text: The convection-diffusion equation is a particular example of conservation equation. A conservation equation has the general form:
  Where j is the current density term associated to the variable of interest .
  In a convection-diffusion equation, the current density of the quantity  is the sum of two terms:
  * The first, , describes diffusion according to Fick's law. Imagine that  is the concentration of a chemical. When concentration is low somewhere compared to the surrounding areas (e.g. a local minimum of concentration), the substance will diffuse in from the surroundings, so the concentration will increase. Conversely, if concentration is high compared to the surroundings (e.g. a local maximum of concentration), then the substance will diffuse out and the concentration will decrease. The net diffusion is proportional to the Laplacian (or second derivative) of concentration if the diffusivity  is a constant.
  * The second contribution, , describes convection (or advection). For example, in the continuity equation it is present only this term in the current density. Imagine standing on the bank of a river, measuring the waters salinity (amount of salt) each second. Upstream, somebody dumps a bucket of salt into the river. A while later, you would see the salinity suddenly rise, then fall, as the zone of salty water passes by. Thus, the concentration at a given location' can change because of the flow.