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Numerical Heat Transfer, Part B: Fundamentals
An International Journal of Computation and Methodology
Volume 47, 2005 - Issue 2
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Original Articles

DESIGN, FORMULATION, AND SOLUTION OF MULTIDIMENSIONAL INVERSE HEAT CONDUCTION PROBLEMS

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Pages 111-133 | Received 03 Oct 2003, Accepted 05 Jun 2004, Published online: 01 Sep 2006

REFERENCES

  • J. Beck , B. Blackwell , and C St. Clair , Inverse Heat Conduction. Ill-Posed Problems , Wiley , New York , 1985 .
  • J. Blum and W. Marquardt , Model-Based Design, Control, and Evaluation of Transient Boiling Experiments , in F. Mayinger and B. Giernoth (eds.), Transient Phenomena in Multiphase and Multicomponent Systems , pp. 229 – 240 , Wiley-VCH , Weinheim , 2000 .
  • H. W. Engl , Regularization Methods for the Stable Solution in Inverse Problems , Surv. Math. Ind. , 2 , no. 2–3 , pp. 71 – 143 , 1993 .
  • A. N. Tikhonov and V. Y. Arsenin , Solutions of Ill-Posed Problems , V. H. Winston and Sons , Washington , 1977 .
  • M. Raynaud and J. Bransier , A New, Finite-Difference Method for the Nonlinear Inverse Heat Conduction Problem , Numer. Heat Transfer , 9 , pp. 27 – 42 , 1986 .
  • Y. Jarny , M. Ozisik , and J. Bardon , A General Optimization Method Using Adjoint Equation for Solving Multidimensional Inverse Heat Conduction , Int. J. Heat Mass Transfer , 34 , 11 , pp. 2911 – 2919 , 1991 . [CROSSREF]
  • M. Imber , Temperature Extrapolation Mechanism for Two-Dimensional Heat Flow , AIAA J. , 12 , pp. 1089 – 1093 , 1974 .
  • T. Yoshimura , and K. Ikuta , Inverse Heat-Conduction Problem by Finite-Element Formulation , Int. J. Syst. Sci. . 16 , pp. 1365 – 1376 , 1985 . [CSA]
  • H.-J. Reinhardt , A Numerical Method for the Solution of Two-Dimensional Inverse Heat Conduction Problems , Int. J. Numer. Meth. Eng. , 32 , pp. 363 – 383 , 1991 . [CSA]
  • T. Hsu , N. Sun , G. Chen , and Z. Gong , Finite Element Formulation for Two-Dimensional Inverse Heat Conduction Analysis, ASME J. Heat Transfer , 114, pp. 553–557, 1992. [CSA]
  • A. Haji-Sheikh , L. Yan , Multidimensional Inverse Heat Conduction Using Alternative Green's Function Solution , Int. Commun. Heat Mass Transfer , 19 , pp. 661 – 672 , 1992 . [CROSSREF] [CSA]
  • D. A. Murio , Y. Liu , and H. Zheng , Numerical Experiments in Multidimensional IHCP on Bounded Domains , in H. W. Engl and W. Rundell (eds.), Inverse Problems in Diffusion Processes. Proc. GAMM-SIAM Symp. , pp. 151 – 180 , SIAM , Philadelphia , 1995 .
  • N. M. Al-Najem , A. M. Osman , M. M. El-Refaee , and K. M. Khanafer , Two Dimensional Steady-State Inverse Heat Conduction Problems , Int. Commun. Heat Mass Transfer , 25 , 4 , pp. 541 – 550 , 1998 . [CROSSREF] [CSA]
  • C.-H. Huang and S.-P. Wang , Three-Dimensional Inverse Heat Conduction Problem in Estimating Surface Heat Flux by Conjugate Gradient Method , Int. J. Heat Mass Transfer , 42 , pp. 3387 – 3403 , 1999 . [CROSSREF] [CSA]
  • H. M. Park , and W. S. Jung , On the Solution of Multidimensional Inverse Heat Conduction Problems Using an Efficient Sequential Method , J. Heat Transfer , 123 , pp. 1021 – 1029 , 2001 . [CROSSREF]
