Small distance expansion for radiative heat transfer between curved objects

TL;DR

This paper introduces a small distance expansion method for radiative heat transfer between curved objects, improving accuracy beyond the proximity approximation by including curvature effects and analyzing convergence properties.

Contribution

It develops a gradient expansion approach for radiative heat transfer that accounts for curvature, extending the proximity transfer approximation with validated convergence analysis.

Findings

The expansion converges faster for derivatives of transfer than for transfer itself.

Logarithmic correction to the leading term has a small prefactor for various materials.

The method applies to sphere-plate configurations with improved accuracy.

Abstract

We develop a small distance expansion for the radiative heat transfer between gently curved objects, in terms of the ratio of distance to radius of curvature. A gradient expansion allows us to go beyond the lowest order proximity transfer approximation. The range of validity of such expansion depends on temperature as well as material properties. Generally, the expansion converges faster for the derivative of the transfer than for the transfer itself, which we use by introducing a near-field adjusted plot. For the case of a sphere and a plate, the logarithmic correction to the leading term has a very small prefactor for all materials investigated.