Higher order perturbation analysis of stochastic thermal systems with correlated uncertain properties

Journal of Heat Transfer

Volumn 123, Issue 2, 2001, Pages 390-398

  Emery, A F ^a  

^a University of Washington   (United States)

Author keywords

Computational; Heat transfer; Inverse; Modeling

Indexed keywords

EID: 0012879930     PISSN: 00221481     EISSN: 15288943     Source Type: Journal    
DOI: 10.1115/1.1351144     Document Type: Article

References (33)

1. Abernethy, R. B., Benedict, R. P., andDowell, R. B., 1985, “ASME Measurement Uncertainty,” ASME J. Fluids Eng., 107, pp. 161-164.
2. Moffat, R. J., 1988, “Describing the Uncertainties in Experimental Results,” Exp. Therm. Fluid Sci., 1, pp. 3-17.
3. Lin, Y. K., 1995, Probabilistic Structure Dynamics: Advanced Theory and Applications, McGraw-Hill, New York.
4. Papoulis, A., 1991, Probability, Random Variables, and Stochastic Processes, McGraw-Hill, New York.
5. Ljung, L., 1999, System Identification, Prentice-Hall, New York.
6. Inan, E., and Markov, K. Z., 1998, Continuum Models and Discrete Systems, World Scientific, Singapore.
7. Rohsenow, W. M., and Hartnett, J. P., 1973, Handbook of Heat Transfer, McGraw-Hill, New York.
8. Kakac, S., Shah, R. K., and Aung, W., 1987, Handbook of Single-Phase Convective Heat Transfer, Wiley, New York.
9. 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.
10. 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.
11. Ryniecki, A., and Jayas, D. S., 1992, “Stochastic Modeling of Grain Temperature in Near-Ambient Drying,” Drying Technol., 10, pp. 123-137.
12. 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.
13. Pomraning, G. C., 1998, “Radiative Transfer and Transport Phenomena in Stochastic Media,” Int. J. Eng. Sci., 36, pp. 1595-1621.
14. 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.
15. 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.
16. Kieda, S., et al., 1993, “Application of Stochastic Finite Element Method to Thermal Analysis for Computer Cooling,” ASME J. Electron. Packag., 115, pp. 270-275.
17. Madera, A. G., 1993, “Modelling of Stochastic Heat Transfer in a Solid,” Appl. Math. Model., 17, pp. 664-668.
18. Emery, A. F., 1999, “Computing Temperature Variabilities due to Stochastic and Fuzzy Thermal Properties,” Proc. 1999 ASME/AIChE National Heat Transfer Conference, Albuquerque, NM.
19. Haldar, A., and Mahadevan, S., 2000, Probability, Reliability, and Statistical Methods in Engineering Design, Wiley, New York.
20. 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.
21. 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.
22. Smith, D. L., 1991, Probability, Statistics, and Data Uncertainties in Nuclear Science and Technology, American Nuclear Society, LaGrange Part, IL.
23. Haldar, A., and Mahadevan, S., 2000, Reliability Assessment Using Stochastic Finite Element Analysis, J. Wiley & Sons, New York, NY.
24. Breitung, K., 1984, “Asymptotic Approximations for Multinormal Integrals,” J. Eng. Mech., 110, pp. 357-366.
25. Anderson, T. W., 1958, An Introduction to Multivariate Statistical Analysis, Wiley, New York.
26. Rosenblatt, M., 1952, “Remarks on a Multivariate Transformation,” Ann. Math. Stat., 23, pp. 470-472.
27. Bickel, P. J., and Doksum, K. A., 1978, Mathematical Statistics: Basic Ideas and Selected Topics, Holden-Day, San Francisco, CA.
28. 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.
29. Cook, R. D., Malkus, D. S., and Plesha, M. E., 1989, Concepts and Applications ofFinite Element Analysis, Wiley, New York.
30. Incropera, F., and DeWitt, D. P., 1996, Introduction to Heat Transfer, Wiley, New York.
31. Vanmarcke, E., 1984, Random Fields, Analysis and Synthesis, The MIT Press, Cambridge, MA.
32. 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.
33. Guttman, I., Wilks, S. S., and Hunter, J. S., 1971, Introductory Engineering Statistics, Wiley, New York.