An oscillating-wave engine or refrigerator having a regenerator or a stack in which oscillating flow of a working gas occurs in a direction defined by an axis of a trunk of the engine or refrigerator, incorporates an improved heat exchanger. First and second connections branch from the trunk at locations along the axis in selected proximity to one end of the regenerator or stack, where the trunk extends in two directions from the locations of the connections. A circulating heat exchanger loop is connected to the first and second connections. At least one fluidic diode within the circulating heat exchanger loop produces a superimposed steady flow component and oscillating flow component of the working gas within the circulating heat exchanger loop. A local process fluid is in thermal contact with an outside portion of the circulating heat exchanger loop.