Heat Transfer in a Pipe With Turbulent Flow and Arbitrary Wall-Temperature Distribution

The first three eigenvalues and constants for the problem of heat flow to a constant property fluid in established turbulent flow in a round pipe are presented for all important values of Reynolds and Prandtl Moduli. These results permit one to compute heat transfer from nonisothermal pipe walls. Comparisons with experiment are good for all fluids from oils to liquid metals. The thermal entry length and rate of heat transfer for low Prandtl Moduli are shown to depend markedly on the wall-temperature profile.