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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 74, 2018 - Issue 6
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Original Articles

Identification of boundary conditions for non-Fourier heat conduction problems by differential transformation DRBEM and improved cuckoo search algorithm

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Pages 818-839 | Received 19 Oct 2018, Accepted 03 Feb 2019, Published online: 05 Apr 2019

References

  • M. J. Maurer and H. A. Thompson, “Non-Fourier effects at high heat flux,” J. Heat Transfer, vol. 95, no. 2, pp. 284–286, 1973. DOI: 10.1115/1.3450051.
  • D. E. Glass, M. N. Özişik, and B. Vick, “Hyperbolic heat conduction with surface radiation,” Int. J. Heat Mass Transfer, vol. 28, no. 10, pp. 1823–1830, 1985. DOI: 10.1016/0017-9310(85)90204-2.
  • F. Wu, Q. Gao, and W. X. Zhong, “Fast precise integration method for hyperbolic heat conduction problems,” Appl. Math. Comput., vol. 34, pp. 791–800, 2013. DOI: 10.1007/s10483-013-1707-6.
  • S. N. Li and B. Y. Cao, “Approximate analyses of Fourier and non-Fourier heat conduction models by the variational principles based on Laplace transforms,” Numer. Heat Transfer A, vol. 71, pp. 962–977, 2017.
  • H. Askarizadeh and H. Ahmadikia, “Analytical study on the transient heating of a two-dimensional skin tissue using parabolic and hyperbolic bioheat transfer equations,” Appl. Math. Model, vol. 39, no. 13, pp. 3704–3720, 2015. DOI: 10.1016/j.apm.2014.12.003.
  • H. L. Lee, W. J. Chang, S. C. Wu, and Y. C. Yang, “An inverse problem in estimating the base heat flux of an annular fin based on the hyperbolic model of heat conduction,” Int. Commun. Heat Mass., vol. 44, pp. 31–37, 2013. DOI: 10.1016/j.icheatmasstransfer.2013.02.007.
  • Y. C. Yang, W. L. Chen, H. M. Chou, and J. L. L. Salazar, “Inverse hyperbolic thermoelastic analysis of a functionally graded hollow circular cylinder in estimating surface heat flux and thermal stresses,” Int. J. Heat Mass Transfer, vol. 60, pp. 125–133, 2013. DOI: 10.1016/j.ijheatmasstransfer.2012.12.052.
  • K. Veerabhadrappa, G. Vinayakaraddy, K. N. Seetharamu, P. G. Hegde, and V. Krishna, “Transient behavior of three-fluid exchanger with three thermal communications under step change in inlet temperature of fluids using finite element method,” Appl. Therm. Eng., vol. 108, pp. 1390–1400, 2016. DOI: 10.1016/j.applthermaleng.2016.08.008.
  • S. C. Mishra, A. Stephen, and M. Y. Kim, “Analysis of non-Fourier conduction-radiation heat transfer in a cylindrical enclosure,” Numer. Heat Transfer A, vol. 58, no. 12, pp. 943–962, 2010. DOI: 10.1080/10407782.2010.529029.
  • N. P. Karagiannakis, G. C. Bourantas, A. N. Kalarakis, E. D. Skouras, and V. N. Burganos, “Transient thermal conduction with variable conductivity using the meshless local Petrov-Galerkin method,” Appl. Math. Comput., vol. 272, pp. 676–686, 2016. DOI: 10.1016/j.amc.2015.02.084.
  • J. Sladek, V. Sladek, and C. Zhang, “Transient heat conduction analysis in functionally graded materials by the meshless local boundary integral equation method,” Comp. Mater. Sci., vol. 28, no. 3-4, pp. 494–504, 2003. DOI: 10.1016/j.commatsci.2003.08.006.
  • P. W. Partridge and, C. A. Brebbia, Dual Reciprocity Boundary Element Method. Southampton Boston: Computational Mechanics Publication, 1992.
  • M. Tanaka and W. Chen, “Dual reciprocity BEM applied to transient elastodynamic problems with differential quadrature method in time,” Comput. Method Appl. M, vol. 190, no. 18-19, pp. 2331–2347, 2001. DOI: 10.1016/S0045-7825(00)00237-1.
  • B. Yu, H. L. Zhou, H. L. Chen, and Y. Tong, “Precise time-domain expanding dual reciprocity boundary element method for solving transient heat conduction problems,” Int. J. Heat Mass Transfer, vol. 91, pp. 110–118, 2015. DOI: 10.1016/j.ijheatmasstransfer.2015.07.109.
