A numerical procedure which solves the compressible boundary-layer equations is used to study the heat transfer characteristics of gaseous laminar and turbulent flows in mini- and microtubes. Uniform wall heat flux and isothermal wall boundary conditions are simulated. The numerical results show that when the tube diameter is large and the Reynolds number is small, the numerically predicted Nusselt numbers agree with conventional correlations. As the tube diameter gets small and the Reynolds number gets large, the heat transfer characteristics become quite different from those given by the conventional correlations. The reasons for the differences can be explained satisfactorily by the compressibility and the accompanying strong expansion process of the gas along the longitudinal axis. The parabolic character of the boundary-layer equations renders the numerical procedure a very efficient, accurate, and robust tool for studying compressible microtube flows. It took less than 3 min for this numerical procedure to run a typical case on a Pentium IV 2.4 G PC and is at least two to three orders of magnitude faster than the full Navier-Stokes simulations.
