Semi-analytic calculation of turbulent, in-tube forced convection heat transmission of metallic liquids

An analysis of forced convection flow of metallic liquids in an isothermal tube with fully developed, turbulent velocity is performed in a semi-analytic manner. Cebeci's modification of Prandtl's mixing length model is adopted for the eddy diffusivity of momentum, whereas two popular models, one by Azer and Chao and the other by Dwyer and Tu are employed for the eddy diffusivity of heat. The special feature of the calculation procedure is the beneficial combination of the methods of lines, the finite volume technique, and a coordinate transformation in the cross-stream direction. The energy equation is reformulated into an equivalent system of first-order ordinary differential equations, where each equation regulates the temperature along each concentric line in the grid. Reliable semi-analytic series for the distributions of mean bulk temperatures and Nusselt numbers in the thermal entrance region can be determined for any union of Reynolds and Prandtl numbers utilizing ten lines only in the cross-stream direction. For the metallic liquids tested, the predicted thermal quantities compare satisfactorily with the experimental data.