Near-field Heat Radiation & Transfer
Emission from a single object (Sphere or Cylinder):
Emission is proportional to volume for small objects, crossing over to surface proportionality.
Emission from a cylinder is polarized (also switching as a function of size)
"Polarized light emission from individual incandescent carbon nanotubes,"
S. B. Singer, Matthew Mecklenburg, E. R. White, and B. C. Regan, Phys. Rev. B. 83, 233404 (2011)
"Thermalization of Heat radiation of an Individual Object Thinner than the Thermal Wavelength,"
C. Wuttke and A. Rauschenbeutel, Phys. Rev. Lett. 111, 024301 (2013)
Heat Transfer from a plate to a sphere (and other objects at proximity):
Breaking the law, at the nanoscale (MIT news, July 29, 2009)
Due to its "divergence" heat transfer is dominated by points of close proximity.
A "Proximity Transfer Approximation (PTA)" with "gradient correction" can by used to compute results for arbitrary smooth shapes at close proximity.
"Small distance expansion for radiative heat transfer between curved objects,"
V.A. Golyk, M. Kruger, A.P. McCauley, M. Kardar, EuroPhys. Lett.101, 34002 (2013)