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Experiments were conducted at the University of Minnesota (UMN) for simulating the hot end of a Stirling engine. This experimental test rig included the acceptor (normally a heater), expansion space, regenerator, and displacer. To establish a temperature difference for the purpose of measuring convective heat transfer coefficients between the heater wall and the flow, one was heated and the other cooled. The expansion space has a 127 mm (5-inch) diameter dome and a minimum spacing between the dome and the displacer of 4.8 mm (0.1912 inch), at maximum displacer amplitude. The regenerator was simulated as a porous medium. Velocity and temperature measurements were made at seven different locations (P1, P2,...and P7) along the dome surface and on lines normal to the dome surface that extended a distance from 4.5 to 6 mm (0.18 to 0.24 inches) into the flow field. In this paper a 2-D computational model was developed to simulate the UMN experimental test rig. The acceptor was modeled with a 2-D annular geometry that had three annuli matching the UMN hydraulic diameter, Dh, and approximating the UMN flow- and heat-transfer areas. The CFD (Computational Fluid Dynamics) model has 2-D geometry, no metal thicknesses (heat capacities), laminar flow, and one thermal boundary conditions case Ts-315. These simplifications were made to reduce the computational (CPU) time required. Fluent, commercial software version 6.3.26 was used in this effort. The CFD simulations provided more insight into the details of the flow and thermal fields in the expansion space, acceptor channels and porous media. Many of these details were not obtained via the experiment (particularly for the acceptor and porous media) and will likely provide helpful information for future Stirling-device modeling and design efforts.