Transmission conditions for thin curvilinear close to circular heat-resistant interphases in composite ceramics

TL;DR

This paper develops and validates asymptotic transmission conditions for heat transfer across thin, curved, heat-resistant interphases in composite ceramics, simplifying FEM analysis while maintaining accuracy.

Contribution

It introduces a novel asymptotic model for imperfect interfaces with curved geometries, enhancing the analysis of heat transfer in composite ceramics.

Findings

Asymptotic conditions accurately approximate heat transfer across curved interphases.

Curvature significantly affects the accuracy of transmission conditions.

The approach simplifies FEM analysis without compromising precision.

Abstract

This paper considers the problem of heat transfer in a composite ceramic material where the structural elements are bonded to the matrix via a thin heat resistant adhesive layer. The layer has the form of a circular ring or close to it. Using an asymptotic approach, the interphase is modeled by an infinitesimal imperfect interface, preserving the main features of the temperature fields around the interphase, and allowing a significant simplification where FEM analysis is concerned. The nonlinear transmission conditions that accompany such an imperfect interface are evaluated, and their accuracy is verified by means of dedicated analytical examples as well as carefully designed FEM simulations. The interphases of various geometries are analysed, with an emphasis on the influence of the curvature of their boundaries on the accuracy of the evaluated conditions. Numerical results demonstrate the benefits of the approach and its limitations.