Exact formulas for radiative heat transfer between planar bodies under arbitrary temperature profiles: Modified asymptotics and sign-flip transitions

We derive exact analytical formulas for the radiative heat transfer between parallel slabs separated by vacuum and subject to arbitrary temperature profiles. We show that, depending on the derivatives of the temperature at points close to the slab--vacuum interfaces, the flux can exhibit one of several different asymptotic low-distance (d behaviors, obeying either 1/d^2 1/d or logarithmic power laws, or approaching a constant. Tailoring...