Thermal hydraulics related to the design of the spallation target module of an accelerator-driven subcritical system (ADSS) was investigated numerically using a streamline upwind Petrov-Galerkin (SUPG) finite element (FE) method. A large amount of heat is deposited on the window and in the target during the course of nuclear reaction between the proton beam and the molten lead-bismuth eutectic (LBE) target. Simulations were carried out to predict the characteristics of the flow and temperature fields in the target module with a funnel-shaped flow guide and spherical bottom of the container. The beam window was kept under various thermal conditions. The analysis was extended to the case of heat generation in the LBE. The principal purpose of the analysis was to trace the temperature distribution on the beam window and in the LBE. In the case of turbulent flows, the number of recirculation regions is decreased and the maximum heat transfer was found to take place downstream of the stagnation zone on the window. Copyright © 2007 by ASME.