Recovering temperature dependence of heat transfer coefficient in electronic circuits

Inverse Problems in Science and Engineering

Volumn 17, Issue 8, 2009, Pages 1129-1142

  Janicki, M ^a,c   Kindermann, S ^b  

^a JOHANN RADON INSTITUTE FOR COMPUTATIONAL AND APPLIED MATHEMATICS   (Austria)

^b JOHANNES KEPLER UNIVERSITY LINZ   (Austria)

^c LODZ UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

Heat equation; Heat transfer coefficient temperature dependence

Indexed keywords

ELECTRONIC CIRCUITS; ELECTRONIC SYSTEMS; HEAT EQUATION; HEAT EXCHANGE; HYBRID CIRCUIT; PROBLEM SOLVERS; TEMPERATURE DEPENDENCE; TEMPERATURE DEPENDENT; TEMPERATURE GRADIENT; THERMAL MODEL; THERMAL SIMULATIONS;

DIFFERENTIAL EQUATIONS; ELECTRON TUBES; ELECTRONIC STRUCTURE; GREEN'S FUNCTION; HEAT TRANSFER COEFFICIENTS; INVERSE PROBLEMS; SIMULATORS; TEMPERATURE DISTRIBUTION; THERMOGRAPHY (TEMPERATURE MEASUREMENT);

HEAT EXCHANGERS;

EID: 70350745959     PISSN: 17415977     EISSN: 17415985     Source Type: Journal    
DOI: 10.1080/17415970903222997     Document Type: Article

References (25)

1. M.N. Ozisik, Heat Conduction, John Wiley & Sons, New York, 1993.
2. F.P. Incropera and D.P. De Witt, Fundamentals of Heat and Mass Transfer, John Wiley & Sons, New York, 2002.
3. Y. Gerstenmaier and G. Wachutka, Transient temperature fields with general nonlinear boundary conditions in electronic systems, IEEE Trans. Compon. Pack. Technol. 28 (2005), pp. 23-33.
4. M. Rencz and V. Szekely, Studies on the nonlinearity effects in the dynamic compact model generation of packages, IEEE Trans. Compon. Pack. Technol. 27 (2004), pp. 124-130.
5. J.P. Holman, Heat Transfer, McGraw-Hill, New York, 1985.
6. A. Friedman, Partial Differential Equations of Parabolic Type, Prentice Hall, Englewood Cliffs, NJ, 1964.
7. C.V. Pao, Quasilinear parabolic and elliptic equations with nonlinear boundary conditions, Nonlinear Anal. Theor. 66 (2007), pp. 639-62.
8. R.E. Showalter, Monotone Operators in Banach Space and Nonlinear Partial Differential Equations, AMS, Providence, RI, 1997.
9. J.V. Beck, K.D. Cole, A. Haji-Sheikh, and B. Litkouhi, Heat Conduction Using Green's Functions, Hemisphere, New York, 1992.
10. A. Haji-Sheikh and J.V. Beck, Temperature solution in multi-dimensional multi-layer bodies, Int. J. Heat Mass Transfer 45 (2002), pp. 1865-1877.
11. M. Janicki, G. De Mey, and A. Napieralski, Thermal analysis of layered electronic circuits with Green's functions, Microelectron J. 38 (2007), pp. 177-184.
12. E. Zeidler, Applied Functional Analysis: Main Principles and Applications, Springer, Berlin, 1995.
13. O.M. Alifanov, Solution of an inverse problem of heat conduction by iteration methods, J. Eng. Phys. Thermophys. 26 (1974), pp. 471-476.
14. J. Beck, B. Blackwell, and C. Clair, Inverse Heat Conduction Ill-posed Problems, John Wiley & Sons, New York, 1985.
15. A. Roesch, Stability estimates for the identification of nonlinear heat transfer laws, Inv. Problems 12 (1996), pp. 743-756.
16. M. Pilant and W. Rundell, Identification of nonlinear flux terms in a parabolic initial-boundary value problem, in Invariant Imbedding and Inverse Problems: Proceedings of the SIAM Applied Mathemetics, J.P. Corones, ed., 1992, pp. 241-257.
17. O.M. Alifanov, E.A. Artyukhin, and I.Y. Gedzhadze, Iterative regularized solution of an inverse heat conduction problem, Dokl. Math. 59 (1999), pp. 145-148.
18. G. Chavent and P. Lemonnier, Identification de la non-linearite d'une equation parabolique quasilineaire, Appl. Math. Opt. 1 (1974), pp. 121-162.
19. H.W. Engl, M. Hanke, and A. Neubauer, Regularization of Inverse Problems, Kluwer Academic Publishers, Dordrecht, 1996.
20. L. Landweber, An iteration formula for Fredholm integral equations of the first kind, Amer. J. Math. 73 (1951), pp. 615-624.
21. P. Kuegler, A derivative-free Landweber iteration for parameter identification in certain elliptic PDEs, Inv. Problems 19 (2003), pp. 1407-1426.
22. O. Scherzer, Convergence criteria of iterative methods based on Landweber iteration for solving nonlinear problems, J. Math. Anal. Appl. 194 (1995), pp. 911-933.
23. B. Kaltenbacher, A. Neubauer, and O. Scherzer, Iterative Regularization Methods for Nonlinear Ill-Posed Problems, de Gruyter, Berlin, 2008.
24. M. Hanke, A. Neubauer, and O. Scherzer, A convergence analysis of the Landweber iteration for nonlinear ill-posed problems, Numer. Math. 72 (1995), pp. 21-37.
25. M. Janicki, P. Pietrzak, B. Vermeersch, J. Banaszczyk, M. Kaminski, G. De Mey, and A. Napieralski, Determining thermal simulation data from transient measurements, in Proceedings of the 24th IEEE Semiconductor Thermal Measurement and Management Symposium (SEMI-THERM'08), R. Wilcoxon, ed., San Jose, USA, 16-20 March, 2008, IEEE, Piscataway, 2008, pp. 200-204.