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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Abernethy,  R. B., Benedict,  R. P., and Dowell,  R. B., 1985, “ASME Measurement Uncertainty,” ASME J. Fluids Eng., 107, pp. 161–164.
Moffat,  R. J., 1988, “Describing the Uncertainties in Experimental Results,” Exp. Therm. Fluid Sci., 1, pp. 3–17.
Lin, Y. K., 1995, Probabilistic Structure Dynamics: Advanced Theory and Applications, McGraw-Hill, New York.
Papoulis, A., 1991, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York.
Ljung, L., 1999, System Identification, Prentice-Hall, New York.
Inan, E., and Markov, K. Z., 1998, Continuum Models and Discrete Systems, World Scientific, Singapore.
Rohsenow, W. M., and Hartnett, J. P., 1973, Handbook of Heat Transfer, McGraw-Hill, New York.
Kakaç, S., Shah, R. K., and Aung, W., 1987, Handbook of Single-Phase Convective Heat Transfer, Wiley, New York.
Andersen,  K., Madsen,  H., and Hansen,  L., 2000, “Modelling the Heat Dynamics of a Building using Stochastic Differential Equations,” Energy Build., 31, pp. 13–24.
Loveday,  D., and Craggs,  C., 1992, “Stochastic Modelling of Temperatures Affecting the in situ Performance of a Solar Assisted Heat Pump: The Multivariate Approach and Physical Interpretation,” Sol. Energy, 49, pp. 289–298.
Ryniecki,  A., and Jayas,  D. S., 1992, “Stochastic Modeling of Grain Temperature in Near-Ambient Drying,” Drying Technol., 10, pp. 123–137.
Nicolai, B. M., and De Baerdemaeker, J., 1992, “Simulation of Heat Transfer in Foods with Stochastic Initial and Boundary Conditions,” Inst. Chemical Engineers Symposium Series Food Engineering in a Computer Climate, pp. 247–252.
Pomraning,  G. C., 1998, “Radiative Transfer and Transport Phenomena in Stochastic Media,” Int. J. Eng. Sci., 36, pp. 1595–1621.
Kolditz,  O., and Clauser,  C., 1998, “Numerical Simulation of Flow and Heat Transfer in Fractured Crystalline Rocks: Application to the Hot Dry Rock Site in Rosemanowes (U.K.),” Geothermics, 27, pp. 1–23.
Hien,  T. D., and Kleiber,  M., 1997, “Stochastic Finite Element Modelling in Linear Transient Heat Transfer,” Comput. Methods Appl. Mech. Eng., 144, pp. 111–124.
Kieda,  S., , 1993, “Application of Stochastic Finite Element Method to Thermal Analysis for Computer Cooling,” ASME J. Electron. Packag., 115, pp. 270–275.
Madera,  A. G., 1993, “Modelling of Stochastic Heat Transfer in a Solid,” Appl. Math. Model., 17, pp. 664–668.
Emery, A. F., 1999, “Computing Temperature Variabilities due to Stochastic and Fuzzy Thermal Properties,” Proc. 1999 ASME/AIChE National Heat Transfer Conference, Albuquerque, NM.
Haldar, A., and Mahadevan, S., 2000, Probability, Reliability, and Statistical Methods in Engineering Design, Wiley, New York.
Fadale,  T. D., and Emery,  A. F., 1994, “Transient Effects of Uncertainties on the Sensitivities of Temperatures and Heat Fluxes using Stochastic Finite Elements,” ASME J. Heat Transfer, 116, pp. 808–814.
Emery,  A. F., and Fadale,  T. D., 1997, “Handling Temperature Dependent Properties and Boundary Conditions in Stochastic Finite Element Analysis,” Numer. Heat Transfer, Part B, 31, pp. 37–51.
Smith, D. L., 1991, Probability, Statistics, and Data Uncertainties in Nuclear Science and Technology, American Nuclear Society, LaGrange Part, IL.
Haldar, A., and Mahadevan, S., 2000, Reliability Assessment Using Stochastic Finite Element Analysis, J. Wiley & Sons, New York, NY.
Breitung,  K., 1984, “Asymptotic Approximations for Multinormal Integrals,” J. Eng. Mech., 110, pp. 357–366.
Anderson, T. W., 1958, An Introduction to Multivariate Statistical Analysis, Wiley, New York.
Rosenblatt,  M., 1952, “Remarks on a Multivariate Transformation,” Ann. Math. Stat., 23, pp. 470–472.
Bickel, P. J., and Doksum, K. A., 1978, Mathematical Statistics: Basic Ideas and Selected Topics, Holden-Day, San Francisco, CA.
Emery,  A. F., and Fadale,  T. D., 1999, “Calculating Sensitivities of Thermal Systems with Uncertain Properties using the Stochastic Finite Element Method and Finite Differencing,” Inverse Problems Eng., 7, pp. 291–307.
Cook, R. D., Malkus, D. S., and Plesha, M. E., 1989, Concepts and Applications of Finite Element Analysis, Wiley, New York.
Incropera, F., and DeWitt, D. P., 1996, Introduction to Heat Transfer, Wiley, New York.
Vanmarcke, E., 1984, Random Fields, Analysis and Synthesis, The MIT Press, Cambridge, MA.
Madera,  A. G., 1996, “Heat Transfer from an Extended Surface at a Stochastic Heat Transfer Coefficient and Stochastic Environmental Temperatures,” Int. J. Eng. Sci., 34, pp. 1093–1099.
Guttman, I., Wilks, S. S., and Hunter, J. S., 1971, Introductory Engineering Statistics, Wiley, New York.


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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