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Sizing a Heat Exchanger for Cold Plate Applications

 Figure 1: Liquid Cooling LoopFigure 1:
Liquid Cooling Loop

In many liquid cooling loops, the heat that is picked up by a cold plate is rejected to the ambient air via a heat exchanger. Figure 1 shows a typical liquid cooling loop, consisting of a cold plate (CP), pump, and heat exchanger (HX) connected by hoses or tubing. Since the components are part of a system, it is important to select them together to ensure proper component sizing for your application. Manufacturers typically provide performance data for cold plates and heat exchangers individually, with cold plate performance in thermal resistance and heat exchanger performance in thermal capacity. So how do you select the optimal heat exchanger and cold plate for the complete system? It is easier than you might think, since the equations needed to determine the right cold plate and heat exchanger combination reduce to a very simple format:

 Liquid Cooling Loop Formula 1

To arrive at this equation, the first step is to calculate the cold plate thermal resistance, symbol , which is defined as the difference between the maximum required surface temperature, TS, MAX, and the fluid exit temperature, TH, divided by a heat load, Q, evenly distributed over the entire cold plate surface:

 Liquid Cooling Loop Formula 2

Similarly, the heat exchanger thermal capacity, CHX, which is defined as the heat load, Q, divided by the temperature differential between the two incoming fluids, TH -TAIR, is described by the following equation:

 Liquid Cooling Loop Formulat 3

Thermal capacity is also equal to the inverse of thermal resistance:

 Liquid Cooling Loop Formula 4

Assuming no heat gains from the pump or heat losses through connecting hoses or tubing between the cold plate and heat exchanger (since these are usually minor), equations (2), (3) and (4) can be combined into one simple equation:

 Liquid Cooling Loop Formula 1

The hot process fluid temperature TH has dropped out of the formula. Because the liquid temperature has been removed from the equation, we do not have to calculate the flow rates and heat capacities of the liquid. We are just left with the desired surface temperature of the cold plate, as well as the temperature of the ambient air that is cooling the heat exchanger, and the performance is fully characterized by the thermal resistances of the cold plate and the heat exchanger. Therefore, we no longer have to analyze the individual components of the system. Instead we determine the thermal resistance of the entire system, SYSTEM. Note that the effect of the flow is not excluded from the results because it is already incorporated within the thermal resistance values.

A customer wants to use a Lytron Press-Lock CP12, a 12" (30.48 cm) cold plate (plate side), to remove 1200 W of heat from a 12"x5" (30.48 cm x 12.70 cm) electronic device. The coolant is 1 gpm (3.785 lpm) of water and the room temperature is 20°C. He wants the smallest heat exchanger that will remove the 1200 W of heat generated by this device, while maintaining a maximum surface temperature of 80°C.

Step 1: First we determine the system thermal resistance, SymbolSYSTEM:

 Liquid Cooling Formula 5

Step 2: Any combination of cold plates and heat exchangers that provide a thermal resistance less than or equal to the total system requirement will work. In other words:

 Liquid Cooling Loop Formula 6

Step 3: Table 1 shows the resistance and flow rates of the CP12 cold plate and three different heat exchanger/fan combinations:

Table 1

Flow
Rate
(gpm)

 symbol
(CP12)
(°C/W)

 symbol
(6110 w/Muffin XL fan)
(°C/W)

 symbol
(6210 w/Falcon fan)
(°C/W)

 symbol
(6210 w/Patriot fan)
(°C/W)

0.5

0.013

0.049

0.018

0.019

1.0

0.009

0.046

0.016

0.017

1.5

0.007

0.044

0.015

0.016

2.0

0.006

0.042

0.015

0.016

Table 1 shows that the CP12/6110 combination satisfies the 0.050 °C/W condition at 2 gpm (0.006 +0.042 = 0.048

Click here for a PDF of Lytron's standard cold plate and heat exchanger thermal resistances.)

By looking at the system as a whole, we can start to see trade offs between the components, including how flow rate can impact heat exchanger selection. At low flow rates, the cold plate thermal resistance increases. This requires a larger heat exchanger with more thermal capacity, and therefore lower thermal resistance. At higher flow rates, it is possible to use a smaller heat exchanger.

Liquid-to-air heat exchangers and cold plates are often combined in a fluid circuit, so it is important to understand how to select the components simultaneously to optimize your system's performance. With accurate specifications and a simplified equation, selecting the components in your liquid cooling loop can be relatively straightforward. In addition, by selecting components from the same thermal vendor, you will be using components that are tested in a similar manner and are more likely to work well as a system.