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

## TL;DR

This paper investigates the temperature distribution and heat radiation of patterned surfaces at short wavelengths, developing a recursive scattering method to efficiently determine equilibrium temperatures and revealing universal relations linked to surface geometry.

## Contribution

It introduces a recursive multiple scattering method for rapid convergence in calculating surface temperatures and uncovers universal relations between temperature statistics and geometric features.

## Key findings

- Temperature distributions depend on surface shape details.
- Universal relations exist between temperature statistics and geometric features.
- The method enables efficient analysis of patterned surfaces at short wavelengths.

## Abstract

We analyze the equilibrium spatial distribution of surface temperatures of patterned surfaces. The surface is exposed to a constant external heat flux and has a fixed internal temperature that is coupled to the outside heat fluxes by finite heat conductivity across surface. It is assumed that the temperatures are sufficiently high so that the thermal wavelength (a few microns at room temperature) is short compared to all geometric length scales of the surface patterns. Hence the radiosity method can be employed. A recursive multiple scattering method is developed that enables rapid convergence to equilibrium temperatures. While the temperature distributions show distinct dependence on the detailed surface shapes (cuboids and cylinder are studied), we demonstrate robust universal relations between the mean and the standard deviation of the temperature distributions and quantities that characterize overall geometric features of the surface shape.