ADSS (Accelerator Driven Sub-critical System) nuclear reactors are expected to play a significant role in nuclear power generation in future due to their ability to utilize Thorium as the nuclear fuel, operating in sub-critical conditions and to transmute radioactive nuclear wastes. Numerical investigation of fluid flow and heat transfer characteristics of an ADSS has been accomplished using a finite element method based on Streamline Upwind Petrov-Galerkin (SUPC) technique. The time-dependent governing equations for conservation of mass, momentum and energy are solved. The simulations have been carried out to predict the heat transfer in the spallation regime. At the first place, laminar regime of the flow is considered for the ADSS geometry. The Reynolds number of interest were varied over a specified range. Copyright © 2005 by ASME.