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Mathematical Problems in Engineering
Volume 2017, Article ID 5907856, 7 pages
https://doi.org/10.1155/2017/5907856
Research Article

Stochastic Analysis of Natural Convection in Vertical Channels with Random Wall Temperature

Department of Mechanical Systems Engineering, National Institute of Technology, Asahikawa College, 2-2-1-6 Shunkodai, Asahikawa 071-8142, Japan

Correspondence should be addressed to Ryoichi Chiba; pj.ca.tcn-awakihasa@abihc

Received 31 May 2017; Accepted 17 July 2017; Published 13 August 2017

Academic Editor: Sergey A. Suslov

Copyright © 2017 Ryoichi Chiba. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Miyata, S. Iijima, R. Ooshima, T. Abe, T. Hisamatsu, and T. Hamamatsu, “Application technology on ceramics for structural components of high temperature machines,” Transactions of the Japan Society of Mechanical Engineers Series A, vol. 54, no. 505, pp. 1700–1708, 1988. View at Publisher · View at Google Scholar · View at Scopus
  2. D. E. Hutchinson and M. P. Norton, “Applicability of stochastic process theory to heat conduction in solids with random temperature fields,” Applied Energy, vol. 22, no. 4, pp. 241–269, 1986. View at Publisher · View at Google Scholar · View at Scopus
  3. R. A. Heller and S. Thangjitham, “Probabilistic methods in thermal stress analysis,” in Thermal Stresses, Elsevier Science, R. B. Hetnarski, Ed., pp. 190–268, New York, NY. USA, 1987. View at Google Scholar
  4. R. Chiba, “Stochastic analysis of heat conduction and thermal stresses in solids: a review,” in Heat Transfer Phenomena and Applications, InTech, S. N. Kazi, Ed., Rijeka, Croatia, 2012. View at Google Scholar
  5. A. Campo and T. Yoshimura, “Random heat transfer in flat channels with timewise variation of ambient temperature,” International Journal of Heat and Mass Transfer, vol. 22, no. 1, pp. 5–12, 1979. View at Publisher · View at Google Scholar · View at Scopus
  6. A. G. Madera and A. N. Sotnikov, “Method for analyzing stochastic heat transfer in a fluid flow,” Applied Mathematical Modelling, vol. 20, no. 8, pp. 588–592, 1996. View at Publisher · View at Google Scholar · View at Scopus
  7. M. Kamiński, “Stochastic problem of viscous incompressible fluid flow with heat transfer,” ZAMM, vol. 81, pp. 827–837, 2001. View at Google Scholar
  8. O. P. Le Maitre, M. T. Reagan, H. . Najm, R. G. Ghanem, and O. M. Knio, “A stochastic projection method for fluid flow: II. Random process,” Journal of Computational Physics, vol. 181, no. 1, pp. 9–44, 2002. View at Publisher · View at Google Scholar · View at MathSciNet
  9. B. Ganapathysubramanian and N. Zabaras, “Sparse grid collocation schemes for stochastic natural convection problems,” Journal of Computational Physics, vol. 225, no. 1, pp. 652–685, 2007. View at Publisher · View at Google Scholar · View at MathSciNet · View at Scopus
  10. B. Schieche and J. Lang, “Uncertainty quantification for thermo-convective Poiseuille flow using stochastic collocation,” International Journal of Computational Science and Engineering, vol. 9, no. 5-6, pp. 465–477, 2014. View at Publisher · View at Google Scholar · View at Scopus
  11. T. P. Sommer, R. M. C. So, and H. S. Zhang, “Heat transfer modeling and the assumption of zero wall temperature fluctuations,” Transactions - ASME: Journal of Heat Transfer, vol. 116, no. 4, pp. 855–863, 1994. View at Publisher · View at Google Scholar · View at Scopus
  12. E. Semma, V. Timchenko, M. El Ganaoui, and E. Leonardi, “The effect of wall temperature fluctuations on the heat transfer and fluid flow occuring in a liquid enclosure,” International Journal of Heat and Fluid Flow, vol. 26, no. 4, pp. 547–557, 2005. View at Publisher · View at Google Scholar · View at Scopus
  13. B. M. Nicolai and J. De Baerdemaeker, “Simulation of heat transfer in foods with stochastic initial and boundary conditions,” Trans IChemE, Food and Bioproducts Processing, vol. 70 (Part C), pp. 78–82, 1992. View at Google Scholar
  14. Y. Joshi and B. Gebhart, “Vertical transient natural convection flows in cold water,” International Journal of Heat and Mass Transfer, vol. 27, no. 9, pp. 1573–1582, 1984. View at Publisher · View at Google Scholar · View at Scopus
  15. T. Paul, B. K. Jha, and A. K. Singh, “Transient free convective flow in a vertical channel with constant temperature and constant heat flux on walls,” Heat and Mass Transfer/Waerme- und Stoffuebertragung, vol. 32, no. 1-2, pp. 61–63, 1996. View at Publisher · View at Google Scholar · View at Scopus
  16. A. K. Singh, H. R. Gholami, and V. M. Soundalgekar, “Transient free convection flow between two vertical parallel plates,” Heat and Mass Transfer/Waerme- und Stoffuebertragung, vol. 31, no. 5, pp. 329–331, 1996. View at Publisher · View at Google Scholar · View at Scopus
  17. M. N. Ozisik, Boundary value problems of heat conduction, New York, NY, USA, Dover, 1989.
  18. J. C. Samuels, “Heat conduction in solids with random external temperatures and/or random internal heat generation,” International Journal of Heat and Mass Transfer, vol. 9, no. 4, pp. 301–314, 1966. View at Publisher · View at Google Scholar · View at Scopus
  19. D. R. Axelrad, Stochastic Mechanics of Discrete Media, Springer Berlin Heidelberg, Berlin, Heidelberg, 1993. View at Publisher · View at Google Scholar
  20. V. Krishnan, Probability and random processes, John Wiley and Sons, Hoboken, 2nd edition, 2015.
  21. S. Amada, “Thermal stresses in bodies with random temperature distribution at their boundaries,” Zairyo/Journal of the Society of Materials Science, vol. 31, no. 342, pp. 251–257, 1982. View at Publisher · View at Google Scholar · View at Scopus
  22. R. Chiba and Y. Sugano, “Stochastic thermoelastic problem of a functionally graded plate under random temperature load,” Archive of Applied Mechanics, vol. 77, no. 4, pp. 215–227, 2007. View at Publisher · View at Google Scholar · View at Scopus
  23. R. F. Stengel, Optimal Control and Estimation, Dover, New York, NY, USA, 1994. View at MathSciNet
  24. G. A. Pavliotis, Stochastic processes and applications: diffusion processes, the Fokker-Planck and Langevin equations, Texts in Applied Mathematics, Springer, New York, NY, USA, 2014. View at Publisher · View at Google Scholar · View at MathSciNet