Stochastic heat transfer analysis and reliability assessment under non-stationary random thermal load using the explicit time-domain method

Abstract

Efficient and accurate reliability assessment is of utmost importance for a safe and economical design of engineering equipment involving stochastic heat transfer. However, the stochastic analysis of large-scale heat transfer problems under non-stationary random thermal loads is still a challenging task due to the heavy computational burden. This paper extends the explicit time-domain method (ETDM), an efficient method initially developed for random structural vibration, to stochastic heat transfer problems. In ETDM, the underlying physical law driving the uncertainty propagation is first converted to a discrete and algebraic form through deterministic impulse analyses, resulting in the explicit expressions of concerned responses in the time domain. Using the explicit expressions, the statistics of the random system responses can be efficiently evaluated. With the deterministic impulse analyses serving as a bridge, the physical mechanism is treated separately from the stochastic evolution mechanism. Thus, ETDM can be deemed a general method for stochastic problems governed by various physical laws. Its capability is demonstrated by solving large-scale heat transfer problems subjected to non-stationary random thermal loads. The efficiency and accuracy of the method are highlighted by the reliability assessment of a CPU heat sink discretized by a very fine finite element mesh.