In fluid mechanics, two of the most widely used optimization approaches are shape and topology optimization, which are generally treated as mutually-exclusive. This paper presents a general continuous adjoint formulation for both shape and topology optimization, focusing on (a) crucial aspects of computing accurate shape sensitivity derivatives such as the differentiation of the turbulence model PDEs and the proper treatment of grid sensitivities and (b) a synergistic, sequential application of topology and shape optimization, in which topology is used to define a preliminary solution from which shape optimization can be initiated. To achieve this, a transition process is used to accurately represent and parameterize the topological solution with NURBS surfaces. The flow cases presented in this work and the in-house code pertaining to the optimization and transition process are implemented within OpenFOAM. Results from purely aerodynamic as well as multidisciplinary applications including Conjugate Heat Transfer (CHT) are presented.