Dependency of thermal spreading resistance on convective heat transfer coefficient

This paper presents a study of the thermal spreading resistance RthRth of a small heat source on a conductive substrate subject to bottom-side convective cooling. This problem has been investigated for a very long time and is well covered in the literature. However, instead of using the design curves found in many papers, the results are presented as function of the heat transfer coefficient h  . Doing so, a remarkable property is revealed. The thermal resistance is proportional to the logarithm of the reciprocal heat transfer coefficient, for a broad range of at least three decades (h=1-1000W/m2K). This behaviour can be reasonably explained using an approximate one-dimensional heat spreading model. Being dictated by a logarithmic law, the dependency of RthRth on h is rather weak. This is made clearer by the temperature profiles at the substrate bottom. Decreasing h leads to a wider spreading and hence a larger surface with the coolant is utilised, which partly compensates the poorer cooling.