Millisecond Time-Scale Measurements of Heat Transfer to Confined He II

TL;DR

This study investigates millisecond-scale heat transfer dynamics between a confined superfluid helium II and a heater, revealing limitations of steady-state models for rapid transient heating events.

Contribution

It provides experimental data and analysis on transient heat transfer in superfluid helium II at millisecond timescales, highlighting the inadequacy of steady-state models for fast transients.

Findings

Steady-state Kapitza model agrees with measurements during slow heating.

Model fails to predict heater response during fast pulses.

Helium response to power steps matches model, heater response does not.

Abstract

We explore transient heat transfer, on the millisecond time-scale, from a narrow, rectangular stainless steel heater cooled from one side by He II confined to a channel of 120 $\mu$m depth. The helium is isolated from the external bath with the exception of two pin-holes of cross section about 10% that of the channel. We measure the temperatures of both the heater strip and the channel helium during slow-pulse heating that reaches peak power after 9 ms, fast-pulse heating that reaches peak power after 100 $\mu$s, and step heating that reaches steady power after 100 $\mu$s. Using the steady state Kapitza heat transfer expression at the interface between heater and helium, and the Gorter-Mellink heat transfer regime in the helium channel, we obtain excellent agreement between simulation and measurement during the first 5 ms of slow-pulse tests. Using instead the measured helium temperature in the Kapitza expression, we obtain excellent agreement between the simulated and measured heater response during the first 150 ms of slow-pulse tests. The same model fails to explain the fast-pulse transient response of the heater and helium, while it can explain the helium response to a step in applied power but not the heater response. The steady state Kapitza expression may therefore not be applicable to heating events that are over within a single millisecond.