Natural convection heat transfer from horizontal rod bundles in liquid sodium. Part 2: Correlations for horizontal rod bundles based on theoretical results

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Natural convection heat transfer from horizontal rod bundles in Nxm × Nym arrays (Nxm, Nym = 5–9) in liquid sodium was numerically analyzed for three types of the bundle geometry (in-line rows, staggered rows I and II). The unsteady laminar two-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 surface heat fluxes for each cylinder were equally given for a modified Rayleigh number, Rf, ranging from 0.0637 to 63.1 (q = 1×104 to 7×106 W/m2). Sx/D and Sy/D for the rod bundle, which are the ratios of the distance between center axes on the abscissa and the ordinate to the rod diameter, respectively, were ranged from 1.6 to 2.5 on each bundle geometry. The spatial distribution of Nusselt numbers, Nu, on horizontal rods of a bundle was clarified. The average value of Nusselt number, Nuav, for three types of bundle geometry with various values of Sx/D and Sy/D were calculated to examine the effect of the array size, S/D and Rf on heat transfer. The bundle geometry for the higher Nuav value under the condition of Sx/D×Sy/D = 4 was examined by changing the ratio of Sx/Sy. A correlation for Nuav for the three types of bundle geometry above mentioned including the effects of Sx/D and Sy/D was developed. The correlation can describe the theoretical values of Nuav for the three types of bundle geometry in Nxm × Nym arrays (Nxm, Nym = 5–9) for Sx/D and Sy/D ranging from 1.6 to 2.5 within 10% difference.