A NUMERICAL METHOD TO ESTIMATE TEMPERATURE INTERVALS FOR TRANSIENT HEAT TRANSFER PROBLEMS

This paper presents a numerical method to solve transient heat transfer problems with interval uncertainty. In virtue of Taylor series expansion and interval analysis, two deterministic equations are derived for the bounds estimation of temperature when thermal parameters are interval variables. A temporally piecewise adaptive algorithm is employed to maintain a steady accuracy over a whole time domain, either for constant or variable sizes of time steps. A numerical example is provided to verify the proposed approach, and a good accordance can be observed by comparing the results given by the combinatorial, probability and proposed approaches. The effects of the order of a Taylor expansion and the size of a time step on the results are discussed.