Convective heat transfer in microchannels

Heat-transfer microstructures for cooling silicon chips wherein water flows through mi-crochannels etched in the back of silicon wafers have been considered by a number of authors. Under a set of reasonable assumptions, the problem can be reduced to a quasi-two-dimensional differential equation. To date, these equations have only been solved approximately. We present exact solutions to these equations and analytically obtain optimum dimensions for the channel width and spacing. Using numerical examples, we show that the thermal resistance can be lowered by using these optimum values.