Boiling peak heat flux for steady inhomogeneous heat transfer in superfluid He4

Superfluid helium-4 (He II) is a widely adopted coolant in scientific and engineering applications owing to its exceptional heat transfer capabilities. However, boiling can spontaneously occur on a heating surface in He II when the heat flux exceeds a threshold value $q^*$, referred to as the peak heat flux. While the parameter $q^*$ holds paramount importance in the design of He II based cooling systems, extensive research has primarily focused on its behavior in steady homogeneous heat transfer from a flat heating surface. For inhomogeneous heat transfer from curved surfaces, $q^*$ exhibits intricate dependance on parameters such as the He II bath temperature $T_b$, the immersion depth $h$, and the curvature radius $R_0$ of the heating surface. A comprehensive understanding on how $q^*$ depends on these parameters remains elusive. In this paper, we report our systematic study on $q^*$ for steady heat transfer from cylindrical and spherical heaters in He II. We compute $q^*$ for a wide range of parameter combinations $(T_b, h, R_0)$ by solving the He II two-fluid equations of motion. The generated data have allowed us to develop a robust correlation that accurately reproduces $q^*$ for all the parameter combinations we explored. Furthermore, our findings, particularly the establishment of the correlation, carry valuable implications for emergent applications that involve steady inhomogeneous heat transfer in He II systems.