Heat Conduction in Printed Circuit Boards: A Mesoscale Modeling Approach

An analytical model is developed to study the heat transfer performance of PCBs. The PCB under study is the substrate for a ball-grid-array (BGA) package, having a belt of densely populated through-thickness vias and continuous copper layers that extend to a larger area beyond the via zone. The analytical formulas are derived to estimate the effects of the geometric and thermal parameters without resorting to resource-demanding numerical analysis. Calculations are performed on the example board that has a footprint area 11 times11 cm ², a thickness 1.26 mm, 2 continuous copper layers, and a 4.4times4.4 cm² BGA package. The impacts of some parameters such as the width of the insulation gap around the via, the area of copper coverage at the via bottom, and the population of vias on the temperature and the heat flow are presented in graphs