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Example

The fluid temperature rise would be 20 degrees C as it flows through the cold plate. The fluid exit temperature would be 50 degrees C. Since the “ambient” in the liquid cooled case is not constant, the analysis should use a logarithmic mean or the average fluid temperature to determine the average ambient. The logarithmic mean temperature is:

Note that the arithmetic mean temperature would be 40 degrees C without great error in this case. The analysis has assumed that the cold plate is isothermal; that is at uniform temperature. The basic equations outlined for air-cooling apply, except the ambient temperature in this case is the logarithmic fluid temperature.

Using the conditions for the air-cooled example gives:

Therefore the maximum cold plate resistance would be:

The cold plate must have a maximum thermal resistance of to prevent the chip juncture from reaching 120 degrees C.

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