Three-dimensional transient heat conduction analysis with non-linear boundary conditions by boundary element method

A computational method based on boundary element method (BEM) has been developed to analyze transient temperature distribution in a three-dimensional solid having non-linear boundary condition (for example boiling or thermal radiation). To obtain high numerical accuracy, the heat transfer coefficient which depends on the surface temperature was approximated as a linear combination of interpolation functions with respect to time and analytical time integration of the non-linear term included in boundary integral equation was made. To investigate feasibility of the present method, it was applied to calculations of the temperature distribution in an infinite flat plate cooled on one side. The heat transfer coefficient of cooling surface was in proportion to n-th power of the surface temperature. Results are (1) the method has given a stable solution for non-linear boundary value problems such as conventional BEM could not solve, (2) it has given an accurate solution for large time increment except for first time step, and (3) an optimal relaxation factor decreases with strength of non-linearity of the heat transfer coefficient. Applying the method to thermal analysis of limiter and divertor plate installed in a fusion test facility and fusion reactor respectively, availability of the method has been confirmed. (author)