Steady State and Transient Analytical Modeling of Non-Uniform Convective Cooling of a Microprocessor Chip Due to Jet-Impingemen

Heat removal from microprocessor chips with multiple regions of dynamic heat generation remains a critical technological challenge. Excessive temperature rise is undesirable for performance as well as reliability. Jet impingement cooling has been widely investigated as a potential thermal management technique due to the capability of localized cooling and of dynamically following the heat generation distribution. A jet offers large local convective heat transfer coefficient, for which theoretical models and correlations have been proposed for a variety of scenarios. However, not much work exists on using this information to determine the resulting temperature distribution. This work addresses this need by developing analytical steady state and transient heat transfer models that account for the spatial variation in convective heat transfer coefficient and for spatially non-uniform heat flux. The solution is derived in the form of an infinite series, the coefficients of which are determined by solving a set of algebraic equations. Temperature rise predicted by the models are found to be in excellent agreement with finite-element simulations, while offering faster computation time and easier integration with design and performance optimization tools used in microelectronics. The analytical model is used for predicting temperature rise in a variety of scenarios to examine interesting optimization problems such as the cooling of multiple hotspots with a single jet, determining the optimal location of a jet, etc. Results presented here may facilitate improved thermal design and real-time performance optimization of microprocessor chips.