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.
Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels1
Contributed by the Heat Transfer Division for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received by the Heat Transfer Division April 6, 2001; revision received August 21, 2001. Associate Editor: J. G. Georgiadis.
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Hadjiconstantinou , N. G., and Simek, O. (August 21, 2001). "Constant-Wall-Temperature Nusselt Number in Micro and Nano-Channels." ASME. J. Heat Transfer. April 2002; 124(2): 356–364. https://doi.org/10.1115/1.1447931
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