  • J. K. Zhou, Differential Transformation and Its Applications for Electrical Circuits. Wuhan: Huazhong Science & Technology University Press, 1986.
  • S. Sadri, M. R. Raveshi, and S. Amiri, “Efficiency analysis of straight fin with variable heat transfer coefficient and thermal conductivity,” J. Mech. Sci. Technol., vol. 26, no. 4, pp. 1283–1290, 2012. DOI: 10.1007/s12206-012-0202-4.
  • A. Moradi, T. Hayat, and A. Alsaedi, “Convection-radiation thermal analysis of triangular porous fins with temperature-dependent thermal conductivity by DTM,” Energ. Convers. Manage., vol. 77, pp. 70–77, 2014. DOI: 10.1016/j.enconman.2013.09.016.
  • B. Yu, H. L. Zhou, J. Yan, and Z. Meng, “A differential transformation boundary element method for solving transient heat conduction problems in functionally graded materials,” Numer. Heat Transfer A, vol. 70, no. 3, pp. 293–309, 2016. DOI: 10.1080/10407782.2016.1173471.
  • D. B. Ingham, and Y. Yuan, “The solution of a nonlinear inverse problem in heat transfer,” IMA J. Appl. Math., vol. 50, no. 2, pp. 113–132, 1993. DOI: 10.1093/imamat/50.2.113.
  • D. Lesnic, L. Elliott, and D. B. Ingham, “An iterative boundary element method for solving numerically the Cauchy problem for the Laplace equation,” Eng. Anal. Bound. Elem., vol. 20, no. 2, pp. 123–133, 1997. DOI: 10.1016/S0955-7997(97)00056-8.
  • N. S. Mera, L. Elliott, D. B. Ingham, and D. Lesnic, “The boundary element solution of the Cauchy steady heat conduction problem in an anisotropic medium,” Int. J. Numer. Methods Eng., vol. 49, no. 4, pp. 481–499, 2000. DOI: 10.1002/1097-0207(20001010)49:4<481::AID-NME970>3.0.CO;2-5.
  • A. Behbahani-Nia, and F. Kowsary, “A dual reciprocity BE-based sequential function specification solution method for inverse heat conduction problems,” Int. J. Heat Mass Transfer, vol. 47, no. 6-7, pp. 1247–1255, 2004. DOI: 10.1016/j.ijheatmasstransfer.2003.09.023.
  • M. Cui, L. Zhou, J. Mei, and B. W. 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. DOI: 10.1080/10407782.2017.1394129.
  • M. Cui, J. Mei, B. W. Zhang, B. B. Xu, L. Zhou, and Y. W. Zhang, “Inverse identification of boundary conditions in a scramjet combustor with a regenerative cooling system,” Appl. Therm. Eng., vol. 134, pp. 555–563, 2018. DOI: 10.1016/j.applthermaleng.2018.02.038.
  • M. R. Golbahar Haghighi, P. Malekzadeh, H. Rahideh, and M. Vaghefi, “Inverse transient heat conduction problems of a multilayered functionally graded cylinder,” Numer. Heat Transfer A, vol. 61, no. 9, pp. 717–733, 2012. DOI: 10.1080/10407782.2012.671017.
  • H. T. Chen, S. Y. Peng, P. C. Yang, and L. C. Fang, “Numerical method for hyperbolic inverse heat conduction problems,” Int. Commun. Heat Mass Transfer, vol. 28, no. 6, pp. 847–856, 2001. DOI: 10.1016/S0735-1933(01)00288-3.
  • C. H. Huang and H. H. Wu, “An inverse hyperbolic heat conduction problem in estimating surface heat flux by the conjugate gradient method,” J. Phys. D Appl. Phys., vol. 39, no. 18, pp. 4087–4096, 2006. DOI: 10.1088/0022-3727/39/18/020.
  • C. H. Huang and C. Y. Lin, “An iterative regularization method in estimating the unknown energy source by laser pulses with a dual-phase-lag model,” Int. J. Numer. Methods Eng., vol. 76, no. 1, pp. 108–126, 2008. DOI: 10.1002/nme.2325.
  • S. Payan, S. M. Hosseini Sarvari, and A. Behzadmehr, “Reconstruction of temperature distribution in the combustion region of a non-gray medium,” Numer. Heat Transfer A, vol. 68, no. 8, pp. 908–924, 2015. DOI: 10.1080/10407782.2015.1023125.
