  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. Our findings, particularly the establishment of the
correlation, carry valuable implications for emergent applications that involve
steady inhomogeneous heat transfer in He II systems.
