Laminar hydrodynamic and thermal entrance lengths for simultaneously hydrodynamically and thermally developing forced and mixed convective flows in horizontal tubes

Correlations to predict the hydrodynamic and thermal entrance lengths in a smooth horizontal tube heated at a constant heat flux are often restricted to forced convection conditions. The reason being that most scholars do not distinguish very well between forced and mixed convection conditions. Furthermore, most correlations have been developed for hydrodynamically fully developed and thermally developing flows. The purpose of this study was to experimentally investigate the hydrodynamic and thermal entrance lengths for laminar flows in smooth horizontal tubes heated at a constant heat flux. Simultaneously hydrodynamically and thermally developing flows were investigated in both forced and mixed convection conditions. Two smooth circular test sections with inner diameters of 4 mm and 11.5 mm, and maximum length-to-diameter ratios of 1 373 and 872, respectively, were used. Heat transfer and pressure drop measurements were taken at Reynolds numbers between 460 and 3 200 at different heat fluxes. A large database with a total of 513 mass flow rate measurements, 43 501 temperature measurements, and 1 665 pressure drop measurements were used. The test fluid was water and the Prandtl number ranged between 3 and 8. For the first time, correlations were developed to calculate the hydrodynamic and thermal entrance lengths for simultaneously hydrodynamically and thermally developing flow in smooth horizontal tubes. The correlations were valid for tubes heated at a constant heat flux in both forced and mixed convection conditions. For ease of use, the correlations were developed in terms of the local, inlet, and bulk fluid properties. Furthermore, the mixed convection correlations were developed in terms of both the Grashof and modified Grashof numbers.