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The shape derivative of the objective functional was formulated using the rearrangement method, and this derivative was later on used for gradient descent methods. Additionally, an augmented Lagrangian method and a class of solenoidal deformation fields were considered to take into account the goal of volume preservation. Lastly, numerical examples based on gradient descent and the volume preservation methods are presented.<\/jats:p>","DOI":"10.1007\/s40314-022-01876-5","type":"journal-article","created":{"date-parts":[[2022,5,6]],"date-time":"2022-05-06T13:04:41Z","timestamp":1651842281000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":2,"title":["A shape design problem for the Navier\u2013Stokes flow with a convective boundary condition"],"prefix":"10.1007","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7711-9582","authenticated-orcid":false,"given":"J. S. 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