Simulation of temperature profiles at the superfluid to normal-fluid interface in helium-4 for prediction of temperature measurement accuracy

The purpose of this work was to model the conditions in a test cell containing normal-fluid and superfluid helium-4 and to predict the accuracy of temperature measurements made on this system in the presence of non-ideal wall materials and probe geometries. A thermal model of helium-4 in the vicinity of its normal-fluid to superfluid transition temperature was used to calculate the temperature profiles within a helium-4 filled experimental test cell. Calculated temperature profiles were used to predict the temperature measurement accuracy which could be expected from a test cell and temperature probe design. The superfluid phase of helium-4 was represented as a highly-conductive, diffusive material to approximate a superconductor of heat. The thermal model included the influences of temperature, heat flux, and hydrostatic pressure on the properties of helium-4. The model was solved for quasi-static temperature profiles using a finite clement method and employing a transformed and expanded temperature scale to allow resolution of nK/cm temperature gradients in the presence of a 2 K absolute temperature.