The performance characteristics of micro heat exchangers consisting of
straight channels fabricated in a silicon wafer and operating with li
quid nitrogen are evaluated theoretically. The three-dimensional conju
gate temperature and flow fields are calculated numerically. The therm
al resistance is computed as a function of various geometric parameter
s. The optimal dimensions which minimize the heat exchanger's thermal
resistance are identified. Additionally, a simple, approximate, analyt
ical model, adequate when the ratio of the solid and liquid thermal co
nductivities is large, is presented and used to predict the heat excha
nger's optimal dimensions. The approximate model's predictions are com
pared with the numerical results.