Anomalous near-field heat transfer between a cylinder and a perforated   surface
  We predict that the radiative heat-transfer rate between a cylinder and a perforated surface depends non-monotonically on their separation. This anomalous behavior, which arises due to near-field effects, is explained using a heuristic model based on the interaction of a dipole with a plate. We show that nonmonotonicity depends not only on geometry and temperature but also on material dispersion - for micron and submicron objects, nonmonotonicity is present in polar dielectrics but absent in metals with small skin depths. 
Alejandro W. Rodriguez, M. T. Homer Reid, Jaime Varela, John D.   Joannopoulos, Federico Capasso, and Steven G. Johnson
cond-mat.mtrl-sci