About this note
A plain-language summary of the 1 publication listed under this topic on Academic Publications (Topic-wise). Full citations are under References.
Why this matters
Electronic devices must be kept below a safe temperature, typically somewhere between 80 and 110 °C, because heat strongly affects their reliability and performance. One way to cool them is to cut fine coolant channels (micro-channels) into a heat sink. The usual straight, parallel channels have two drawbacks: they need a large pressure to push the coolant through, and they leave the heat sink with an uneven temperature.
Many natural flow systems branch like trees, and work by Bejan and co-workers showed that when a flow system must balance resistance to flow against resistance to heat transfer, the best design often becomes a tree. We wanted to know how such tree-shaped channel networks perform in a realistic electronics heat sink, not only at steady state but also as the device switches on and off.
What we did
With B. V. K. Reddy and P. V. Ramana, we simulated a silicon disc, 20 mm in radius and 2 mm thick, heated uniformly from below and cooled by water flowing outward from the centre through a network of micro-channels (Reddy et al., 2008). The network starts as three channels at the centre, and each channel splits into two at every branching level, up to four levels. The channel sizes at each split follow Murray’s law, a branching rule for laminar flow, with hydraulic diameters between about 0.67 and 0.44 mm. We solved the flow and heat conduction together in the coolant and the solid (a conjugate heat transfer problem), allowing the water properties to vary with temperature.
The study had three steps. First, for each level of branching we found the smallest coolant flow rate that keeps the disc below a set point of 90 °C at steady state. Second, we supplied each network with exactly this critical flow and followed how the disc temperature evolves in time after the heat load is applied. Third, we made the channels slightly deeper toward the rim, a small radial inclination, to see whether this reduces the pressure needed to drive the coolant.
What we found
Compared with straight radial channels, every tree network needed less coolant flow to stay below the set point. More branching lowered the maximum disc temperature and brought it closer to the average, giving a more uniform temperature, although each extra level of branching helped less than the one before.
When each network was supplied with its own critical flow rate, the transient behaviour of the disc was nearly the same for all levels of branching, with the maximum temperatures differing by less than 2 percent. This matters in practice, because electronics are repeatedly started up and shut down, and the heat sink must stay within its limit throughout.
The more complex networks did, however, need a higher overall pressure drop. Tilting the channels helped: a radial inclination of 0.1 mm reduced the pressure drop by 45 percent for the simplest branched network and by 25 percent for the most complex one, compared with flat channels (Reddy et al., 2008). Branching for uniform temperature, combined with inclination for lower pressure, therefore offers a practical route to better heat sinks.
Related
- Bi-disperse Porous Media, another of our approaches to cooling distributed electronics, also with B. V. K. Reddy
- Phase Change Material Applications, on heat sinks that store heat instead of carrying it away
References
- Reddy, B. V. K., Ramana, P. V. and Narasimhan, A., (2008), “Steady and Transient Thermo-hydraulic Performance of Disc with Tree-shaped Micro-channel Networks with and without Radial Inclination”, Int. J. Thermal Sci. 47 (11), 1482-1489. [DOI 10.1016/j.ijthermalsci.2007.11.003]