An accurate computational method for the calculation of flow and heat transfer in compact heat exchangers is developed and implemented on the massively parallel Connection Machine, CM-5. In this method, the unsteady Navier-Stokes and energy equations are solved. The current study shows that the inclusion of flow unsteadiness plays a very important role in the accurate prediction of heat exchanger performance quantities of interest such as the Colburn j factor and the friction factor. It is also shown that at higher Reynolds numbers, the additional effect introduced by the intrinsic three-dimensionality of the flow plays another important role in determining the overall heal exchanger performance. Therefore, the above two effects have to be taken into account in order to accurately predict heat exchanger performance.