Q:

When is the heat transfer between a solid and fluid conduction or convection?

I know that the heat transfer between solids and liquids occur via both conduction and convection. 
However, I am not sure about the fine line that separates them. For example, what is the mode of heat transfer when a hot piece of steel is put out in the air. Does the wind change the situation?
Or is, for instance, the heat transfer between a hot solid and a cold static liquid, which are in the same container conduction or convection and why?

A:

I will use the term fluid, that refers to both liquid and gas phase.
It is conduction if single fluid particles transport heat via Brownian motion. It is convection if a macro scale movement of fluid particles is involved. Usually both are playing a role, but for smaller differences of fluid and solid temperatures conduction is more important and conversely induced convection is more important in larger temperature differences.
Convection can be induced or forced. Forced convection occurs when for example a fan blows fluid to the solid and induced convection is when the solid for example is so hot compared to the surrounding fluid that the nearest fluid change their density and become more buoyant and start moving up. Then colder fluid converges the solid from around and heat transfer is enhanced due to larger local temperature differences.
Like the comments above mentioned radiation is also important, although it is more important in gases where the conductivity is smaller than in liquids.

