An analytical solution of thermal resistance of cubic heat spreaders for electronic cooling

A three-dimensional analytical solution using the method of Fourier expansion is developed for determination of the spreading thermal resistance of a cubic heat spreader for electronic cooling applications. The model assumes that the heat spreader is receiving a uniform heat flux centroidally with a projected heating area from the heat source. Heat is conducted inside the heat spreader in a three-dimensional coordinate, then transferred to a heat sink with a constant convective heat transfer coefficient. Dimensionless expressions in the form of infinite series are provided to compute the maximum spreading thermal resistance, the surface temperature fields and the heat flux distribution as a function of relative projected heating area, plate thickness and Biot number. The correlation developed herein is effective and accurate to predict the spreading thermal resistance.