In this three-dimensional steady-state inverse heat transfer problem, we determine the magnitude of the spatially dependent volumetric heat source originating from multiple encapsulated chips mounted on a printed circuit board (PCB). Prior to the estimations, the functional form of the multiple heat sources is treated as unknown, leading to its classification as a function estimation challenge within the realm of inverse problems. The utilization of the conjugate gradient method (CGM) as an optimization tool is rooted in its distinct advantage of not requiring any a priori knowledge regarding the functional form of the unidentified quantities. Furthermore, the CGM empowers the simultaneous correction and estimation of multiple unknowns during each iteration, thereby ensuring the consistent possibility of precise estimates.
To affirm the precision of the estimated heat source attributed to multiple chips, a series of numerical experiments were conducted. These experiments encompassed varying inlet air velocities and introduced measurement errors. Notably, the results revealed that meticulous measurements consistently yielded accurate heat generation assessments for the chips, regardless of the prevailing air velocity conditions. The findings underscored that the accuracy of chip heat generation estimates diminished as measurement errors escalated, predominantly due to the ill-posed nature inherent in the inverse problem.
Citation: Cheng-Hung Huang, Ya-Rou Zhong. An inverse problem to estimate simultaneously the heat source strength for multiple integrated circuit chips on a printed circuit board[J]. AIMS Mathematics, 2024, 9(4): 8848-8867. doi: 10.3934/math.2024431
In this three-dimensional steady-state inverse heat transfer problem, we determine the magnitude of the spatially dependent volumetric heat source originating from multiple encapsulated chips mounted on a printed circuit board (PCB). Prior to the estimations, the functional form of the multiple heat sources is treated as unknown, leading to its classification as a function estimation challenge within the realm of inverse problems. The utilization of the conjugate gradient method (CGM) as an optimization tool is rooted in its distinct advantage of not requiring any a priori knowledge regarding the functional form of the unidentified quantities. Furthermore, the CGM empowers the simultaneous correction and estimation of multiple unknowns during each iteration, thereby ensuring the consistent possibility of precise estimates.
To affirm the precision of the estimated heat source attributed to multiple chips, a series of numerical experiments were conducted. These experiments encompassed varying inlet air velocities and introduced measurement errors. Notably, the results revealed that meticulous measurements consistently yielded accurate heat generation assessments for the chips, regardless of the prevailing air velocity conditions. The findings underscored that the accuracy of chip heat generation estimates diminished as measurement errors escalated, predominantly due to the ill-posed nature inherent in the inverse problem.
| [1] |
M. Janicki, M. Zubert, A. Napieralski, Application of inverse heat conduction methods in temperature monitoring of integrated circuits, Sensor. Actuat. A-Phys., 71 (1998), 51–57. https://doi.org/10.1016/S0924-4247(98)00171-X doi: 10.1016/S0924-4247(98)00171-X
|
| [2] |
C. H. Huang, S. C. Cheng, Three-dimensional inverse estimation of heat generation in board mounted chips, J. Thermophys. Heat Tr., 15 (2001), 439–446. https://doi.org/10.2514/2.6630 doi: 10.2514/2.6630
|
| [3] |
L. Yang, Y. Wang, H. Liu, G. Yan, W. Kou, Infrared identification of internal overheating components inside an electric control cabinet by inverse heat transfer problem, Proceedings of International Symposium on Optoelectronic Technology and Application 2014: Infrared Technology and Applications, 2014, 930002. https://doi.org/10.1117/12.2072030 doi: 10.1117/12.2072030
|
| [4] |
D. Cuadrado, A. Marconnet, G. Paniagua, Inverse conduction heat transfer and Kriging interpolation applied to temperature sensor location in microchips, J. Electron. Packag. Mar, 140 (2018), 010905. https://doi.org/10.1115/1.4039026 doi: 10.1115/1.4039026
|
| [5] |
P. Krane, D. G. Cuadrado, F. Lozano, G. Paniagua, A. Marconnet, Sensitivity coefficient-based inverse heat conduction method for identifying hot spots in electronics packages: a comparison of grid-refinement methods, J. Electron. Packag. Mar, 144 (2022), 011008. https://doi.org/10.1115/1.4050200 doi: 10.1115/1.4050200
|
| [6] | O. M. Alifanov, Inverse heat transfer problems, Berlin: Springer-Verlag, 1994. https://doi.org/10.1007/978-3-642-76436-3 |
| [7] |
C. H. Huang, L. C. Jan, R. Li, A. J. Shih, A three-dimensional inverse problem in estimating the applied heat flux of a Titanium drilling-theoretical and experimental studies, Int. J. Heat Mass Tran., 50 (2007), 3265–3277. https://doi.org/10.1016/j.ijheatmasstransfer.2007.01.031 doi: 10.1016/j.ijheatmasstransfer.2007.01.031
|
| [8] |
C. H. Huang, C. T. Lee, An inverse problem to estimate simultaneously six internal heat fluxes for a square combustion chamber, Int. J. Therm. Sci., 88 (2015), 59–76. https://doi.org/10.1016/j.ijthermalsci.2014.08.021 doi: 10.1016/j.ijthermalsci.2014.08.021
|
| [9] |
C. H. Huang, K. J. He, A steady-state inverse heat conduction-convection conjugated problem in determining unknown spatially dependent surface heat flux, Case Stud. Therm. Eng., 39 (2022), 102411. https://doi.org/10.1016/j.csite.2022.102411 doi: 10.1016/j.csite.2022.102411
|
| [10] |
C. H. Huang, Y. R. Zhong, An inverse heat conduction-convection conjugated problem in estimating the unknown volumetric heat generation of an encapsulated chip, Thermal Science and Engineering Progress, 39 (2023), 101710. https://doi.org/10.1016/j.tsep.2023.101710 doi: 10.1016/j.tsep.2023.101710
|
| [11] |
O. M. Alifanov, Solution of an inverse problem of heat conduction by iteration methods, J. Eng. Phys., 26 (1974), 471–476. https://doi.org/10.1007/BF00827525 doi: 10.1007/BF00827525
|
| [12] |
L. C. Hong, S. J. Hwang, Study of warp age due to P-V-T-C relation of EMC in IC packaging, IEEE T. Compon. Pack. T., 27 (2004), 291–295. https://doi.org/10.1109/TCAPT.2004.828579 doi: 10.1109/TCAPT.2004.828579
|
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Cheng-Hung Huang, Ya-Rou Zhong. An inverse problem to estimate simultaneously the heat source strength for multiple integrated circuit chips on a printed circuit board[J]. AIMS Mathematics, 2024, 9(4): 8848-8867. doi: 10.3934/math.2024431
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