A new model for substrate heat spreading to two convective heat sinks: Application to the BGA package

The thermal heat conduction from a circular heat source to a circular conductive substrate exposed to distinct convective heat sinks on its upper and lower surfaces is treated rigorously by formally solving a mixed boundary value problem through the singular integral equation technique. The effects of the two heat sinks are consolidated into one effective heat sink that is derived by application of a current source transformation to the DC circuit representation of the problem. The utility of the model is shown by applying it to a compact thermal model of a ball grid array (BGA) package.

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