☆ 4.3 Article

Modeling of Uncertainty Propagation for Transient Heat Rejection Problems

JOURNAL OF THERMOPHYSICS AND HEAT TRANSFER (2023)

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Summary: This article investigates the transient temperature variation profile of a plate heated from the top and convection cooled at the bottom, considering the transient processes and uncertainty propagation. The dimensionless input parameters, such as the Biot number and dimensionless initial conditions, are used to describe the physical properties of the plate and ambient medium, affecting the dimensionless temperature variation. The study reveals that for small Biot numbers, the dimensionless relaxation time of the temperature variation towards its steady state is proportional to 1/Bi and can be very large. For large Biot numbers, the temperature variation usually goes through a peak before reaching its stationary profile. The stochastic nature of the dimensionless temperature variation is explored, showing that the amplitude of its stochastic spread generally depends on the mean values of the dimensionless inputs with a fixed standard deviation. Additionally, the dimensionless time evolution of the uncertainty amplitude is shown to crucially depend on the standard deviations of the dimensionless input parameters, which may increase or decrease with time, or remain small over time. Finally, uncertainty propagation in a high-fidelity model of a copper block, used in an experimental setup, is compared with the developed generic plate model.

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