[Paper Review] Modeling near-field radiative heat transfer from sharp objects using a general 3d numerical scattering technique

Alexander P. McCauley, M. T. Homer Reid+2 more|arXiv (Cornell University)|Jul 11, 2011

Thermal Radiation and Cooling Technologies22 references63 citations

TL;DR

This paper presents a general 3D numerical scattering technique combining scattering theory with boundary-element methods to model near-field radiative heat transfer from sharp 3D objects like cones and cylinders to a dielectric plate. The method enables accurate prediction of total heat transfer and spatial heat flux profiles, revealing a unique local minimum in heat flux directly below sharp conical tips due to dipole-like radiation patterns, a feature absent in flat or smoothly curved bodies.

ABSTRACT

We examine the non-equilibrium radiative heat transfer between a plate and finite cylinders and cones, making the first accurate theoretical predictions for the total heat transfer and the spatial heat flux profile for three-dimensional compact objects including corners or tips. We find qualitatively different scaling laws for conical shapes at small separations, and in contrast to a flat/slightly-curved object, a sharp cone exhibits a local \emph{minimum} in the spatially resolved heat flux directly below the tip. The method we develop, in which a scattering-theory formulation of thermal transfer is combined with a boundary-element method for computing scattering matrices, can be applied to three-dimensional objects of arbitrary shape.

Motivation & Objective

• To develop a general numerical method for computing near-field radiative heat transfer from arbitrary 3D compact objects, including those with sharp tips or corners.
• To predict total thermal transfer and spatially resolved heat flux profiles for cone-plate, cylinder-plate, and sphere-plate configurations beyond the limits of analytic solutions.
• To investigate how geometric sharpness—particularly in conical shapes—affects near-field heat transfer scaling and flux distribution.
• To validate the method against known analytic results (e.g., sphere-plate) and extend it to non-spherical, non-planar geometries.
• To explain the counterintuitive observation of a local flux minimum directly below a sharp cone tip using a modified dipole model.

Proposed method

• Formulates near-field radiative transfer using Rytov's fluctuation-dissipation theorem and scattering theory, expressing the electric field correlator in a cylindrical-wave basis.
• Employs a boundary-element method (BEM) to numerically compute the scattering matrix of arbitrary 3D objects from surface meshes, enabling resolution concentration near the plate interface.
• Uses a cylindrical-wave basis (Bessel beams) instead of spherical waves to better resolve near-field interactions, especially for axisymmetric objects.
• Applies Gaussian quadrature to discretize continuous integrals over radial wavevector kρ, enabling numerical matrix operations.
• Computes total power and spatial Poynting flux via trace operations on scattering matrices and correlators, with polarization contributions handled via a single-polarization approximation (SPA) for efficiency.
• Validates results using analytic solutions for spheres and performs high-resolution meshing near cone tips to confirm non-monotonic flux profiles without SPA.

Experimental results

Research questions

• RQ1 How does the total radiative heat transfer scale with separation for sharp 3D objects like cones compared to flat or smoothly curved bodies?
• RQ2 What is the spatial distribution of heat flux on the substrate surface when a sharp cone is placed near a dielectric plate?
• RQ3 Why does a sharp conical tip exhibit a local minimum in heat flux directly below it, contrary to expectations from flat or spherical sources?
• RQ4 To what extent does the single-polarization approximation (SPA) affect the accuracy of flux profiles for conical and cylindrical objects?
• RQ5 Can the observed flux minimum be explained by a modified dipole radiation model?

Key findings

• Conical shapes exhibit a distinct scaling law for total heat transfer at small separations, differing qualitatively from flat or spherical geometries.
• A sharp cone produces a local minimum in the spatially resolved Poynting flux directly below its tip, a feature absent in cylinders and spheres.
• This flux minimum becomes more pronounced as the cone becomes sharper, with the 40° cone showing a flux at x=0 less than half its peak value.
• The dip is confirmed using high-resolution BEM simulations without the single-polarization approximation, proving it is not an artifact of numerical simplification.
• The effect is explained by the cone’s radiation pattern approaching that of a normal dipole, which has zero Poynting flux along its axis, consistent with numerical verification for thin cylinders.
• The method enables accurate, general 3D modeling of near-field heat transfer for arbitrary compact objects, extending beyond analytic solutions to spheres and plates.