  • A. M. Osman , K. J. Dowding , and J. V. Beck , Numerical Solution of the General Two-Dimensional Inverse Heat Conduction Problem (IHCP) , Trans. ASME , vol. 119 , pp. 38 – 45 , February 1997 .
  • A. Kirsch , An Introduction to the Mathematical Theory of Inverse Problems , Springer-Verlag , Berlin , 1995 .
  • N. Al-Najem and M. Özişik , On the Solution of Three-Dimensional Inverse Heat Conduction in Finite Media , Int. J. Heat Mass Transfer , 28 , pp. 2121 – 2128 , 1985 . [CROSSREF] [CSA]
  • D. N. Hào , H. J. Reinhardt , Gradient Methods for Inverse Heat Conduction Problems , Inverse Probl. Eng. , 6 , pp. 177 – 211 , 1998 .
  • C. Le Niliot and P. Gallet , Infrared Thermography Applied to the Resolution of Inverse Heat Conduction Problems: Recovery of Heat Line Sources and Boundary Conditons , Rev. Gen. Therm. , 37 , pp. 629 – 643 , 1998 .
  • E. Videcoq , and D. Petit , Model Reduction for the Resolution of Multidimensional Inverse Heat Conduction Problems , Int. J. Multiphase Flow , 44 , pp. 1899 – 1911 , 2001 .
  • H. M. Park , and J. H. Lee , A Method of Solving Inverse Convection Problems by Means of Mode Reduction , Chem. Eng. Sci. , 53 , 9 , pp. 1731 – 1744 , 1998 . [CROSSREF]
  • J. Blum , W. Marquardt , An Optimal Solution to Inverse Heat Conduction Problems Based on Frequency Domain Interpretation and Observers , Numer. Heat Transfer B , 32 , pp. 453 – 478 , 1997 . [CSA]
  • S. Skogestad , and I. Postlethwaite , Multivariable Feedback Control. Analysis and Design , Wiley , New York , 1996 .
  • L. Silverman , Inversion of Multivariable Linear Systems , IEEE Trans. Automatic Control , vol. AC-14, no. 3, pp 270 – 276 , 1969 . [CROSSREF]
  • S. S. Rao , The Finite Element Method in Engineering , Pergamon Press , Oxford , 1988 .
  • W. Marquardt , Nonlinear Model Reduction for Optimization Based Control of Transient Chemical Processes , Tech. Rept., LFPT Aachen, Aachen, Germany , 2001 .
  • Y. Lui , and D. O. Anderson , Singular Perturbation Approximation of Balanced Systems , Int. J. Process Control , 50 , pp. 1379 – 1405 , 1989 .
  • A. Varga , Model Reduction Routines for SLICOT , Tech. Rept. NICONET Report 1999-8, Working Group on Software WGS, ESAT—Katholieke Universiteit Leuven , 1999 .
  • O. M. Alifanov , E. A. Artyukhin , and S. V. Rumyantsev , Extreme Methods for Solving Ill-Posed Problems with Applications to Inverse Heat Transfer Problems , Begell House , New York , 1995 .
  • A. V. Wouwer , N. Point , S. Porteman , and M. Remy , An Approach to the Selection of Optimal Sensor Locations in Distributed Parameter Systems , J. Process Control , 10 , pp. 291 – 300 , 2000 . [CROSSREF]
  • S. P. Asprey , S. Macchietto , Designing Robust Optimal Dynamic Experiments , J. Process Cont. , 12 , pp. 545 – 556 , 2002 . [CROSSREF] [CSA]
  • D. Gorenflo , W. Fust , A. Luke , E. Danger , and U. Chandra , Pool Boiling Heat Transfer from Tubes with Basic Surface Modifications for Enhancement, 3rd European Thermal-Sciences Conf., Heidelberg , Germany , 2000.

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