## Calculating the Thermal Resistance of a Liquid Cold Plate

To select the best cold plate for your application, you need to know the cooling fluid flow rate, fluid inlet temperature, heat load of the devices attached to the cold plate, and the maximum desired cold plate surface temperature, Tmax. From these you can determine the maximum allowable thermal resistance of the cold plate.

First, calculate the maximum temperature of the fluid when it leaves the cold plate, Tout. This is important because if Tout is greater than Tmax, there is no solution to the problem.

Alternatively, you can use the heat capacity graphs found in our Thermal Reference Guide in the technical library. These graphs describe the change in temperature, ΔT, that occurs along the fluid path. To find Tout, add ΔT to the inlet temperature, Tin.

Assuming Tout is less than Tmax, the next step is to determine the required normalized thermal resistance (θ) for the cold plate using this equation:

Any cold plate technology that provides a normalized thermal resistance less than or equal to the calculated value will be a suitable solution.

## Example of Selecting a Liquid Cold Plate

A cold plate is used to cool a 2˝ x 4˝ IGBT that generates 500 W of heat. It is cooled with 20°C water at a 0.5 gpm flow rate. The surface of the cold plate must not exceed 55°C. We know: T_{in}: 20°C, T

_{max}: 55°C, Q: 500 Watts, Area: 8 in2 We need to calculate T

_{out}and θ. First calculate T

_{out}. Using the heat capacity graphs in our technical reference, we can see that the temperature change for 500W at a 0.5 gpm flow rate is 4°C. Therefore T

_{out}= 20°C + 4°C = 24°C. T

_{out}is less than T

_{max}so we can proceed to the second part of the problem. The required thermal resistance is given by this equation: We then plot this point on the normalized thermal resistance graph. Any technology below this point will meet the thermal requirement. CP15, CP20, and CP30 provide the necessary thermal resistance. But because the cooling fluid is water, you should only consider the CP15 cold plate.

_{out}is less than T

_{max}so we can proceed to the second part of the problem. The required thermal resistance is given by this equation: We then plot this point on the normalized thermal resistance graph. Any technology below this point will meet the thermal requirement. CP15, CP20, and CP30 provide the necessary thermal resistance. But because the cooling fluid is water, you should only consider the CP15 cold plate.

## Cold Plate Performance Comparison

We present cold plate performance data using local thermal resistance – the surface temperature versus the local liquid temperature. This methodology enables more precise thermal analysis for high heat loads. See full details on thermal resistance calculations and how to select a cold plate technology.

## Normalized Performance Curves

Thermal resistance is normally expressed as °C per Watt. Thermal resistance describes how much hotter the surface of a cold plate is relative to the temperature of the fluid flowing through the cold plate, under a given thermal load. These performance curves show the normalized thermal resistance for our standard cold plate products (i.e. thermal resistance per square inch). These curves are a good way to compare cold plate technologies, since they are independent of individual part geometries. The lower the thermal resistance, the better the performance of the cold plate.## Notes

Thermal resistance is inversely proportional to area. To find the thermal resistance of a 25 square inch cold plate, divide the normalized performance by 25.

Our CP30 standard cold plate is designed for prototyping purposes. It has a thick surface plate for machining. We show two traces – before machining (0.5″ / 13 mm) and after machining (0.05″ / 1.3 mm). The performance of a custom vacuum-brazed cold plate is usually significantly better than this standard part.

For comparison purposes, the performance of all cold plates is shown using water as the coolant. Treated water is recommended with aluminum (CP20 & CP30) cold plates.