Interval analysis of steady-state heat convection-diffusion problem with uncertain-but-bounded parameters

In this paper, a sensitivity-based interval analysis method (SIAM) and an interval parameter perturbation method (IPPM) are proposed to estimate temperature intervals for the steady-state heat convection-diffusion problem with uncertainties in material properties, external loads and boundary conditions. Interval variables are used to characterize the uncertain parameters in the face of limited information. The first-order Taylor expansions are employed in SIAM, while IPPM introduces the surface rail generation method to approximate interval matrices and vectors. Some high-order terms of the Neumann series are retained to calculate the interval matrix inverse in IPPM. By comparing the results with traditional Monte Carlo simulations, two numerical examples are given to demonstrate the feasibility and effectiveness of the proposed approaches at predicting the uncertain temperature field.