Temperature Depression Under Heat Sources With Cylindrical Contact Thermocouples

The thermal performance of heat sinks is commonly measured using heat sources with spring loaded thermocouples contained within plastic poppets that press against the heat sink to measure its surface temperature where the heat is applied. However, when the thickness of the heat sink base is small or the effective heat transfer coefficient on the fin side is large, the temperature at the thermocouple contact point is less than the nearby temperature where the heat source contacts the heat sink. This temperature depression under the contact thermocouples has been studied. The heat conduction equation is solved analytically to determine the temperature distribution around the contact thermocouple using a one-dimensional approximation and also a detailed two-dimensional approach. Two dimensionless groups are identified that characterize the detailed two-dimensional solution. The combination of the two dimensionless groups also appears in the one dimensional solution. The temperature distributions are validated using finite difference numerical solutions. It is shown that the one dimensional solution is the limit of the detailed solution when one of the dimensionless groups tends to infinity. A simple equation is provided to estimate the temperature measurement error on the heat sink surface.