Cooling with a subsonic flow of quantum fluid

Abstract: Miniature heaters are immersed in flows of quantum fluid and the efficiency of heat transfer is monitored versus velocity, superfluid fraction and time. The fluid is $<sup>4$He helium with a superfluid fraction varied from 71% down to 0% and an imposed velocity up to 3 m/s, while the characteristic sizes of heaters range from 1.3 $\mu$m up to few hundreds of microns. At low heat fluxes, no velocity dependence is observed. In contrast, some velocity dependence emerges at larger heat flux, as reported previously, and three non-trivial properties of heat transfer are identified. First, at the largest superfluid fraction (71%), a new heat transfer regime appears at non-null velocities and it is typically 10% less conductive than at zero velocity. Second, the velocity dependence of the mean heat transfer is compatible with the square-root dependence observed in classical fluids. Surprisingly, the prefactor to this dependence is maximum for an intermediate superfluid fraction or temperature (around 2 K). Third, the heat transfer time series exhibit highly conductive short-lived events. These \textit{cooling glitches} have a velocity-dependent characteristic time, which manifest itself as a broad and energetic peak in the spectrum of heat transfer time series, in the kHz range. After showing that the velocity dependence can be attributed to the breaking of superfluidity within a thin shell surrounding heaters, an analytical model of forced heat transfer in a quantum flow is developed to account for the properties reported above. We argue that large scale flow patterns must form around the heater, having a size proportional to the heat flux (here two decades larger than the heater diameter) and resulting in a turbulent wake. The observed spectral peaking of heat transfer is quantitatively consistent with the formation of a Von K\'arm\'an vortex street in the wake of a bluff body.