Numerical simulation of heat and fluid flow has been performed to estimate the value of time-averaged heat transfer coefficient between the working gas and the wall in oscillatory flows. Transient two-dimensional equations of continuity, momentum and energy were solved utilizing a TVD scheme. A physical model of a simple circular tube was used for the numerical simulation. In this study, the value of heat transfer coefficient in a heat exchanger was clarified by analyzing the numerical results of the two-dimensional simulation.