Extended Reynolds analogy for slip and transition flow heat transfer in microchannels and nanochannels

Abstract

It is significant to develop an expression for the rarefaction correction to the continuum solution for heat transfer. An extended Reynolds analogy for slip and transition flow heat transfer in microchannels and nanochannels is proposed. A relationship between the rate of the dimensionless mean wall shear stress reduction and the rate of the dimensionless mean wall heat flux reduction may exist. The extended Reynolds analogy can be utilized to obtain an initial engineering approximation of the Nusselt number. As slip flow heat transfer is inherently complex, the proposed simple model may provide an insight into the mechanism of slip flow heat transfer. This paper cultivates the facility to perform the kind of engineering analysis which, although not exact, still provides useful information concerning real engineering needs.