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, T_max. 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, T_out. This is important because if T_out is greater than T_max, 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 T_out, add ΔT to the inlet temperature, T_in.

Assuming T_out is less than T_max, 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:

Tin: 20°C, Tmax: 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.