  Tidal heating is the prime suspect behind Enceladus's south polar heating
anomaly and global subsurface ocean. No model of internal tidal dissipation,
however, can explain at the same time the total heat budget and the focusing of
the energy at the south pole. I study here whether the non-uniform icy shell
thickness can cause the north-south heating asymmetry by redistributing tidal
heating either in the shell or in the core. Starting from the non-uniform tidal
thin shell equations, I compute the volumetric rate, surface flux, and total
power generated by tidal dissipation in shell and core. If the shell is
laterally uniform, the thin shell approach predicts shell dissipation with a
few percent error while the error on core dissipation is negligible. Variations
in shell thickness strongly increase the shell dissipation flux where the shell
is thinner. For a hard shell with long-wavelength variations, the shell
dissipation flux can be predicted by scaling with the inverse local thickness
the flux for a laterally uniform shell. If Enceladus's shell is in conductive
thermal equilibrium with isostatic thickness variations, the nominal shell
dissipation flux at the south pole is about three times its value for a shell
of uniform thickness, which remains negligible compared to the observed flux.
The shell dissipation rate should be ten times higher than nominal in order to
account for the spatial variations of the observed flux. Dissipation in an
unconsolidated core can provide the missing power, but does not generate any
significant heating asymmetry as long as the core is homogeneous. Non-steady
state models, though not investigated here, face similar difficulties in
explaining the asymmetries of tidal heating and shell thickness.
