An increase in the thermal performance of heat exchangers leaves a dramatic influence on the energy consumption of industries, addressing why such studies are of interest. The current numerical work, therefore, aims to increase heat transfer in a shell-and-tube heat exchanger by innovative, novel topological changes, using Cassini cross-sectional tubes and proposed segmental curved baffles. Cassini oval and triple Cassini cross sections in horizontal, vertical, and oblique tube arrangements are applied, not investigated yet. Further, the heat transfer is augmented by adding carbon nanotubes to the pure water. The inlet Reynolds number is chosen between 10,000 and 30,000 and the nanotube volume fraction falls in the range of 0 and 2%. The friction factor, Nusselt number, performance evaluation criteria as well as the second law of thermodynamics analysis, including thermal and frictional entropy generation, are monitored. The Witte–Shamsunder efficiency is also detected to consider both the first and second low. Using the water as the working fluid and irrespective of the baffle geometry, the case with the triple Cassini cross-section tube has the highest value of the Nusselt number up to 100, while the circular tube case sets in the lowest rank, with the value near 50. Additionally, the circular tubes show the worst PEC value, while triple Cassini tubes pretend as the most valuable case, with values of 40–50% higher than those of circular tubes, highlighted more at the lower Reynolds numbers. The cases with curved baffles make the PEC increment in all cases up to 15% compared to those with simple baffles. The entropy generation reduces by using the curved baffles up to 20%.