Natural convection heat transfer from vertical 5×5 rod bundles in liquid sodium was numerically analyzed for two types of the bundle geometry (equilateral square and triangle arrays, ESA and ETA). The unsteady laminar three dimensional basic equations for natural convection heat transfer caused by a step heat flux were numerically solved until the solution reaches a steady-state. The PHOENICS code was used for the calculation considering the temperature dependence of thermophysical properties concerned. The 5×5 test rods for diameter (D = 7.6 mm), heated length (L = 200 mm) and L/d (= 26.32) were used in this work. The surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, (Rf,L)ij and (Rf,L)5×5,S/D, ranging from 3.08 × 104 to 4.19 × 107 (q = 1 × 104∼7 × 106 W/m2) in liquid temperature (TL = 673.15 K). The values of S/D, which are ratios of the diameter of flow channel for bundle geometry to the rod diameter, for vertical 5×5 rod bundles were ranged from 1.8 to 6 on each bundle geometry. The spatial distribution of local and average Nusselt numbers, (Nuav)ij and (Nuav,B)5×5,S/D, on vertical rods of a bundle was clarified. The average value of Nusselt number, (Nuav)ij and (Nuav,B)5×5,S/D, for two types of the bundle geometry with various values of S/D were calculated to examine the effect of the bundle geometry, S/D, (Rf,L)ij and (Rf,L)5×5,S/D on heat transfer. The bundle geometry for the higher (Nuav,B)5×5,S/D value under the condition of S/D = constant was examined. The correlations for (Nuav,B)5×5,S/D for two types of bundle geometry above mentioned including the effects of (Rf,L)5×5,S/D and S/D were developed. The correlations can describe the theoretical values of (Nuav,B)5×5,S/D for two types of the bundle geometry for S/D ranging from 1.8 to 6 within −11.77 to 13.34 % difference.
Effect of Prandtl Number on the Natural Convection Heat Transfer of Small Particles
