Heat transfer in all pipe flow regimes: laminar, transitional/intermittent, and turbulent

A predictive theory is presented which is capable of providing quantitative results for the heat transfer coefficients in round pipes for the three possible flow regimes: laminar, transitional, and turbulent. The theory is based on a model of laminar-to-turbulent transition which is also viable for purely laminar and purely turbulent flow. Fully developed heat transfer coefficients were predicted for the three regimes. The present predictions were brought together with the most accurate experimental data known to the authors as well as with several algebraic formulas which are purported to be able to provide fully developed heat transfer coefficients in the so-called transition regime between Re = 2300 and 10,000. It was found that over the range Re > 4800, both the present predictions and those of the Gnielinski formula [V. Gnielinski, New equations for heat and mass transfer in turbulent pipe and channel flow, Int. Chem. Eng. 16 (1976) 359–367] are very well supported by the experimental data. However, the Gnielinski model is less successful in the range from 2300 to 3100. In that range, the present predictions and those of Churchill [S. Churchill, Comprehensive correlating equations for heat, mass, and momentum transfer in fully developed flow in smooth tubes, Ind. Eng. Chem. Fundam. 16 (1977) 109–116] are mutually reinforcing. Heat transfer results in the development region have also been obtained. Typically, regardless of the Reynolds number, the region immediately downstream of the inlet is characterized by laminar heat transfer. After the breakdown of laminar flow, a region characterized by intermittent heat transfer occurs. Subsequently, the flow may become turbulent and fully developed or the intermittent state may persist as a fully developed regime. The investigation covered both of the basic thermal boundary conditions of uniform heat flux (UHF) and uniform wall temperature (UWT). In the development region, the difference between the respective heat transfer coefficients for the two cases was approximately 25% (UHF > UWT). For the fully developed case, the respective heat transfer coefficients are essentially equal in the turbulent regime but differ by about 25% in the intermittent regime. The reported results are for a turbulence intensity of 5% and flat velocity and temperature profiles at the inlet.