On the role of the Knudsen number with respect to heat transfer in micro-scale flows [in microelectronics circuits]

Advances in microelectronics and in microelectromechanical systems have resulted in devices with characteristic lengths approaching that of the molecular mean free path of gases. In certain applications, it has been proposed that gaseous flows be used to cool such devices. Prior research has revealed a fundamental lack of knowledge regarding the behavior of such micro-flows. The primary dimensionless parameter associated with gaseous micro-scale transport is the Knudsen number. A critical examination of the effects of an increasing Knudsen number on heat and momentum transfer characteristics of gaseous micro-flows is presented. The importance of thermal radiation, accurate thermophysical property models, and the introduction of higher order constitutive relations, i.e. the Burnett relations, are also discussed in relation to micro-flows. Conclusions are drawn regarding the relative importance of each of the above topics