We investigate the constant-wall-temperature convective heat-transfer characteristics of a model gaseous flow in two-dimensional micro and nano-channels under hydrodynamically and thermally fully developed conditions. Our investigation covers both the slip-flow regime 0⩽Kn⩽0.1, and most of the transition regime 0.1<Kn⩽10, where Kn, the Knudsen number, is defined as the ratio between the molecular mean free path and the channel height. We use slip-flow theory in the presence of axial heat conduction to calculate the Nusselt number in the range 0⩽Kn⩽0.2, and a stochastic molecular simulation technique known as the direct simulation Monte Carlo (DSMC) to calculate the Nusselt number in the range 0.02<Kn<2. Inclusion of the effects of axial heat conduction in the continuum model is necessary since small-scale internal flows are typically characterized by finite Peclet numbers. Our results show that the slip-flow prediction is in good agreement with the DSMC results for Kn⩽0.1, but also remains a good approximation beyond its expected range of applicability. We also show that the Nusselt number decreases monotonically with increasing Knudsen number in the fully accommodating case, both in the slip-flow and transition regimes. In the slip-flow regime, axial heat conduction is found to increase the Nusselt number; this effect is largest at Kn=0 and is of the order of 10 percent. Qualitatively similar results are obtained for slip-flow heat transfer in circular tubes.

*Application of Microfabrication to Fluid Mechanics*, ASME, New York, pp. 57–66.

*Molecular Gas Dynamics and the Direct Simulation of Gas Flows*, Clarendon Press, Oxford.

*The Boltzmann Equation and Its Applications*, Springer-Verlag, New York.

*Proceedings of the 2000 IMECE*, HTD-Vol. 366-2, pp. 13–22.

*Proceedings of the 2001 IMECE*.

*Heat Transfer*, Irwin.

*Heat Transfer 1998: Proceedings of the Eleventh International Heat Transfer Conference*, Vol. 3, pp. 127–132.

*Laminar Flow Forced Convection in Ducts*, Academic Press.

*Proceedings of the 2001 IMECE*.

*Proceedings of the First MIT Conference on Computational Fluid and Solid Mechanics*, Vol. 2, pp. 1019–1021.