Using a known solution of the potential equation for heat conduction it is possible to determine boundaries which fulfill the boundary conditions. This idea was applied to the heat flow with parallel streamlines, from a line source and from a point source. From the parallel flow, fins have been derived on a plane surface having circular arc flanks. From the line source, fins axially and radially on a cylindrical surface and from a point source fins on a sphere are obtained. The improvement of the heat transfer has been found in these examples to depend only on the surface direction at the base of the fins.