Interval Estimation of Convection-Diffusion Heat Transfer Problems

This article presents two approaches to tackle the steady-state convection-diffusion heat transfer problem with interval uncertainty. The finite-element method and expansion techniques are combined in the modeling process, and the lower and upper bounds of the uncertain intervals of temperatures are estimated by solving two sets of deterministic equations in terms of central values and the radius of the intervals. A 2-D numerical example is provided to verify the proposed approaches. In comparison with the combinatorial and probabilistic methods, the estimated bounds are reasonable.