Numerical instability and its treatment for steady state heat conduction problems in exchanger tubes using the dual boundary element method

Abstract

In this paper, we employed the boundary element method (BEM) to determine the heat conduction shape factor (CSF) for the steady-state heat conduction problem in the heat exchanger tube. Various doubly-connected geometric shapes were considered. Numerical results of the conduction shape factor matched well with the theoretical data. Numerical instability was found for a special size. Degenerate scale occurred for all cases of regular N-gons in determining the conduction shape factor and matched the data as analytically predicted. Numerical results showed that a degenerate scale is only dependent on the outer boundary instead of the inner boundary. Three regularization techniques, the dual BEM, the CLEEF(UT), and the CLEEF(LM), were provided to avoid numerical instability. It was found that the larger number of sides for the N-gon shape is given, the lower the CSF is obtained. As N approaches infinity, it converges to the minimum value of the solution for an annulus.