Developing an Empirical Correlation for the Thermal Spreading Resistance of a Heat Sink

Heat sinks are a critical component in numerous thermal management strategies, ranging from consumer electronics to data centers. The ability to perform an accurate thermal performance analysis of a heat sink is a crucial step in the design process. In situations where the heat sink is larger in area than the component it is being used to cool, a phenomena known as thermal spreading resistance takes effect. Thermal spreading resistance is not as easily calculated as other components of the thermal resistance of a heat sink (i.e. material and external thermal resistance). However, multiple solutions have been proposed and published that can be used to calculate thermal spreading resistance. The difficulty lies in that most of these solutions contain a very complex set of equations and are not very practical for use by the industry. As a result, the present research is aimed at developing a simple equation that can be used to calculate the thermal spreading resistance of a heat sink based on certain geometric and thermal characteristics. Using a commercial CFD software package, a model was developed that was shown to accurately model the spreading resistance within a heat. Using this model, a set parametric studies was conducted that varied the base thickness, heat source/heat sink side length ratio, heat sink material, external resistance, and the aspect ratio in order to obtain the effects they have on the spreading resistance. Using these results, an extensive data analysis was conducted and resulted in the development of a much simpler equation that can be used to calculate the thermal spreading resistance of heat sink. The developed equation was shown to be in excellent agreement with previous analytical solutions, in most cases with +/- 5%. As a result, it was confirmed that the developed equation can be used to accurately calculate spreading resistance over the stated range of valid parameters.