Analysis of turbulent pipe flow with a variable heat transfer coefficient using integral equations

A solution methodology is developed to investigate the problem of heat transfer to fully developed turbulent flow in a pipe subject to a variable external heat transfer coefficient. The variable convection coefficient serves to model a tube fitted with an array of external fins. The solution technique consists of using a Green's function to derive a singular Volterra integral equation for the wall temperature, which is then resolved using a standard integration scheme with the aid of singularity subtraction. The technique provides a straightforward combination of analytical and numerical methods which can handle a large class of problems involving variable boundary condition parameters. The method is used to present a parameter study displaying the effects of the variation of the heat transfer coefficient, the Reynolds number, and the Prandtl number on the heat transfer in turbulent pipe flow. © American Institute of Aeronautics and Astronautics, Inc., 1987. All rights reserved.