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Power can be converted with high efficiently between thermal energy and mechanical (acoustic) energy by using thermoacoustic technologies. Thus, the heat transfer characteristics are significant to the understanding of mechanisms, and improvement of efficiency for thermoacoustic devices, notably in heat exchangers. This paper introduces a two-dimensional computational fluid dynamics model of flow across a parallel-plate heat exchanger and investigates the effect of plate spacing on heat transfer characteristics. The open source CFD software OpenFOAM is applied because of the highly customizable capabilities to vary the control parameters. Firstly, the computational model including geometry, boundary conditions, equations, discretization scheme, turbulence and thermophysical properties’ models are presented, and then grid-independence validation is presented to verify the quality of mesh. The simulation results show that plate spacing influences the heat transfer between plates and adjacent area of heat exchanger, and the heat transfer coefficient goes up when the plate spacing decreases. The analysis also indicates that a possible flow transition to turbulence occurred within Re number between 247.2 and 321.4. The results in this work can help the understanding of heat transfer inside thermoacoustic system, and form a basis for future research.