Revamped Cooling of a Rectangular Shaped Chip Inserting a Highly Conductive Solid: Coupled vs. Uncoupled Conceptions

The performance of highly conductive inserts embedded into a heated chip has been investigated in recent years. The role of the insert was to gather the heat current within the chip and remove it to a low temperature heat sink. The central goal of this study is to invoke several reconsiderations, which results in the plausible reduction of the peak temperature in a heated rectangular chip in comparison with the lowest peak temperature achieved in previous works. It is proved that for the configuration under study with its bottom surface receiving a constant uniform heat flux, the branching patterns of the insert must be avoided, instead the appropriate revisions in the architecture (width, location and cross section area) of the insert are accounted for the simple patterns. An uncoupled analytical solution for predicting the peak temperatures in the rectangular chip containing the cooling insert is also addressed. It is also proved that under the same volume fraction and thermal conductivity of the insert, the peak temperature can be reduced to 2.9 °C, which is 94% below the lowest temperature reported in the archival literature, which was around 50.5 °C.