#### Jet Impingement an Incomplete Solution

“Many researchers working on diverse applications have identified jet impingement as an attractive way to cool surfaces,” said Dede. “But while jet impingement performs well with respect to heat dissipation close to the jet, it’s less than optimum as you move away from the orifice.”The reason is that the highest heat transfer occurs close to the jet entrance where the fluid is the coolest and velocity is the highest. As a result, much heat-transfer capability is lost by the time the coolant reaches the exit of the cold plate.

One solution to this problem is to combine jet impingement with a peripheral channel structure to increase the area average heat transfer. “It’s in your interest to make those channels short to keep pressure drop to a minimum, but short, straight channels aren’t efficient enough for our use,” Dede explained. “Our goal was to come up with a combination jet-impingement/channel-flowbased cold plate with optimally designed branching channels to uniformly remove the most heat with the least pressure drop.”

The CFD and Heat Transfer Modules of COMSOL Multiphysics software were essential to the numerical simulations at the heart of this work. COMSOL’s Live-Link™ for MATLAB® also enabled Dede to work with the multiphysics simulations in a high-level scripting language as he went about the task of optimizing the cold plate’s topology.

He examined how topology influenced such variables as steady-state convection- diffusion heat transfer and fluid flow. He did this using well-established material interpolation techniques and a Method of Moving Asymptotes (MMA) optimizer, moving back and forth between COMSOL and MATLAB in an iterative fashion to investigate cooling channel layouts. (MMA is a convexapproximation strategy to aid in optimizing physical structures.)Although the aspect ratio of the channels (i.e. ratio of height to width) is quite important, to simplify the numerical simulations Dede assumed a thin 3D structure and then further “flattened” it. Once an initial channel topology was derived, the height of the fins that separate the cooling channels could be investigated and incorporated with a separate parametric sizing study.

Dede’s group had separately performed such studies so his assumptions were well informed. Ultimately, these numeric simulations produced an optimal cooling channel topology with fluid streamlines in branching channels (Figure 1).

Because these channels efficiently distribute coolant throughout the plate and create relatively uniform temperature and pressure distributions that are a function of branching complexity, this fractal-like topology was in turn used to guide the design of a cold plate prototype (Figure 2). The size of the plate was set to approximately 60 mm × 45 mm with a middle cooling zone covering a 25 mm × 15 mm-sized area to match a specific heat source. The plate’s base substrate thickness was assumed to be 1 mm.

#### Real-World Performance

“Once we used COMSOL and MATLAB for the topology optimization routine, we then used the final channel concept from it to design and evaluate a prototype using COMSOL’s LiveLink™ for SolidWorks®,” Dede said. “COMSOL has a nice feature that allows you to actively link to computer-aided design tools, and it was easy to import various structures from SolidWorks back into COMSOL to verify pressure drop and heat transfer.“I think this is really the future of simulation, to be able to link your CAD tool to your simulation tool so that you can streamline the development of fast, accurate design iterations,” Dede added. “It’s not necessarily going to solve all of your problems, but it helps you to quickly establish a reasonable starting point and to progress from there quickly.”

Using the SolidWorks designs, two prototypes were fabricated from aluminum using standard micromachining techniques. Two such prototypes were produced that compared unit thermal resistance and pressure drop in a combined jet/hierarchical microchannel version against a version that utilized jet impingement of a simple flat plate (Figure 3). The prototypes were then incorporated into a double-sided cooling test setup to see whether a dual configuration might provide higher-performance cooling in an ultra-compact package size.

On average, the dual-hierarchical microchannel version dissipated 12.8 percent more power than the flat plate version (Figure 4 left). Indeed, using water as the coolant, it demonstrated very high heat transfer when cooling on both sides of the heat source was accounted for. With regard to pressure drop, both cold plates demonstrated similar results, although the dual-hierarchical version performed slightly better at higher flow rates (Figure 4 right).