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Research Papers

An Inverse Problem in Estimating the Volumetric Heat Generation for a Three-Dimensional Encapsulated Chip

[+] Author and Article Information
Cheng-Hung Huang

Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, Taiwan 701, R.O.Cchhuang@mail.ncku.edu.tw

Wei-Lun Chang

Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan, Taiwan 701, R.O.C

J. Electron. Packag 132(1), 011004 (Mar 04, 2010) (9 pages) doi:10.1115/1.4000720 History: Received August 10, 2009; Revised October 25, 2009; Published March 04, 2010; Online March 04, 2010

A three-dimensional inverse heat conduction problem is solved in the present study by using the conjugate gradient method (CGM) and the general-purpose commercial code CFDACE+ to estimate the strength of the unknown heat generation for an encapsulated chip in a three-dimensional irregular domain. The advantage of calling CFDACE+ code as a subroutine in the present inverse calculation lies in that many difficult but practical 3D inverse problem can be solved under this construction since the general-purpose commercial code has the ability to solve the direct problem easily. The results obtained by using the CGM to solve this 3D inverse problem are justified based on the numerical experiments using the simulated exact and inexact measurements. It is concluded that reliable heat generation can be estimated by the present inverse algorithm.

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Copyright © 2010 by American Society of Mechanical Engineers
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Figures

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Figure 1

(a) The geometry and coordinates for an encapsulated chip and (b) the grid system for the present study

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Figure 2

The (a) exact and (b) estimated heat source g(x,y) with σ=0.0 in test case 1

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Figure 3

The (a) simulated measured and (b) estimated surface temperatures on ST with σ=0.0 in case 1

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Figure 4

The estimated heat source g(x,y) in test case 1 using (a) σ=0.005 and (b) σ=0.008

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Figure 5

The 2D plots for the exact and estimated heat source g(x,y) in test case 1 at x=0.001412 m

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Figure 6

The (a) exact and (b) estimated heat source g(x,y) with σ=0.0 in test case 2

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Figure 7

The (a) simulated measured and (b) estimated surface temperatures on ST with σ=0.0 in case 2

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Figure 8

The estimated heat source g(x,y) in test case 2 using (a) σ=0.004 and (b) σ=0.009

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Figure 9

The 2D plots for the exact and estimated heat source g(x,y) in test case 2 at x=0.001412 m

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Figure 10

The (a) exact and (b) estimated heat source g(x,y) with σ=0.0 in test case 3

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Figure 11

The (a) simulated measured and (b) estimated surface temperatures on ST with σ=0.0 in case 3

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Figure 12

The estimated heat source g(x,y) in test case 3 using (a) σ=0.005 and (b) σ=0.008

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Figure 13

The 2D plots for the exact and estimated heat source g(x,y) in test case 3 at x=0.001412 m

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