Analytic study of conduction and convective heat transfer in finite tube bundles

Exact analytic expressions for the static temperature fields and the heat fluxes for given velocity profiles are obtained over the cross section of a nuclear fuel rod-clustered circular coolant channel. The thermally fully developed region of the coolant channel is considered in this study. The temperatures and the heat fluxes at the fuel-cladding and the cladding-coolant interfaces are taken to be continuous. The analysis is carried out for both slug and fully developed laminar flows. For the latter case, the fully developed laminar velocity profile is determined by using the method of weighted residuals. The effect of the peripheral fuel rods on the temperature field is studied by using the method of Howland functions. The result of this study show how appreciable circumferential variations of the temperature and the heat flux in the fuel rod and the cladding can arise.