Turbulent-Flow Heat Transfer for In-Line Flow Through Unbaffled Rod Bundles: Molecular Conduction Only

The results of a theoretical study of molecular-conduction heat transfer to liquid metals flowing in-line through unbaffled rod bundles are reported. The flow is turbulent and fully developed, the heat transfer is fully developed, the bundles have equilateral triangular spacing, and there are no effects due to spacing devices. Circumferentially local heat transfer coefficients, rod-average heat transfer coefficients, and circumferential variation of wall temperatures have been obtained and correlated in terms of the various independent variables. The rods represent reactor fuel pins which consist of ceramic cores encased in metallic claddings. The following thermal boundary conditions were treated: (a) uniform wall heat flux in the axial direction and uniform wall temperature in the circumferential direction, on the outside surface of the cladding; (b) uniform wall heat flux in all directions on the outside surface of the cladding; and (c) uniform wall heat flux in all directions on the inside surface of the cladding. For boundary conditions (a) and (b), the independent variables are Reynolds number (Re) and rod spacing (P/D), while for boundary condition (c) there are two additional independent variables, i.e., relative cladding conductivity (k_w/k_f) and relative cladding thickness [(r₂ - r₁)/r₂]. The results, all expressed in the form of convenient dimensionless groups, are presented in tables and charts and in the form of simple mathematical expressions for ready use by the design engineer.