Dynamics of vortex line density and heat transfer processes in superfluid helium

Abstract

Three dynamics equations for vortex line density are analyzed. It is shown that the Vinen equation gives the values of vortex tangle development time in the case of a constant counterflow more accurately than other alternative equations. Within the system of equations of superfluid turbulence hydrodynamics, obtained using a phenomenological approach, helium boiling times as a function of heat flux density are found, using alternative dynamics equations of vortex tangle density. Unlike the experiments in which different dependences of boiling time tboil on the heat flux density Q (tboil ∝ Qn, −4 ≤ n ≤ −2) are observed, in this case we get only a power-law dependence with an exponent of n = −4. We obtain a velocity distribution of the normal component along the channel, and the temperature dependence of the time near the heater. We conduct a comparison against the numerical and experimental results that were previously obtained in literature.