13. High up the roof is best.

The exit point for the head of a chimney is another critical factor in its performance. Every effort should be made to locate the terminal high up on the roof in an area where the wind blows across it horizontally.
XXThe ridge of a roof creates turbulence and down-draughts as do dormer windows and other projections. The safest bet is to bring the chimney head out within the top third of the slope.
XXLocating the chimney far down the slope towards the eaves invites surging and blow-back which will vary according to wind speed and direction. To compensate for this it is often necessary to increase the height of the chimney, but due to increased exposure it will then run colder with all the attendent problems noted earlier.
XXIn addition, a tall, exposed chimney sprouting from down around the eaves is an eyesore, and access for cleaning purposes can become a real problem.
XXA shallow-pitch roof creates less turbulence that a steep-pitch roof, making location of the chimney head less critical.