Fig. 1 Schematic of the 3D, straight, long, horizontal tube with boundary conditions for computational fluid dynamics analyses More

Fig. 2 Generated structured mesh for 3D computational fluid dynamics analyses More

Fig. 3 Grid independence test using the time-averaged axially varying ( a ) fluid temperature at the centerline and ( b )the inner wall temperature for 2 ≤ z (in m) < 4 More

Fig. 4 Comparison between ( a ) CFD-analyzed and wall-law for U + with coarse, medium, and fine meshes at z  =   1.9 m and Re   =   20,000, and ( b ) CFD-analyzed overall, surface-area-averaged, Nusselt number ( Nu CFD ), and the Gnielinski correlation ( Nu Gnielinski ) for TVP1 with 5000 ≤ ... More

Fig. 5 RANS-based axial velocity contour at the different axial locations for TVP1 with Re   =   5000, without and with gravity effect ( g  =   0 and 9.81 m/s 2 ), and different heat flux ratios ( q r  = 1 and 50) More

Fig. 6 RANS-based axial velocity contour at the different axial locations for TVP1 with Re   =   20,000, without and with gravity effect ( g  =   0 and 9.81 m/s 2 ), and different heat flux ratios ( q r  = 1 and 50) More

Fig. 7 ( a )–( h ) RANS-based axial velocity for simulations without gravity effect and with gravity effect, different Reynolds number Re   =   5000 and 20,000, and different heat flux ratios q r  = 1 and 50 More

Fig. 8 A comparison between the RANS-analyzed nondimensional axial velocity with the standard logarithmic law at θ = 90 deg and θ = 270 deg for simulations without and with the effect of gravity More

Fig. 9 ( a )–( h ) The RANS-analyzed streamlines at various axial locations for q r  = 1 and q r  = 50 considering the effect of gravity at Re   =   5000 More

Fig. 10 The RANS-analyzed, statistical, fluid temperature contour at different axial locations for Re   =   5000, g  =   0, 9.81 m/s 2 , and different heat flux ratios q r  = 1 and 50 More

Fig. 11 The RANS-analyzed, statistical, fluid temperature contour at different axial locations for Re   =  20, 000, g  =   0, 9.81 m/s 2 , and different heat flux ratios q r  = 1 and 50 More

Fig. 12 ( a )–( h ) RANS-based statistic fluid and solid temperatures for simulations without gravity effect and with gravity effect, different Reynolds number Re = 5000 and 20,000, and different heat flux ratios q r  = 1 and 50 More

Fig. 13 RANS-based ( a ) fluid and solid temperatures for simulations with gravity effect at z  =   3.75 m, Re   =   5000, and q r  = 5, 10, 20, 40, and 50, and ( b ) Richardson number using the maximum temperature difference, local thermophysical properties for TVP1, and Re   =   5000 and 2... More