Natural laminar-to-turbulent transition inside an electrically heated circular tube

The natural laminar-to-turbulent transitional flow and convective heat transfer inside an electrically heated circular tube are analyzed. It is proposed that the transitional flow can be decomposed into the fully developed laminar flow and the turbulent flow, under the assumption that the fluctuating velocity in the radial direction does not change with varying flow modes. The composite ratios are adopted to define the composite flow, and they fluctuate during the flow transition. The minimum entropy production criterion is used to derive an equation which can describe the evolution of the transitional flow. It is deduced that the transitional behavior is governed by the fluctuations of the composite ratios. One fluctuation function is given to attain agreements with measurements including those obtained in heat transfer and flow experiments. It is pointed out that the process of the laminar-to-turbulent transition inside the tube can be compared with continuous phase transitions in a thermodynamic equilibrium system, and similar and separate processes for the transitions of the velocity and temperature inside the tube can be allowed.