Modeling conjugate heat transfer

Modeling conduction heat transfer in electronic systems has gained some maturity over the past 3 decades. Although new modeling challenges were associated with 3D stacked dies or packages, some modeling approaches were proposed to handle this rather complicated multiple heat source problem. An even newer problem has started to emerge related to this growing tendency towards exploiting the vertical direction. In fact cooling becomes more and more 3D also, in the sense intermediate micro-channels are proposed going between dies and or packages. This brings convection into play aside with convection in an intimate coupling, commonly called conjugate heat transfer. It is no longer possible to treat convection as an “external” phenomenon, to be modeled by a simple external resistance. In this lecture, fundamental aspects about conjugate heat transfer are revised to obtain a realistic model that avoids large errors that could have been encountered had we treated conduction and convection separately. Fundamental concepts are revised, going up to the notion of heat transfer coefficient in order to elaborate a better model of forced convection in its most general form. The new modeling strategy will build upon progress already realized in Compact Thermal Models (CTM) for conduction in complicated electronic systems. Advanced conduction CTM will be generalized to include convection as well. This will allow a better modeling of convection, but more important a homogeneous and coherent modeling of conjugate heat transfer. Cooling of electronic systems is continuously raising new challenges not only for innovative solutions, but also for modeling of new atypical cases. The higher frequency we ask for, the greater number of functionalities we require as well, both tend to increase heat flux densities to unprecedented levels in industrial applications. Densities higher than those of a nuclear reactor were already realized in electronic systems. We are heading towards densities of rocket nozzle. Complexity related to these high heat fluxes has many origins that will be addressed, in order to motivate subsequent discussions. A summary of recent advances in conduction modeling will be given before generalizing them to convection. Conjugate convection will be studied.