Sensitivity-Coefficient Based Inverse Heat Conduction Method for Identifying Hot Spots in Electronics Packages: A Comparison of Grid-Refinement Methods

Estimating the distribution and magnitude of heat generation within electronics packages is pivotal for thermal packaging design and active thermal management systems. Inverse heat conduction methods can provide estimates using measured temperature profiles acquired using infrared imaging or discrete temperature sensors. However, if the heater locations are unknown, applying a fine grid of potential heater locations across the surface where heat generation is expected can result in prohibitively-large computation times. In contrast, using a more computationally-efficient coarse grid can reduce the accuracy of heat flux estimations. This paper evaluates two methods for reducing computation time using a sensitivity-coefficient method for solving the inverse heat conduction problem. One strategy uses a coarse grid that is refined near the hot spots, while the other uses a fine grid of potential heaters only near the hot spots. These grid-refinement methods are compared using both input temperature maps acquired from a "numerical experiment" (where the outputs of a 3D steady-state thermal model in FloTHERM are used for input temperatures) and temperature maps procured using infrared microscopy on a real electronics package. Compared to the coarse-grid method, the fine-grid method reduces computation time without significantly reducing accuracy, making it more convenient for designing and testing electronics packages. It also avoids the problem of "false hot spots" that occurs with the coarse-grid method. Overall, this approach provides a mechanism to predict hot spot locations during design and testing and a tool for active thermal management.