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

Abstract

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 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.