How does small-scale convection manifest in surface heat flux?

Small-scale convection in the suboceanic mantle, if present, is commonly thought to manifest in surface heat flux, and the steady-state scaling of sublithospheric convection has often been used to interpret heat flow data from old ocean basins. Relations among small-scale convection, surface heat flux, and the steady-state scaling, however, have been vague. A series of transient cooling modeling are conducted here to quantify such relations. Given the strong temperature-dependency of mantle viscosity, results suggest that small-scale convection could take place without noticeably disturbing surface heat flux, and that the use of steady-state scaling may not be warranted for the present-day suboceanic mantle.