Modeling of Uncertainty Propagation for Transient Heat Rejection Problems

Abstract

Generic plate and experiment-related high-fidelity models to study uncertainty propagation and transient processes for heat rejection problems are developed. The stochastic Biot numbers on the top and bottom surfaces of the plate, [Formula: see text] and [Formula: see text], and stochastic dimensionless input parameters, describing initial and convection boundary conditions, are introduced to define temperature variation in the modeled systems. The resulting uncertainty amplitude demonstrates a varying time evolution across a wide range of mean values of the input parameters. Depending on which input parameters are stochastic, the uncertainty may increase or decrease over time, or remain small for a given time interval in the case of the plate model. For small [Formula: see text], dimensionless characteristic time for a temperature variation curve to approach its steady state is [Formula: see text] and large. An extremum in a temperature variation curve may appear when the Biot numbers are unequal and disappears if [Formula: see text]. Results are nonsymmetric with respect to interchanging [Formula: see text] and [Formula: see text]. Despite the difference in shape, the temperature variation profile over a specific region in the experimental test section numerically described by the high-fidelity model is close to the corresponding results provided by the plate model for the same Biot numbers, convection boundary, and initial conditions.