A new numerical technique for interval analysis of convection-diffusion heat transfer problems using LSE and optimization algorithm

Abstract

This article devotes to the uncertain analysis of steady-state convection-diffusion heat transfer problems with interval input parameters in material properties, thermal source and boundary conditions. The optimization strategy is adopted to ensure a reliable bounds estimation when scales of interval width is larger, and a Galerkin system is derived to construct a Legendre Series Expansion (LSE) to surrogate FE solutions of deterministic problems, so as to reduce the computational expense in the optimization based bounds estimation with sufficient accuracy. A LSE-GS (global search), and a LSE-CM (combinatorial method) are presented to solve uncertain steady-state convection-diffusion heat transfer problems with multiple interval variables, and are extended to the fuzzy analysis. Various numerical examples are provided to verify the performance of the proposed method, and evidence the accuracy and effectiveness of the proposed methods for interval prediction of steady-state convection-diffusion heat transfer problems.