Laminar-to-Turbulent Transition Flow inside a Heated Circular Tube

The natural transition flow and convective heat transfer inside an electrically heated circular tube are analyzed. The transition flow is treated as a composition of fully developed laminar and turbulent flows by assuming the fluctuating velocity in radial direction exists as if the flow is fully turbulent. The composite ratios are used to define the composite flow, and they fluctuate in transition flow. The criterion of minimum entropy production is used to derive an equation which can describe how transition evolves. It is pointed out that the fluctuations of the composite ratios govern the transition behavior. One fluctuation function is given to attain agreements with measurements including those obtained in heat transfer and flow experiments.