We use a general theory of the fluctuating electromagnetic field and a generalized Kirchhoff's law (Ref. 8) to calculate the heat transfer between macroscopic and nanoscale bodies of arbitrary shape, dispersive, and absorptive dielectric properties. We study the heat transfer between: (a) two parallel semi-infinite bodies, (b) a semi-infinite body acid a spherical body, and (c) two spherical bodies. We consider the dependence of the heat transfer on the temperature T, the shape and the separation d, and discuss the role of nonlocal and retardation effects. We find that for low-resistivity material the heat transfer is dominated by retardation effects even for the very short separations.
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