A Fourier Series-Based Analytical Solution for Three-Dimensional Conjugate Heat Transfer Problems in Microprocessor Cooling

A fully analytical steady state solution is presented for the problem of 3-D conjugate heat transfer in flip chip electronic packages with multiple general areal power sources, cooled by heatsinks using forced convection. The inherent simplicity of the proposed approach allows for expedient yet detailed package cooling/thermal analysis and evaluation of what-if scenarios while requiring only modest computational resources such as a personal computer. The soundness of the approach presented is demonstrated via excellent correlation with the results of experimental tests on flip-chip thermal test packages in a wind tunnel. The techniques developed herein are fairly general and can be readily adapted to other package designs wherein the primary heat transfer path is through the die, die-lid interface, lid, lid-sink interface and heatsink to the airflow through the fins.