What is the difference between non-convective entropy flux and convective entropy flux?

your written sources define them somethings like this;

lets denote entropy flux as Ef.

then, convective CEf = C. Ef nonconvective NEf = N. Ef

where C is a parameter (like velocity or its gradients) related to the mass motion. N is a parameter in a case of zero mass motion (in human scale).

for ex., in a conductive heat transfer, you can use NEf as velocity (at human scale) is zero there. In micro scales, all fluxes can be considered as convective as all matters/photons/etc having a mass, hence mass transportation. Ok? No, your books define these differently?