Numerical study on transient heat transfer in forced flow of superfluid helium

Abstract This study presents a two-dimensional numerical investigation of transient heat transfer in forced flow superfluid helium, using Landau’s two-fluid model with Vinen’s vortex density equation. Our program successfully reproduced temperature variations observed in Fuzier’s experiments. Results show superfluid helium exhibiting radial velocity near the heater, creating a “nozzle” effect leading to contraction and flow expansion. After heating stops, this “nozzle” detaches and dissipates downstream. Higher inlet velocity intensifies axial motion and reduces thermal contraction, though the “nozzle” persists downstream. The counterflow mechanism remains active even under forced flow conditions. Post-heating, velocity decreases upstream of the heater while velocity and temperature increase downstream. At 2 m/s inlet velocity and 9.9 W/cm² heating power, normal fluid velocity decreased 12.25% upstream but increased 50% downstream. The superfluid component showed reversed behavior, consistent with momentum conservation. As inlet velocity increases, thermal counterflow effects diminish, reducing velocity variations.