Convective heat transfer in pressure-driven nitrogen slip flows in long microchannels: The effects of pressure work and viscous dissipation

An analytical and numerical study is carried out to examine the convective heat transfer in two-dimensional pressure-driven nitrogen slip flows in long microchannels, whose length-to-height ratios are above 500. The momentum and the energy equations are solved, where variable properties, rarefaction that involves velocity slip, thermal creep and temperature jump, pressure work, and viscous dissipation are all taken into account. Nitrogen is assumed to be a perfect gas. The effects of pressure work and viscous dissipation, which are particularly significant for long microchannels, are examined by analyzing the uniform wall temperature and the uniform wall heat flux cases. It is found that the degree of rarefaction, which is characterized by the Knudsen number, is the key factor that determines the relative importance of pressure work and viscous dissipation. It is demonstrated that, for perfect gases, rarefaction promotes the conversion of internal energy to mechanical energy. Specifically, regardless of the fluid field development, pressure work and viscous dissipation cancel out in the absence of rarefaction, while pressure work is greater than viscous dissipation with rarefaction and its dominance increases as the Knudsen number increases. It is shown that the combination of pressure work and viscous dissipation makes a significant impact on the Nusselt number in both the continuum and the rarefaction cases. Therefore, it is concluded that for convective heat transfer in internal gas flows, both pressure work and viscous dissipation need to be considered in analysis.