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Convection is a combination of advection and diffusion, where the former is a macroscopic movement of bulk fluid and the latter is a microscopic movement of fluid particles. But often in literature, I see sentences like "The second and third terms of the left-hand side are the energy convected (advection) and the energy transferred (diffusion) by the pyrolysis gases, respectively."

I am confused by this. It seems to suggest that diffusion is separate from convection, when conventionally diffusion is just one form of convection and convection=advection+diffusion. Can someone explain why, often, we see convection and diffusion differentiated in literature?

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Convection and advection both refer to macroscopic motion of fluid. Convection, as it is usually understood, is motion of fluid induced by density difference within the fluid in the presence of gravity. Advection refers to transport of something (pollutant, dye etc.) by macroscopic motion of fluid. However sometimes the two terms are used interchangeably, so all you have remember is that both terms make reference to macroscopic motion of fluid and any transport that may result thereby.

Diffusion on the other hand refers of spreading of something (dye, heat, momentum etc.) by means of molecular motion. This mechanism is operative even when there is no macroscopic motion of fluid (i.e. when the fluid is static).

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