Like any manufacturing process, FDM comes with its own unique strengths and weaknesses. Specifically, certain geometric features require support structures to print successfully. By manually modeling in support structures in specific regions, designers can exert much more control over the support process than is typically afforded by algorithmic support techniques available in most consumer level slicers.
See below for a method to manually model support structures.
Answered with a tutorial: https://grabcad.com/tutorials/how-to-design-your-own-support-structures-for-fdm-printing
When - in Step 5 - you made a shell of your proposed support the problem of features dangling overhead returned ... the fins you designed now by itself need support, as does the top wall.