Input Uncertainty and Implication for Modeling Generic and High-Fidelity Transient Convection Problems

Transient processes and uncertainty propagation impacting the transient temperature variation profile for a plate heated from the top and convection cooled at the bottom surface are investigated. The model dimensionless input parameters, such as the Biot number Bi and dimensionless initial conditions, are formulated describing physical properties of the plate and ambient medium with subsequent impact on the dimensionless temperature variation. As is shown, in the case of small Bi, dimensionless relaxation time of the temperature variation toward its steady state is proportional to 1/Bi and can be very large. For large Bi, the temperature variation usually passes through a peak before reaching its stationary profile. Stochastic nature of the dimensionless temperature variation is explored. As is found, the amplitude of its stochastic spread depends, in general, on the mean values of the dimensionless inputs at a fixed standard deviation. As is also shown, dimensionless time evolution of the uncertainty amplitude depends crucially on standard deviations of the dimensionless input parameters; it may increase or decrease with time, or stay 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.

Automated 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.