In this thesis, numerical simulation has been applied on the flows in counter-flow, double-tube heat exchangers with the inner tubes being either alternating horizontal or vertical oval cross section pipes or circular pipes. The results include temperature and pressure contours and velocity vectors at several selected cross sections, axial averaged Nusselt number distributions and distributions of overall friction coefficient, heat transfer coefficient and performance factor versus Reynolds number and tube length. 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. At the conditions of higher Reynolds number and longer tube, the alternating oval tube performs much better than the circular one, with the performance factor reaching 30% higher at Re=2,000 and tube length=1.266 m. However, at some conditions of lower Reynolds number and shorter tube length, the alternating oval tube performs slightly worse than its circular counterpart.