Conjugate heat transfer associated with the flow of sodium in an annulus in the decay heat removal mode of advanced fast reactors is studied. The coupled governing equations of momentum and energy are solved numerically and analytically. The TEACH code with the SIMPLE algorithm has been used for the internal forced flow and wall regions. For turbulent flow, a k-ε model is employed. The integral method is used for natural convection, and one-dimensional analysis is performed for the stratified flow over and underneath the redan. Results are presented for the two-dimensional temperature field in the fluids and the solid for both laminar and turbulent flows. A substantial amount of energy exchange between the hot or cold pool and the sodium flowing in the annulus occurs via the liner. As a result, convective boundary layers form along the liner. The convective motion leads to a stratified flow along the redan. In the absence of a core barrel extending into the hot pool, the fluid stratified in the hot pool, for certain core power and flow conditions, can drain down the radial blanket or be entrained by the fluid exiting the core. In contrast to behavior with an insulated liner, the heat transfer across the liner reduces the average temperature drop of the sodium flowing in the annulus, which in turn leads to a reduction in the hydrostatic head available for driving the fluid through the core.