Hydrodynamically and thermally fully developed, steady, incompressible laminar flow in a concentric curved annular duct is investigated numerically under constant wall temperature boundary condition. The equations of discretized continuity, momentum, and energy have been solved numerically, and a computer code for the present mathematical model has been developed. The secondary flow streamlines, isotherms, and velocity profiles as well as the local and the average Nusselt numbers and friction factors are presented for various values of annulus dimension ratio and Dean number. The secondary flows resulting from centrifugal forces affect the distribution of the velocity and the temperature. As a consequence of this study, it was determined that viscous forces become more effective upon centrifugal forces while the annulus dimension ratio decreases.