Practical analytical steady-state temperature solution for annealed pyrolytic graphite heat spreader
Authors: Nguyen Nhat Minh , Monier-Vinard Eric , Laraqi Najib , Bissuel Valentin , Daniel Olivier 
Published: February 2017

Purpose
The purpose of this paper is to supply an analytical steady-state solution to the heat transfer equation permitting to fast design investigation. The capability to efficiently transfer the heat away from high-powered electronic devices is a ceaseless challenge. More than ever, the aluminium or copper heat spreaders seem less suitable for maintaining the component sensitive temperature below manufacturer operating limits. Emerging materials, such as annealed pyrolytic graphite (APG), have proposed a new alternative to conventional solid conduction without the gravity dependence of a heat-pipe solution.

Design/methodology/approach
An APG material is typically sandwiched between a pair of aluminium sheets to compose a robust graphite-based structure. The thermal behaviour of that stacked structure and the effect of the sensitivity of the design parameters on the effective thermal performances is not well known. The ultrahigh thermal conductivity of the APG core is restricted to in-plane conduction and can be 200 times higher than its through-the-thickness conductivity. So, a lower-than-anticipated cross-plane thermal conductivity or a higher-than-anticipated interlayer thermal resistance will compromise the component heat transfer to a cold structure. To analyse the sensitivity of these parameters, an analytical model for a multi-layered structure based on the Fourier series and the superposition principle was developed, which allows predicting the temperature distribution over an APG flat-plate depending on two interlayer thermal resistances.

Findings
The current work confirms that the in-plane thermal conductivity of APG is among the highest of any conduction material commonly used in electronic cooling. The analysed case reveals that an effective thermal conductivity twice as higher than copper can be expected for a thick APG sheet. The relevance of the developed analytical approach was compared to numerical simulations and experiments for a set of boundary conditions. The comparison shows a high agreement between both calculations to predict the centroid and average temperatures of the heating sources. Further, a method dedicated to the practical characterization of the effective thermal conductivity of an APG heat-spreader is promoted.

Research limitations/implications
The interlayer thermal resistances act as dissipation bottlenecks which magnify the performance discrepancy. The quantification of a realistic value is more than ever mandatory to assess the APG heat-spreader technology.

Practical implications
Conventional heat spreaders seem less suitable for maintaining the component-sensitive temperature below the manufacturer operating limits. Having an in-plane thermal conductivity of 1,600 W.m−1.K−1, the APG material seems to be the next paradigm for solving endless needs of a thermal designer.

Originality/value
This approach is a practical tool to tailor sensitive parameters early to select the right design concept by taking into account potential thermal issues, such as the critical interlayer thermal resistance.