Heat spreading from a small source on a thin plate

In view of the trend towards higher power densities in ever smaller package envelopes, heat spreading of a small source on a thin plate is gaining in importance. In this paper, an alternative description is presented to the popular Song-Lee-Au (SLA) approach. A length scale is derived, depending on geometry, heat transfer coefficient, and material parameters, and the relevance of this length scale is investigated. It is shown that the length scale has physical significance both for the distance that heat spreads out over the plate and for the total amount of heat cooled away. The work is the extension of this author's earlier work on Characteristic Length and Cooling Circle to the domain of finite thin plates and small sources. Thermal resistances were calculated with the Cooling Circle and with SLA, and the results were compared to numerical simulations. In the numerical comparison the difference between the two approaches emerged as different assumptions as to the thermal conductivity of the heat source. Cooling Circle assumes a thin plate, and a uniform temperature, thus very large thermal conductivity, in the source area. SLA incorporates the effect of spreading in the plate thickness, and for the thin plates comparison this boils down to the use of baseplate conductivity in the source area. Both methods match well with the numerical results. For larger plates, the Cooling Circle approach continues to match well with the numerical values. SLA values for large thin plates resulted in higher resistances, contrary to both numerical results and physics based expectations. This was attributed to the SLA correlations being used outside the range for which they were validated. The Cooling Circle approach has great engineering significance as it enables quick engineering estimations and provides a helpful mental image.