Effects of Cladding Thickness and Thermal Conductivity on Heat Transfer to Liquid Metals Flowing In-Line Through Bundles of Closely Spaced Reactor Fuel Rods

This paper summarizes the results of an analytical study carried out for the purpose of determining the effects of cladding thickness and conductivity on fully developed heat transfer to liquid metals flowing in-line through unbaffled rod bundles. The study is based on slug flow and the assumption that the heat flux on the inner wall of the cladding is uniform in all directions. It was shown earlier that slug-flow results for liquid metals are very similar to those for turbulent flow in practical Pe ranges, particularly when the results are put in certain dimensionless forms, and it is shown in the present study that the assumption of circumferentially uniform heat flux on the inner wall of the cladding is perfectly valid for any practical nuclear-reactor design for a central-station power plant. The problem required the simultaneous solution of the differential energy equations for both the coolant and cladding, which are coupled by the local temperature and heat-flux conditions existing at the coolant-cladding interface. There are three prime independent variables: rod spacing (P/D), relative cladding thickness (r₂ − r₁)/r₂, and relative cladding conductivity (k_w/k_f). These have been varied over the ranges 1.05 to 1.30, 0.025 to 0.300, and 0.10 to 4.00, respectively. The following quantities have been calculated as functions of the above independent variables: rod-average heat transfer coefficients, circumferential variation of outer-surface cladding temperature, the same for the inner surface, circumferential variation of local heat flux, and finally, circumferential variation of local heat-transfer coefficient. The results are all expressed in the form of convenient dimensionless groups and are correlated by simple mathematical expressions, for ready use by the design engineer. It is found that, of the three prime independent variables, the P/D ratio has by far the greatest influence on the heat transfer behavior of the system; and that, of the remaining two variables, the thermal conductivity ratio, k_w/k_f, has appreciably more influence than the relative-cladding-thickness ratio (r₂ − r₁)/r₂. The higher the P/D ratio and the lower the (r₂ − r₁)/r₂ and k_w/k_f ratios, the more the system behaves like the uniform-wall-heat-flux case; and it is interesting to note that in many practical situations the simple uniform-wall-heat-flux assumption is quite adequate.