  • C. F. Zhao, Z. Luo, Y. Li, M. N. Feng, and W. B. Xuan, “Inverse heat conduction model for the resistance spot welding of aluminum alloy,” Numer. Heat Transfer A, vol. 70, no. 12, pp. 1330–1344, 2016. DOI: 10.1080/10407782.2016.1244391.
  • D. G. Yang, X. X. Yue, and Q. B. Yang, “Virtual boundary element method in conjunction with conjugate gradient algorithm for three-dimensional inverse heat conduction problems,” Numer. Heat Transfer B, vol. 72, no. 6, pp. 421–430, 2017. DOI: 10.1080/10407790.2017.1409525.
  • H. C. Chen, J. I. Frankel, and M. Keyhani, “Nonlinear inverse heat conduction problem of surface temperature estimation by calibration integral equation method,” Numer. Heat Transfer B, vol. 73, no. 5, pp. 1–29, 2018.
  • Y. C. Yang, “Direct and inverse solutions of the two-dimensional hyperbolic heat conduction problems,” Appl. Math. Model., vol. 33, no. 6, pp. 2907–2918, 2009. DOI: 10.1016/j.apm.2008.10.001.
  • C. L. Karr, I. Yakushin, and K. Nicolosi, “Solving inverse initial-value, boundary-value problems via genetic algorithm,” Eng. Appl. Artif. Intel., vol. 13, no. 6, pp. 625–633, 2000. DOI: 10.1016/S0952-1976(00)00025-7.
  • Y. T. Yang, K. T. Tsai, H. W. Tang, and S. E. Chung, “Numerical simulations and optimization of porous pin fins in a rectangular channel,” Numer. Heat Transfer A, vol. 70, no. 7, pp. 791–808, 2016. DOI: 10.1080/10407782.2016.1214479.
  • F. B. Liu, “A hybrid method for the inverse heat transfer of estimating fluid thermal conductivity and heat capacity,” Int. J. Therm. Sci., vol. 50, no. 5, pp. 718–724, 2011. DOI: 10.1016/j.ijthermalsci.2010.11.020.
  • Y. H. Li, G. J. Wang, and H. Chen, “Simultaneously estimation for surface heat fluxes of steel slab in a reheating furnace based on DMC predictive control,” Appl. Therm. Eng., vol. 80, pp. 396–403, 2015. DOI: 10.1016/j.applthermaleng.2015.01.069.
  • X. S. Yang, and S. Deb, “Cuckoo search via Lévy flights,” in World Congress on Nature and Biologically Inspired Computing (NaBIC 2009), IEEE Publications, Coimbatore, India, pp. 210–214, 2009.
  • T. T. Nguyen, D. N. Vo, and A. V. Truong, “Cuckoo search algorithm for short-term hydrothermal scheduling,” Appl. Energ., vol. 132, pp. 276–287, 2014. DOI: 10.1016/j.apenergy.2014.07.017.
  • D. S. Naumann, B. Evans, S. Walton, and O. Hassan, “A novel implementation of computational aerodynamic shape optimisation using modified cuckoo search,” Appl. Math. Model., vol. 40, pp. 4543–4559, 2016. DOI: 10.1016/j.apm.2015.11.023.
  • E. Valian, S. Tavakoli, S. Mohanna, and A. Haghi, “Improved cuckoo search for reliability optimization problems,” Comput. Ind. Eng., vol. 64, no. 1, pp. 459–468, 2013. DOI: 10.1016/j.cie.2012.07.011.
  • Udayraj, K. Mulani, P. Talukdar, A. Das, and R. Alagirusamy, “Performance analysis and feasibility study of ant colony optimization, particle swarm optimization and cuckoo search algorithms for inverse heat transfer problems,” Int. J. Heat Mass Transfer, vol. 89, pp. 359–378, 2015.
  • H.-L. Zhou, X.-H. Zhao, B. Yu, H.-L. Chen, and Z. Meng, “Firefly algorithm combined with Newton method to identify boundary conditions for transient heat conduction problems,” Numer. Heat Transfer B, vol. 71, no. 3, pp. 253–269, 2017. DOI: 10.1080/10407790.2016.1277915.
  • H. L. Chen, B. Yu, H. L. Zhou, and Z. Meng, “Identification of transient boundary conditions with improved cuckoo search algorithm and polynomial approximation,” Eng. Anal. Bound. Elem., vol. 95, pp. 124–141, 2018.
  • I. Pavlyukevich, “Lévy flights, Non-local search and simulated annealing,” J. Comput. Phys., vol. 226, no. 2, pp. 1830–1844, 2007.
  • D. F. Shanno, “Conditioning of quasi-newton methods for function minimization,” Math. Comput., vol. 24, no. 111, pp. 647–656, 1970. DOI: 10.1090/S0025-5718-1970-0274029-X.

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