Minimum radiative heat transfer between two metallic half-spaces due to propagating waves

The gap dependence of radiative energy transfer due to propagating waves between two identical metallic half-spaces separated by vacuum is investigated. The dielectric function of the metallic half-spaces is described by the Drude model. Analytical expressions for the minimum radiative heat transfer coefficient, hmin, and the gap, dmin, at which the minimum value of radiative transfer is attained are determined in terms of the parameters of the dielectric function and the absolute temperature T. We show that hmin∝T2 in the high temperature limit and hmin∝T7/2 in the low temperature limit.