This study presents a Computational Fluid Dynamics (CFD)-based optimization framework to enhance the performance of bare-tube heat exchangers. The framework comprises a CFD solver, an adjoint solver, and a CAD-based parametrization tool. This framework simultaneously optimizes the tube shape and layout to obtain an optimum heat exchanger configuration with a higher heat transfer rate and lower pressure drop. Firstly, a parametric study of the longitudinal pitch is performed that shows that increasing the longitudinal pitch results in an increase in pressure drop and heat transfer rate. Furthermore, the proposed framework was applied to optimize an in-line elliptical tube configuration. The optimum geometry showed a performance improvement of 29% as compared to the baseline geometry while satisfying the constraint on the heat transfer rate.