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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 74, 2018 - Issue 5
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Articles

Computing sensitivity coefficients by using complex differentiation: Application to heat conduction problem

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Pages 729-745 | Received 29 Oct 2018, Accepted 04 Feb 2019, Published online: 25 Mar 2019

References

  • K. M. Shirvan, S. Mirzakhanlari, A. J. Chamkha, and M. Mamourian, “Numerical simulation and sensitivity analysis of effective parameters on natural convection and entropy generation in a wavy surface cavity filled with a nanofluid using rsm,” Numer. Heat Transf. A Appl., vol. 70, no. 10, pp. 1157–1177, 2016.
  • T. DeGroot Christopher, “Automatic differentiation of a finite-volume-based transient heat conduction code for sensitivity analysis,” Numer. Heat Transf. B Fundam., vol. 73, no. 5, pp. 292–307, 2018.
  • K. J. Dowding, B. F. Blackwell, and R. J. Cochran, “Application of sensitivity coefficient for heat conduction problems,” Numer. Heat Transf. B Fundam., vol. 36, no. 1, pp. 33–55, 1999.
  • B. F. Blackwell, K. J. Dowding, and R. J. Cochran, “Development and implementation of sensitivity coefficient equations for heat conduction problems,” Numer. Heat Transfer B Fundam., vol. 36, no. 1, pp. 15–32, 1999.
  • E. Turgeon, D. Pelletier, and J. Borggaard, “A general continuous sensitivity equation formulation for complex flows,” Numer. Heat Transfer B Fundam., vol. 42, no. 6, pp. 485–498, 2002.
  • W. K. Ki, and W. B. Seung, “Inverse radiation design problem in a two-dimensional radiatively active cylindrical medium using automatic differentiation and Broyden combined update,” Numer. Heat Transfer A Appl. vol. 50, no. 6, pp. 525–543, 2006.
  • N. Daouas, “An alternative sensitivity method for a two-dimensional inverse heat conduction-radiation problem based on transient hot-wire measurements,” Numer. Heat Transfer B Fundam., vol. 73, no. 2, pp. 106–128, 2018.
  • J. N. Lyness, “Numerical algorithms based on the theory of complex variable,” in ACM Proceedings of the 22nd National Conference. Washington, DC: Thompson Book, 1967, pp. 125–133.
  • J. N. Lyness, and C. B. Moler, “Numerical differentiation of analytic functions,” SIAM J. Numer. Anal., vol. 4, no. 2, pp. 202–210, 1967.
  • W. Squire, and G. Trapp, “Using complex variables to estimate derivatives of real functions,” SIAM Rev., vol. 40, no. 1, pp. 110–122, 1998.
  • A. Voorhees, H. Millwater, R. Bagley, and P. Golden, “Fatigue sensitivity analysis using complex variable methods,” Int. J. Fatigue, vol. 40, pp. 61–73, 2012.
  • L. F. Shampine, “Accurate numerical derivative in Matlab,” ACM Trans. Math. Softw., vol. 33, no. 4, 1–17, 2007.
  • J. R. R. A. Martins, A coupled-adjoint method for high fidelity aero-structural optimization. PhD thesis, Stanford University, California, 2002.
  • J. R. R. A. Martins, I. M. Kroo, and J. J. Alonso, “An automated method for sensitivity analysis using complex variables,” AIAA Paper, 2000-0689, 2000.
  • X. Gao, and M. He, “A new analysis approach for multi-region heat conduction BEM using complex variable differentiation method,” Eng. Anal. Boundary Elements, vol. 29, no. 8, pp. 788–795, 2005.
  • B. F. Blackwell, and K. J. Dowding, Handbook of Numerical Heat Transfer, Chapter Sensitivity Aanalysis and Uncertainty Propagation of Computational Models. New Jersey: Wiley, 2006, pp. 443–469.
  • X. Yu, Y. Bai, M. Cui, and X. Gao, “Inverse analysis of thermal conductivities in transient non-homogeneous and non-linear heat conductions using BEM based on complex variable differentiation method,” Science China: Physics, Mechanics & Astronomy, vol. 56, no. 5, pp. 966–973, 2013.
  • M. Cui, L. Nan, Y. Liu, and X. Gao, “Robust inverse approach for two-dimensional transient nonlinear heat conduction problems,” J. Thermophys. Heat Transfer, vol. 29, no. 2, pp. 253–262, 2015.
  • M. Cui, L. Zhou, J. Mei, and B. Zhang, “Estimation of slab surface radiative emissivities by solving an inverse coupled conduction, convection, and radiation problem,” Numer. Heat Transfer A, vol. 72, no. 10, pp. 765–779, 2017.
  • M. Cui, K. Yan, X. Xu, S. Wang, and X. Gao, “A modified Levenberg Marquardt algorithm for simultaneous estimation of multi-parameters of boundary heat flux by solving transient nonlinear inverse heat conduction problems,” Int. J. Heat Mass Transfer, vol. 97, pp. 908–916, 2016.
  • K. Abahri, R. Bennacer, and R. Belarbi, “Sensitivity analyses of convective and diffusive driving potentials on combined heat air and mass transfer in hygroscopic materials,” Numer. Heat Transfer A Appl., vol. 69, no. 10, pp. 1079–1091, 2016.
  • J. V. Beck, and K. J. Arnold, Parameter Estimation in Engineering and Sciences. New York: Wiley, 1977.
  • D. Ucinski, Optimal Measurement Methods for Distributed Parameter System Identification. Boca Raton: CRC Press, 2004.
  • M. N. Ozisik and H. R. Orlande, Inverse Heat Transfer, Fundamentals & Applications. New York: Taylor & Francis, 2000.
  • E. G. Philip, W. Murray, and H. M. Wright, Practical Optimization. London: Emerald Group, 1982.
  • G. Corliss, Automatic Differentiation of Algorithms: From Simulation to Optimization. New York: Springer, 2002.
  • C. Bischof, P. Khademi, A. Mauer, and A. Carle, “Adifor 2.0: Automatic differentiation of Fortran 77 programs,” IEEE Computat. Sci. Eng., vol. 3, no. 3, pp. 18–32, 1996.
  • C. Bischof, A. Carle, G. Corliss, A. Griewank, and P. Hovland, “Adifor: Generating derivative codes from Fortran programs,” Sci. Program., vol. 1, no. 1, pp. 11–29, 1992.
  • M. N. Ozisik, Finite Difference Methods in Heat Transfer. Boca Raton, FL: CRC Press, 1994.
  • G. D. Smith, Numerical Solution of Partial Differential Equations. New York: Oxford University Press, 1985.
  • M. N. Ozisik, Heat Conduction. New York: Wiley, 1993.
  • H. S. Carslaw, and J. C. Jaeger, Conduction of Heat in Solids. Oxford: Clarendon Press, 1959.
  • M. N. Ozisik, and D. W. Hahn, Heat Conduction. Hoboken, NJ: Wiley, 2012.
  • K. D. Cole, J. V. Beck, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green’s Functions. Boca Raton, FL: Taylors & Francis, 2011.
  • J. R. R. A. Martins, P. Sturdza, and J. J. Alonso, “The complex-step derivative approximation,” ACM Trans. Math. Softw., vol. 29, no. 3, pp. 245–262, 2003.
  • R. T. Haftka, and D. S. Malkus, “Calculation of sensitivity derivatives in thermal problems by finite differences,” Int. J. Numer. Methods Eng., vol. 17, no. 12, pp. 1811–1821, 1981.
  • The MathWorks Inc. MATLAB R2017b. 3 Apple Hill Dr., Natick, MA 01760, 2017.

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