A numerical method to estimate temperature intervals for transient convection-diffusion heat transfer problems

摘要

This paper presents a numerical method to estimate intervals of temperature for transient convection-diffusion heat transfer problems when uncertainty of thermal parameters is characterized by the interval. A deterministic relationship of interval variables between temperature and thermal parameters is setup by Taylor series expansion and the interval analysis, and the lower and upper bounds of temperature can be estimated by a temporally piecewise adaptive algorithm and FEM. A prescribed computing accuracy at each discretized time interval can be achieved via an adaptive process for different size of time step, thus the computing accuracy over the whole time domain can be maintained. A 2D numerical example is provided to verify the proposed approach, and a good accordance can be observed in the comparison of results given by the combinatorial, probability and proposed approaches. The impact of the order of Taylor expansion and the size of time step on the result is discussed.