Thermoacoustic theory has been widely used for design of thermoacoustic devices and understanding phenomena in the devices. However, performance in a heat exchanger for thermoacoustic devices has not yet been fully understood because thermoacoustic theory cannot be applied to the heat exchanger absorbing or radiating heat. In this study, numerical analysis without thermoacoustic theory has been performed to evaluate the performance of the heat exchanger for heat absorption or heat radiation. In this paper, the influence of operating frequency on performance of the heat exchanger is investigated by introducing a heat transfer coefficient as an index for evaluating the performance. It was found that the heat transfer coefficient indicates a bigger value with increase in operating frequency and this means that the performance of the heat exchanger is improved with higher operating frequency. It is also found that heat transfer to the wall is enhanced with increase in operating frequency because the range in the radial direction affecting the heat exchange becomes smaller with higher operating frequency and thereby a temperature gradient becomes larger.