What body part has no function?
The Appendix has no known function.
The dorsal aorta is simply the part of the aorta (which is quite long) going down the body, meaning it has the same function of the aorta of the heart, which is transporting oxygenated red blood cells to the rest of the body. The dorsal aorta is the part of the aorta that does down the body. It transports oxygen rich red blood cells to the rest of the body.
In humans, the largest organ of the body is the skin. Yes, the skin is, in fact, an organ, part of the integumentary system. And the most important function it has can be debated, as there are several. However, most scientist would probably agree that the primary function is to protect the body from various pathogens which would otherwise attack the body.