隨著電子產品的普及和性能的提升，主機板晶片的散熱問題愈發嚴重，準確預測熱源位置及其強度對於提升電子產品的性能與可靠性至關重要。然而，由於主機板內部結構複雜且熱源分佈不均，傳統的熱源預測方法在實際應用中往往面臨挑戰。
本研究使用使用共軛梯度法(Conjugate Gradient Method)搭配套裝軟體 CFD-ACE+，通過溫度場的測量數據反推出主機板晶片內部未知熱源的強度。方法的核心技術是利用測得的外部溫度分佈，逆向求解熱傳導方程，以推斷內部熱源的分佈情況。
本論文第二章為模擬穩態熱傳導與熱對流共軛之反算問題於電熱片未知體積熱源之研究，在第二章將反算法之共軛梯度法運用在預測電熱片內部之熱傳及對流問題上，加入不同量測誤差並且使用不同風速進行預測，其結果顯示即使加入量測誤差並且提高風速預測結果仍然相當準確。
第三章則是使用電熱片進行晶片發熱實驗驗證，將三塊不同尺寸及熱源之電熱片安裝在電路板上模擬主機板上晶片發熱情況，並且置於風洞中以不同風速進行強制對流實驗，再以紅外線熱像儀進行拍攝，觀測電熱片在不同風速流場中的發熱情況。再搭配熱像儀分析軟體TAS20，配合內差方法來擷取所需之溫度分佈，進而利用共軛梯度法(Conjugate Gradient Method)藉由平板上表面溫度與商業軟體CFD-ACE+，預測物體表面未知熱源。

This research uses the Conjugate Gradient Method in conjunction with the software package CFD-ACE+ to infer the intensity of unknown heat sources inside a motherboard chip from temperature field measurement data. The core technique of the method involves using the measured external temperature distribution to inversely solve the heat conduction equation, thus deducing the distribution of internal heat sources. An experiment was conducted using electric heating films to verify chip heat generation. Three electric heating films of different sizes and heat sources were installed on a circuit board to simulate chip heat generation on a motherboard. The setup was placed in a wind tunnel for forced convection experiments at different wind speeds. Infrared thermal imaging was used to observe the heat generation of the electric heating films in different wind speed flow fields. Thermal imaging analysis software TAS20, combined with interpolation methods, was used to extract the required temperature distribution. The Conjugate Gradient Method, using the surface temperature of the flat plate and the commercial software CFD-ACE+, was then employed to predict the unknown heat sources on the object's surface.

1. C. P. Wong and M. M. Wong, "Recent advances in plastic packaging of flip-chip and multichip modules (MCM) of microelectronics, " IEEE Trans. Components Pack. Technol. Vol 22, pp.21–25, 1999.
2. Kijkanjanapaiboon, K., & M. Xie , & J. Zhou, & X.Fan. "Investigation of dimensional and heat source effects in Lock-In Thermography applications in semiconductor packages", Applied Thermal Engineering, Volume 113.673-683.2017
3. H. J. Um, & S. M. Lee , & D. W. Lee, & S. G. Ha, &, H.S.Kim, "Mixed mode fracture toughness of epoxy molding compound/printed circuit board interface of semiconductor packages with respect to temperature and moisture", Engineering Fracture Mechanics, Volume 289,2023
4. Z. Wang, & S. Zheng , & S.L. Xu, & Y.L.Dai, &,"Investigation on the thermal and hydrodynamic performances of a micro-pin fin array heat sink for cooling a multi-chip printed circuit board",Applied Thermal Engineering, Volume 239 ,2024
5. R.K. Wu, & X.F. Zhang , & Y.W. Fan, & R. Hu, &, X.B. Luo, "A Bi-Layer compact thermal model for uniform chip temperature control with non-uniform heat sources by genetic-algorithm optimized microchannel cooling",International Journal of Thermal Sciences, Volume 136, Pages 337-346, 2019
6. Sharma,C,S,& Tiwari,M,K, &Zimmermann,S, & Brunschwiler,T, & Schlottig,G, &Michel,B, &Poulikakos,D, "Energy efficient hotspot-targeted embedded liquid cooling of electronics",Applied Energy, Volume 138, Pages 414-422,2015
7. W.F. Li,& N. Mao, &T.B. He, &J. M. Gong, "CFD simulation of novel adaptive pin-fins microchannel heat sink to improve thermal management of electronic chips",Applied Thermal Engineering, Volume 252,123667,2024
8. Y.M.Chu, & Farooq, U, &,Mishra,N,K, & , Ahmad,Z, & , Zulfiqar,F, & ,Yasmin,S,&,Khan,S,A"CFD analysis of hybrid nanofluid-based microchannel heat sink for electronic chips cooling: Applications in nano-energy thermal devices",Case Studies in Thermal Engineering,102818,2023
9. C. H. Huang and S. C. Cheng, "Three-Dimensional Inverse Estimation of Heat Generation in Board Mounted Chips, " J. Thermophys. Heat Transfer, Vol 15, pp. 439–446, 2001.
