Microchannels Take Heatsinks to the Next Level

Nov 1, 2006 12:00 PM
By Stephen A. Solovitz, Mechanical Engineer; Ljubisa D. Stevanovic, Advanced Technology Leader, Ener

Step One: Analytical Optimization

First-order heat transfer is governed by the thermal resistivity (R"), which is defined as the temperature rise divided by the heat flux. Note that this is different from the common metric of thermal resistance, which also divides by the device area. This alternate resistivity metric is more appropriate for this situation due to the challenges of high heat flux. For convective heat transfer in channels having hydraulic diameter (DH), the thermal resistivity is calculated as:

In this equation, K is the fluid thermal conductivity, and NuDH is the Nusselt number for the appropriate flow condition. For example, for laminar, fully developed flow in a circular passage with constant heat flux, NuDH = 4.36. In addition, the pressure loss (Δp) is calculated using the friction factor (f) as:

For this expression, is the fluid density and L is the passage length. In laminar, fully developed flow in a circular passage, the friction factor is f = 64/ReDH. Here, ReDH is the Reynolds number (UDH/ν), where U is the fluid velocity and is the fluid kinematic viscosity.

These basic expressions for R" and p can be used to select the optimal channel sizing. Similar to the method described by Knight et al.[6], the passage dimensions are chosen to minimize the thermal resistivity R" subject to pumping constraints on the maximum pressure loss and flow rate. These expressions can be further modified for more complex situations by using the appropriate equations for NuDH and f, such as those for laminar developing[7] and turbulent[8] flows.

The primary variables to be optimized are the channel width and pitch. In GE's integrated microchannel heatsink, these values were altered by changing the number of cooling passages (from 10 to 200) and the ratio of wall thickness to channel width (from 0.1 to 2) beneath a heat source of 2-cm × 2-cm size. Note that these dimensions result in a range of flow conditions, including laminar, turbulent, developing and fully developed regimes. In addition, the channel height in the AMB substrate was varied from 0.05 mm to 0.3 mm, which was the maximum depth allowed due to the thickness of the bottom copper layer. The coolant was water at room temperature, which is the typical coolant used for comparison by commercial heatsink vendors. The pump constraints were specified as 1-gallon per minute (GPM) maximum flow rate and 25-psi maximum pressure loss, which are representative values for power electronics cooling applications.

An additional constraint is to keep the channel width at or above 100 m, given the difficulty of manufacturing passages below that width in copper. This constraint was applied to GE's heatsink.

After analyzing this array of potential channel dimensions, the optimum shape is then selected based on these pump and manufacturing restrictions. For the integrated microchannel heatsink, the preferred shape has a width of 100 µm, a depth of 300 µm and a wall thickness between channels of 100 µm, a configuration consistent with earlier microchannel studies[2,6]. The narrow channel width and small pitch results in a high surface area-to-volume ratio, while the tall channel height tempers the pressure loss through the passage. The calculated thermal resistivity for this design was 0.042 (K)(cm2)/W, comparable to the best published results for existing microchannel heatsinks.

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