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In order to help the electronic designer to early determine the limits of the   power dissipation of electronic component, an analytical model was   established to allow a fast insight of relevant design parameters of a   multi-layered electronic board constitution. The proposed steady-state   approach based on Fourier series method promotes a practical solution to   quickly investigate the potential gain of multi-layered thermal via clusters.   Generally, it has been shown a good agreement between the results obtained by   the proposed analytical model and those given by electronics cooling software   widely used in industry. Some results highlight the fact that the   conventional practices for Printed Circuit Board modeling can be dramatically   underestimate source temperatures, in particular with smaller sources.   Moreover, the analytic solution could be applied to optimize the heat   spreading in the board structure with a local modification of the effective   thermal conductivity layers

Analytical modeling of multi-layered printed circuit board using multi-stacked via clusters as component heat spreader