Thermoacoustic machines, Stirling engines or coolers, and pulse tube coolers are examples of energy systems that operate based on oscillatory flow principles. This class of technology would achieve an improved efficiency from appropriately designed heat exchangers, stacks, regenerators and thermal buffer tubes. In this paper, heat transfer and oscillatory flow behaviour in three identical parallel-plate heat exchangers, one ‘heat source’ positioned between two ‘heat sinks’, are investigated using numerical method. The effect of different plate edge shapes on heat transfer, flow structures and acoustic pressure drop are examined at a selected drive ratio of 0.3 – 2.0%. Flow parameters show a strong dependency on drive ratio and flow direction, especially at low excitation where gas displacements are below or comparable to the heat exchanger length. Cone edge shape minimises the flow complexity better than other shapes with a negligible effect on the heat transfer. The result of this study will benefit the design and development of compact and high-efficiency heat exchangers for the next generation of oscillatory-flow energy and thermal management systems.