Three-Dimensional Inverse Estimation of Heat Generation in Board Mounted Chips

The conjugate gradient method (CGM) and the general purpose commercial code CFX 4.2-based inverse algorithm are utilized in a three-dimensional inverse heat conduction problem to estimate the strength of heat generation for chips on a printed circuit board (PC-board). The mathematical formulations for simultaneously solving the strength of heat generation for multiple chips are derived. The advantage of calling the CFX 4.2 code as a subroutine in the present inverse calculation lies in that many difficult but practical three-dimensional inverse problems can be solved under this construction because the general-purpose commercial code has the ability to solve the direct problem easily. Results obtained by using the CGM to solve this three-dimensional inverse problem for two chips are justified based on the numerical experiments with the simulated exact and inexact measurements. It is concluded that accurate heat generation for each chip can be estimated simultaneously by the CGM except for the final time. The reason for and improvement of this singularity are addressed.