Natural convection occurs in a "stagnant" fluid. Actually the fluid does move, but not by forcing it to move with a pump or fan. All movement in natural convection occurs because of buoyancy forces due to temperature induced density gradients. You may have heard that "hot air rises." That's what we're talking about.

The small fluid velocities in natural convection lead to much smaller heat transfer rates than in forced convection. Furthermore, since it's tough to change the density of a liquid with temperature changes, natural convection is much more common in gases than in liquids.