What does "nonlocal heat transfer" mean?

Question

I was reading some articles about heat transfer and I found that is quite common to use the term "nonlocal" when refering to an "improved" heat equation, for example: http://www.sciencedirect.com.are.uab.cat/science/article/pii/S0375960107015745

"Title: Nonlocal heat transfer in nanostructures"

"Abstract: Kinetics of electrons in a degenerate conductor heated up by absorption of a high-frequency field localized in a region of about hundred nanometers has been studied. A new law for nonlocal electron thermal flux has been predicted."

What do they refer with nonlocal heat transfer? What is nonlocal?

Thank you very much!

Answer 1

Non-local heat flow means that the heat flow at a given point in the system can't be calculated from the local physical conditions at that point, instead you have to take into account the physical conditions of a larger (or possibly entire) part of the system.

Classical diffusive heat flow gives us a heat flux in terms of the locally calculated thermal conductivity and local temperature gradient: $q=-\kappa \nabla T$. If the heat flow is non-local, it just means, the local quantities are not enough information for you to find $q$.

Physically, one reason for the breakdown of the diffusive approximation (i.e. classical local heat flow) is that the particles that carry the heat have a large mean-free-path (larger than or comparable to the scale-length of the temperature gradient).