10. Huang, C.H., & Ju, T. M..,"An inverse problem of simultaneously estimating contact conductance and heat transfer coefficient of exhaust gases between engine's exhaust value and seat", Int. J. Numerical Methods in Engineering,vol. 38, 735-754. 1995.
11. Huang, C.H., & Tsai, C.C. "A transient inverse two-dimensional geometry problem in estimating time-dependent irregular boundary configurations", Int. J. Heat Mass Transf.vol. 41, 1707–1718. 1998.
12. Huang, C.H., & Chung, Y.L. "An inverse problem in determining the optimum shapes for partially wet annular fins based on efficiency maximization", Int. J. Heat Mass Transf.vol. 90, 364–375. 2015.
13. Lesnic, D., Yousef, S. A., & Ivanchov, M. "Determination of a time-dependent diffusivity from nonlocal conditions", Applied Mathematics and Computation,vol. 41, 301–320. 2013.
14. Liu, F., & Ozisik, M. N. "Inverse analysis of transient turbulent forced convection inside parallel plate ducts". International journal of heat and mass transfer,vol. 39, 2615-2618. 1996.
15. Hsu, P.T., Chen, C. K., & Yang, Y.T. "A 2-D inverse method for simultaneous estimation of the inlet temperature and wall heat flux in a laminar circular duct flow", Numerical Heat Transfer, Part A Applications,vol. 34, 731-745. 1998.
16. VanderVeer, J.R., & Jaluria, Y. "Solution of an inverse convection problem by a predictor–corrector approach". International Journal of Heat and Mass Transfer,vol. 65, 123-130. 2013.
17. Bangian-Tabrizi, A., & Jaluria, Y. "An optimization strategy for the inverse solution of a convection heat transfer problem", International Journal of Heat and Mass Transfer,vol. 124, 1147-1155. 2018.
18. C. H. Huang, & Ozisik, M.N. "Inverse problem of determining unknown wall heat flux in laminar flow through a parallel plate duct", Numerical Heat Transfer, Part A,vol. 21, 55-70. 1992.
19. C. H. Huang and S. P. Wang, “A Three-Dimensional Inverse Heat Conduction Problem in Estimating Surface Heat Flux by Conjugate Gradient Method,” Int. J. Heat and Mass Transfer, Vol 42, pp.3387-3403, 1999.
20. C. H. Huang L. C. Jan, R. Li and 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 and Mass Transfer, Vol 50, pp.3265-3277, 2007.
21. C. H. Huang and H. C. Lo, “A Three-Dimensional Inverse Problem in Predicting the Heat Fluxes Distribution in the Cutting Tools”, Numerical Heat Transfer, part A-Applications, Vol 48, pp.1009-1034, 2005.
22. O. M. Alifanov, “Solution of an Inverse Problem of Heat Conduction by Iteration Methods,” J. of Engineering Physics, Vol 26, pp.471-476, 1974.
23. A. N. Tikhonov and V. Y. Aresenin, “Solution of ill posed problem,” V. H. Wistom&Sons, Washington, DC, 1997.