Non-probabilistic interval process model and method for uncertainty analysis of transient heat transfer problem

Due to the aggressive and changing environmental conditions, various time-varying uncertainties widely exist in many engineering heat transfer problems. This paper introduces a non-probabilistic interval process model to characterize the time-varying uncertainty with limited information, whose lower and upper bounds are quantified as time-dependent functions instead of constant values. Meanwhile, two numerical methods, named as Monte Carlo method under interval process model (MCM-IP) and sensitivity analysis method under interval process model (SAM-IP), are presented for uncertain temperature response prediction. In MCM-IP, the temperature response bounds are directly simulated via substantial sample processes, which are constructed by the interpolation methods from the discrete interval samples. To avoid the huge computational cost of MCM-IP caused by a large number of sample processes, SAM-IP carries out the monotonicity prejudgment via sensitivity analysis, by which only two sample processes are constructed for response bounds prediction. Finally, MCM-IP and SAM-IP are comparatively investigated in a mathematical example and an engineering example, by which the effectiveness of the proposed model and methods are verified.