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

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.