After reading Wikipedia articles on advection and convection, I still cannot determine whether there is a consensus on a difference between these two terms.
Sometimes, the term convection seems to include advection and diffusion, sometimes not. After all, equations exhibit two different terms for advection and diffusion, and we don't call the sum of them a convective term. When we talk about a convective term, it is indeed the advective term!
It seems:
transport of pollutants in a river by bulk water flow downstream relates to advection
boiling water for pasta relates to convection
Maybe, a conserved property such as energy can be advected, but we only use convection for transport of "ensembles of molecules".
So, is there a difference? Could we figure it out with examples?
Answer
Convection is the movement of a fluid, typically in response to heat.
Advection is the movement of some material dissolved or suspended in the fluid.
So if you have pure water and you heat it you will get convection of the water. You can't have advection because there is nothing dissolved or suspended in the fluid to advect.
If you have silt suspended in the water and heat it then you will get convection of the water and advection of the silt.
If you have silt suspended in the water and the water is just flowing in a river you will get advection of the silt, but you would not normally describe the water movement as convection.
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