Elbows are not suggested because they reduce the performance of the stove. A straight run up and out the roof is the best practice. 

Single wall 3” elbows will not connect to our pipe like they should and should not be used, as it will cool off the gasses which reduce the draft and increase creosote build up. 

Double wall 3” elbows are made for pellet stoves which are not rated for the same heat that a wood stove produces. They are also the incorrect diameter. Pellet stoves can have elbows in their flue systems because they have fans that push the air through the pipe. Whereas wood stoves rely on convection draft (hot air wanting to rise) which pulls air into the stove. An elbow slows this vertical movement of air that in turn reduces the efficiency of the stove. 

Wall exits are also discouraged. By exiting the stove at a lower point of the structure, more pipe will be outside in the cold which will cool the gasses and reduce the desire to rise. 

Wall exits require multiple elbows, along with the pipe being more in the cold it will dramatically reduce the performance.  

In all circumstances, finding suitable 3” elbows and/or wall exit components will be very difficult or impossible.