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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Temporal behavior of σ[t0] for variations in k1 computed implicitly: (a) using field equations; (b) using finite differences.
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σ[t0] for k=k1+β(T−TL) computed implicitly: (a) temporal behavior; (b) steady state.
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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.
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Standard deviations of Qf and (T(L)−T)/(Tw−T) with respect to ε for σ[ε]/ε̄=25 percent
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Correlation between the 1st element at the wall with other elements of the fin
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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)
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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.
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Eigenvalues for the radiating fin problem
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Probability distributions of t and the Normal distribution based upon t̄ and σ[t]: (a) Example 1; (b) fin
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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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