My question has 2 parts:
I just followed the derivation of Navier Stokes (for Control Volume CFD analysis) and was able to understand most parts. However, the book I use (by Versteeg) does not derive it in its entirety. He pulls a lot of results directly from Schlichtling and continues his analysis. I want to understand the derivation in its full form. Is there any resource other than Schlichtling (My library doesn't have it) for deriving the NV equations in their full form? I would prefer an online (free) PDF or similar. (I'm not sure my library would have many books on this including the ones discussed here)
After the derivation, most books follow it up with :
$$\underbrace{\frac{\partial (\rho\phi) }{\partial t}}_{\text{Rate of increase of }\phi} +\underbrace{\text{div}(\rho\phi \vec u)}_{\text{Convective Term}} = \underbrace{\text{div}(\Gamma \text{ grad}(\phi))}_{\text{Diffusive Term}} + \underbrace{S_\phi}_{\text{Source Term}}$$ where $\phi$ is property per unit mass, $\vec u$ is velocity vector and $\Gamma$ is diffusive term (Like viscosity or thermal conductivity).
What I can't understand is the use of the terms "convective" and "diffusive"? What do they mean? What is the physical interpretation of these terms?
Their dictionary meanings seem to exacerbate the situation:
(convection) the transfer of heat through a fluid (liquid or gas) caused by molecular motion.
(diffusion) The spreading of something more widely or the intermingling of substances by the natural movement of their particles