor in Cattaneo's equation.…”

“…In particular, in the papers [17], [18], it was proved the existence of a critical 568 A. Muracchini, T. Ruggeri and L. Seccia ZAMP temperatureθ, characteristic of the material, such that the shock structure of an initial rectangular heat pulse changes: in fact, if the unperturbed temperature θ o is less thanθ, the temperature θ behind the shock wave front must be such that θ > θ o (hot shock) and, vice versa, if θ o >θ it happens the contrary, i.e. θ < θ o (cold shock).…”

On the influence of damping in hyperbolic equations with parabolic degeneracy

“…The constitutive functions α(ϑ) > 0, g (ϑ) > 0, f (ϑ) < 0 can be derived from measurable equilibrium properties of c V (ϑ), the heat conductivity K(ϑ), and the second sound velocity, U E (ϑ) (see [9], [10], [11] for details). The system (3), (5) has characteristic speeds…”

Phase Transitions and Change of Type in Low-Temperature Heat Propagation

“…Since the system (2.16), (2.17) is quasilinear and hyperbolic (cf. (2.3)-(2.5)), it is possible to account for this decay, but it also becomes possible for shocks to form in finite times [7], [8], [10] in temperatures below ϑ λ . The present analysis examines the situation under which solutions taking values at temperatures on both sides of ϑ λ should remain smooth.…”