In this paper, a numerical study on the flows in parallel and counter flow double tube heat exchangers with the inner tubes being either alternating horizontal or vertical oval cross section pipes or circular pipes is presented. The results include temperature and pressure contours and velocity vectors at several selected cross sections, axial averaged Nusselt number distributions and distributions of overall heat transfer coefficient and heat transfer enhancement factor versus three different parameters. The computation shows that the introduction of the inner alternating oval tube produces axial vortices in both the inner and outer tube flows, and the tube’s heat transfer performance is improved as a result. In general, the counter flow arrangement returns a higher level of overall heat transfer coefficient than the parallel flow arrangement. However, in terms of the magnitude of heat transfer enhancement, the performance of the parallel flow arrangement is slightly better than that of the counter flow.