Numerical Analysis of Transient Temperature Field with Interval Parameters

A method using interval analysis is presented for transient heat conduction problems of uncertain structure. In this method, each parameter and initial boundary conditions are regarded as interval parameters. In order to solve parabolic equation of heat conduction with interval parameters, the regions of space are discretized by finite elements and the regions of time are discretized by finite difference. The interval finite element method based on the element is established via the combination of interval analysis and the traditional finite element method. The interval finite equation of structure is solved by matrix perturbation formulas, and then the range of temperature field response of the structure is obtained. The proposed method is finally applied to the problem of transient heat conduction which shows its effectiveness.