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RESEARCH PAPER

Determination of Temperatures and Heat Fluxes on Surfaces and Interfaces of Multidomain Three-Dimensional Electronic Components

[+] Author and Article Information
Brian H. Dennis, Zhen-xue Han, George S. Dulikravich

J. Electron. Packag 126(4), 457-464 (Jan 24, 2005) (8 pages) doi:10.1115/1.1827261 History: Received April 26, 2004; Revised April 28, 2004; Online January 24, 2005
Copyright © 2004 by ASME
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References

Dennis,  B. H., and Dulikravich,  G. S., 1999, “Simultaneous Determination of Temperatures, Heat Fluxes, Deformations, and Tractions on Inaccessible Boundaries,” ASME J. Heat Transfer, 121(1), pp. 537–545.
Larsen, M. E., 1985, “An Inverse Problem: Heat Flux and Temperature Prediction for a High Heat Flux Experiment,” Tech. Rep. SAND-85-2671, Sandia National Laboratories, Albuquerque, NM.
Hensel,  E. H., and Hills,  R., 1989, “Steady-State Two-Dimensional Inverse Heat Conduction,” Numer. Heat Transfer, Part A, 15, pp. 227–240.
Martin,  T. J., and Dulikravich,  G. S., 1996, “Inverse Determination of Boundary Conditions in Steady Heat Conduction,” ASME J. Heat Transfer, 3, pp. 546–554.
Olson, L. G., and Throne, R. D., 2000, “The Steady Inverse Heat Conduction Problem: A Comparison for Methods of Inverse Parameter Selection,” 34th National Heat Transfer Conference-NHTC’00, Paper No. NHTC2000-12022, Pittsburg.
Martin,  T. J., Halderman,  J., and Dulikravich,  G. S., 1995, “An Inverse Method for Finding Unknown Surface Tractions and Deformations in Elastostatics,” Comput. Struct., 56, pp. 825–836.
Tikhonov, A. N., and Arsenin, V. Y., 1977, Solutions of Ill Posed Problems, Wistom and Sons, Washington, DC.
Dennis, B. H., and Dulikravich, G. S., 2001, “A 3-D Finite Element Formulation for the Determination of Unknown Boundary Conditions in Heat Conduction,” Proc. of International Symposium on Inverse Problems in Engineering Mechanics, M. Tanaka, ed., Nagano City, Japan.
Neumaier,  A., 1998, “Solving Ill-Conditioned and Singular Linear Systems: A Tutorial on Regularization,” SIAM Rev., 40, pp. 636–666.
Dennis,  B. H., Dulikravich,  G. S., and Yoshimura,  S., 2003, “A Finite Element Formulation for the Determination of Unknown Boundary Conditions for 3-D Steady Thermoelastic Problems,” ASME J. Heat Transfer, (submitted).
Matstoms, P., 1991, “The Multifrontal Solution of Sparse Least Squares Problems,” Ph.D. thesis, Linköping University, Sweden.

Figures

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Cross section showing material regions for BGA model
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Hexahedral mesh for PWB and EMC
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Closeup view of mesh for solder balls, solder mask, and PWB
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Computed temperature on PWB and EMC
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Computed temperature on solder balls, solder mask, and PWB
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Computed inverse and forward temperature on BT substrate bottom
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Computed inverse and forward temperature on die bottom
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Computed forward temperature on package top with measurement errors
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Variation of average relative error in temperature on BT substrate bottom
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Computed inverse and forward temperature on BT substrate bottom with measurement errors and Λ=1.0×10−4
Grahic Jump Location
Computed inverse and forward temperature on die bottom with measurement errors and Λ=1.0×10−4

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