ON THE INFLUENCE OF ELLIPTICAL PERFORATIONS ON THE TEMPERATURE DISTRIBUTION OF A THIN PLATE EXPOSED TO A LOCALIZED RADIATIVE SOURCE

Abstract

This work extends a finite element methodology for nonlinear radiative-conductive heat transfer to complex surfaces, with emphasis on perforated geometries. The governing partial differential equation incorporates Neumann boundary conditions and accounts for incident radiation from a small, high-temperature distant source as well as emis- sion from the surface itself. The perforated configuration is chosen to show how the methodology can be applied to more elaborated geometries, assessing the interplay between source radiation, surface thermal response and the geometric fea- tures of the target. The inherent nonlinearity arising from radiative exchange (Stefan-Boltzmann law) is treated through a weak variational formulation combined with Newton linearization, discretized via finite elements. Using a previously validated framework, the present study focuses on parametric investigations about the influence of perforation geometry, (1) eccentricity, maintaining a fixed area, (2) orientation of the major axis, and (3) offset relative to the source projection, resulting in different, but consistent temperature distribution. An analytical expression for the radiative power intercepted by a coaxial elliptical perforation is derived as an analytical reference for the numerical result. Additionally, systematic mesh refinement studies are conducted to verify solution accuracy on the perforated domain. Results confirm the robust- ness of the Newton-based methodology for perforated geometries, with convergence achieved with tolerance of 10-6. The parametric analysis reveals the sensitivity of thermal response to perforation shape versus source positioning, provid- ing insight into the thermal dominant factors governing heat transfer in more complex configurations. The methodology demonstrates strong potential for extension to other geometries relevant to thermal engineering applications.