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We analyze the equilibrium spatial distribution of surface temperatures ofpatterned surfaces. The surface is exposed to a constant external heat flux andhas a fixed internal temperature that is coupled to the outside heat fluxes byfinite heat conductivity across surface. It is assumed that the temperaturesare sufficiently high so that the thermal wavelength (a few microns at roomtemperature) is short compared to all geometric length scales of the surfacepatterns. Hence the radiosity method can be employed. A recursive multiplescattering method is developed that enables rapid convergence to equilibriumtemperatures. While the temperature distributions show distinct dependence onthe detailed surface shapes (cuboids and cylinder are studied), we demonstraterobust universal relations between the mean and the standard deviation of thetemperature distributions and quantities that characterize overall geometricfeatures of the surface shape.

Temperature Distribution and Heat Radiation of Patterned Surfaces at Short Wave Lengths