Boundary integral formulation of axisymmetric nonlinear transient heat transfer problems

GÜN H., Feng W.

Engineering Analysis with Boundary Elements, vol.181, 2025 (SCI-Expanded, Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 181
  • Publication Date: 2025
  • Doi Number: 10.1016/j.enganabound.2025.106517
  • Journal Name: Engineering Analysis with Boundary Elements
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Compendex, INSPEC, MathSciNet, zbMATH, DIALNET
  • Keywords: Axisymmetric problems, Boundary integral equation, Nonlinear transient heat applications, Radial integration
  • Uşak University Affiliated: Yes

Abstract

The Boundary integral equation approach is extended to cover axially symmetric nonlinear heat conduction problems with temperature-dependent material thermal conductivities. To derive axisymmetric BIE formulation, three-dimensional fundamental solutions are integrated with respect to the hoop direction and then the radial integration procedure employing radial basis functions to approximate the unknown variables is utilized to switch axially symmetric surface integrals to axially symmetric line integrals. This computational process results in a pure line element algorithm. To arrive the solution of a set of linear algebraic equations obtained by its numerical implementation using both line-only-elements and interior points, Newton-Rapson iterative procedure is employed. Numerical applications are given with temperature-dependent thermal conductivity examples including spatially varying thermal properties. The BIE results are shown to be in a satisfactory agreement with Finite Element Analysis (FEA) results.