Computational study of heat transfer from the inner surface of a circular tube to force high temperature liquid metal flow in laminar and transition regions

摘要

Heat transfer through forced convection from the inner surface of a circular tube to force the flow of liquid sodium in the laminar and transition regions were numerically analysed for two types of tube geometries (concentric annular and circular tubes) and two types of equivalent diameters (hydraulic and thermal equivalent diameters). The unsteady laminar three-dimensional basic equations for forced convection heat transfer caused by a step heat flux were numerically solved until a steady state is attained. The code of the parabolic hyperbolic or elliptic numerical integration code series (PHOENICS) was used for calculations by considering relevant temperature dependent thermo-physical properties. The concentric annular tube has a test tube with inner and outer diameters of 7.6 and 14.3 mm, respectively, has a heated length of 52 mm, and an L/d of 6.84. The two circular tubes have inner diameters of 6.7 and 19.3 mm with L/d of 7.76 and 2.69, respectively, and a heated length of 52 mm. The inlet liquid temperature, inlet liquid velocity, and surface heat flux were equally set for each test tube as T ~( in )≅573 to 585 K, u ~( in ) = 0.0852 to 1 m/s, and q  = 2×10_(5)to 2.5×10_(6)W/m_(2), respectively. The increase in temperature from the leading edge of the heated section to the outlet of the circular tubes (with a hydraulic diameter of d ~( H ) = 6.7 mm and a thermal equivalent diameter d ~( te ) = 19.3 mm) was approximately 2.70 and 1.21 times as large as the corresponding values of the concentric annular tube with an inner diameter of 7.6 mm and an outer diameter of 14.3 mm, respectively. A quantity in the laminar and transition regions was suggested as the dominant variable involved in the forced convection heat transfer in the circular tube. The values of the local and average Nusselt numbers, Nu ~( z )and Nu ~( av ), respectively, for a concentric annular tube with d ~( H ) = 6.7 mm and for a circular tube with d ~( H ) = 6.7 mm were calculated to examine the effects of q , T ~( in ), and Pe on heat transfer. The general correlation in the laminar and turbulent regions for a high temperature liquid metal was identified for the circular tube with a hydraulic diameter.