Effects of cladding thickness and thermal conductivity on heat transfer for laminar in-line flow through rod bundles

The results of an analytical study are presented for the case of fully developed heat transfer to fluids in laminar, longitudinal flow through unbaffled rod bundles. The rods represent reactor fuel pins, which consist of ceramic cores encased in a metallic or alloy cladding. The study was based on the thermal boundary condition of uniform heat flux on the inner surface of the cladding. The three prime independent variables are rod spacing (P/D), relative cladding thickness [(r2 − r1)/r2], and relative cladding conductivity (kw/kf). These have been varied over the ranges of 1.05 to 1.30, 0.025 to 0.300, and 0.10 to 4.00, respectively; and the following quantities have been determined as functions of the above variables: rod-average heat transfer coefficients, circumferential variation of outer-surface cladding temperature, same for the inner surface of the cladding, circumferential variation of local heat flux, and finally, circumferential variation of local heat transfer coefficients. It is shown that the assumption of circumferentially uniform heat flux on the inner surface of the cladding is valid for any practical fuel subassembly designs of a sodium-cooled reactor for a central-station power plant. 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 of the remaining two variables, the influence of the kw/kf ratio is about the same as that of the (r2 − r1)/r2 ratio at the lower values of (r2 − r1)/r2, but appreciably greater at the higher values of (r2 − r1)/r2. The greater the P/D ratio and the lower the other two ratios, the more the system behaves like the standard uniform-wall-heat-flux case. 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.