Higher Order Perturbation Analysis of Stochastic Thermal Systems With Correlated Uncertain Properties

[+] Author and Article Information
A. F. Emery

Department of Mechanical Engineering, University of Washington, Seattle, WA 98195-2600e-mail: emery@u.washington.edu

J. Heat Transfer 123(2), 390-398 (Nov 03, 2000) (9 pages) doi:10.1115/1.1351144 History: Received April 12, 2000; Revised November 03, 2000
Copyright © 2001 by ASME
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Grahic Jump Location
Temporal behavior of σ[t0] for variations in k1 computed implicitly: (a) using field equations; (b) using finite differences.
Grahic Jump Location
σ[t0] for k=k1+β(T−TL) computed implicitly: (a) temporal behavior; (b) steady state.
Grahic Jump Location
σ[t0] for a piecewise definition of k(T) and σ[k1]/k̄1=0.1: (a) k2/k1=1.5; (b) k2/k1=0.5.
Grahic Jump Location
Standard deviations of Qf and (T(L)−T)/(Tw−T) with respect to ε for σ[ε]/ε̄=25 percent
Grahic Jump Location
Correlation between the 1st element at the wall with other elements of the fin
Grahic Jump Location
The effect of correlation scale θ on the 1st order estimate of the standard deviation for ε̄=0.5 (dashed lines are the reference values)
Grahic Jump Location
σ[(T(x)−T∞)/(Tw−T)] for a fin with ε=0 and σ[h]/h̄=25 percent: (a) 2nd order and reference values of σ[T] for a Uniformly Distributed h; (b) a comparison of the 1st order estimates and the reference values for independently and uniformly distributed h.
Grahic Jump Location
Eigenvalues for the radiating fin problem
Grahic Jump Location
Probability distributions of t and the Normal distribution based upon t̄ and σ[t]: (a) Example 1; (b) fin
Grahic Jump Location
Finite difference estimates of the derivatives for Example 1 for σ[k1]/k̄1=25 percent: (a) Fo=0.5; (b) steady state



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