Hi Tom,
RE: #1 below,
https://en.wikipedia.org/wiki/Flux seems to indicate that there are two different usages for "flux":
1) Flux as a surface integral (including E&M). Defined as the surface integral of the vector field. In electrical fields for example, the E-field is the electric flux density, and the surface integral is the total electric flux out of the surface.
2) Transport phenomena (including heat flux). Defined as flow rate of property
per unit area. Since the definition on Wikipedia already includes per unit area, it would make more sense (to me) if this quantity was called "heat flux density" instead of "heat flux". I'm totally confused why in one context (#2) "flux" would be per unit area, and in another context (#1) "flux" would be the total over the entire surface...
I wasn't familiar with Fourier's law before coming across it in the text. I could be totally wrong about all of this
Btw, I think part of the reason why I was initially confused was because I didn't realize that the differential form and the integral form were actually different quantities (i.e. they weren't just different forms for heat flow).
If we figure out the remaining details about heat flux vs. heat flux density, I think the errata could be improved if both the differential and integral forms are shown in the explanation, with proper labels (heat flow vs. heat flux [density???]).