This research investigates the adjoint-based optimization of bare tube heat exchangers, aiming to minimize air-side pressure drop. The study focuses on optimizing tube shapes in an in-line bare tube heat exchanger configuration, selected for its inherent advantages in reducing pressure drop. The optimization targets flow conditions characterized by a Reynolds number of approximately 1000, based on the tube diameter. The accuracy of simulations was found to depend significantly on the turbulence modelling approach. Different models were benchmarked against empirical correlations to ensure accuracy, with the most accurate model used to recompute the flow fields of the optimized designs as a post-processing step. The optimized round tubes achieved a pressure drop reduction of up to 20%. For elliptical tubes, the optimization resulted in a pressure drop reduction of up to 10%. This 10% reduction adds to the notable improvement gained by replacing round tubes with elliptical ones.