Thermally developing microtube gas flow with axial conduction and viscous dissipation

A comparative study of the first and second order slip flow models on the thermal development of dilute gas flow in a microtube with axial conduction and viscous dissipation has been performed. The velocity profiles for the two models have been derived analytically assuming the flow to be fully developed hydrodynamically. The energy equation is solved numerically for a constant wall temperature with velocity slip and temperature jump conditions at the wall. Analytical solutions for the asymptotic values of the mean temperature and Nusselt number are given for the second-order slip flow model in terms of Brinkman number Br, Knudsen number Kn, temperature jump parameter κ, and slip parameter ρs. The effect of these parameters and the Peclet number Pe on the development of local mean fluid temperature and the local Nusselt number are displayed graphically and compared with the results available in the literature. For the fully developed hydrodynamic condition, the second-order slip model predicts higher velocities in the central region of the flow but the trend is reversed near the wall region. For fixed values of Pe, Kn, κ, and three different Br, the second order model predicts higher fluid temperatures compared with those predicted by the first-order model. For thermally developing flow, the second order model in general predicts significantly higher mean fluid temperatures (maximum of 21% in one case), compared with those predicted by the first-order model. However, the difference in the local Nusselt number between the two slip models is small.