Baranoglu, BesimManufacturing Engineering2024-10-062024-10-0620191300-3615https://search.trdizin.gov.tr/en/yayin/detay/370264/a-new-formulation-for-the-boundary-element-analysis-of-heat-conduction-problems-with-nonlinear-boundary-conditionshttps://hdl.handle.net/20.500.14411/8848Baranoglu, Besim/0000-0003-2005-050XAn effective numerical method based on the boundary element formulation is presented to solve heat conduction equations which are governed by the Fourier equation, with nonlinear boundary conditions on one or more sections of the prescribed boundary. The solution involves the manipulation of the system matrices of the boundary element method and obtaining a smaller ranked matrix equation in which the unknown is only the temperature difference over the nonlinear boundary condition region. This way, the iterations to deal with the nonlinear conditions are performed faster. After finding the solution over the nonlinear boundary condition region, the solution over the entire boundary is obtained as a post-process through a prescribed relation. An example with a proven exact solution is employed to assess the results.eninfo:eu-repo/semantics/closedAccessBoundary element methodheat conductionnonlinear boundary conditionsArticleQ4Q4392229236WOS:0004908490000113702641