A Boundary Element Method Using DRM For Nonlinear Heat Conduction Problems
Free (open access)
M Tanaka, T Matsumoto & Y Suda
This paper presents a dual reciprocity boundary element method (DRBEM) for solving the steady-state heat conduction problem of temperature-dependent materials. The integral equation formulation uses the fundamental solution of the Laplace equation for homogeneous materials, and a domain integral arises in the boundary integral equation. This domain integral is transformed into boundary integrals through the dual reciprocity method by introducing a new set of radial basis functions. An iterative solution procedure is used, because material constants are temperature-dependent and hence the problem is nonlinear. The details of the proposed DRBEM are presented, and based on this formulation a computer code is developed for two-dimensional problems. Through comparison of the results obtained by the computer code with the exact ones for some examples, the usefulness of the proposed DRBEM is demonstrated.