I would say that for the current scale mems laplace equation still works fine.
The one I found quite different is radiative transfer. Anyway this is
anticipated as the nature of the radiative heat transfer changes when
dinensions approach the IR wavelength. (few um).

What is the length scale that makes the Fourier's law breakdown in solids ?
This research could result in very interesting engineering solutions. Does it
increase or decrease ?

C. H. Mastrangelo
University of Michigan