PurposeThe　main　purpose　of　this　study　is　to　analyze　the　heat　transfer　phenomena　in　a　dynamically　bulging　enclosure　filled　with　Cu-water　nanofluid.　This　study　examines　the　convective　heat　transfer　process　induced　by　a　bulging　area　considered　a　heat　source,　with　the　enclosure＇s　side　walls　having　a　low　temperature　and　top　and　bottom　walls　being　treated　as　adiabatic.　Various　factors,　such　as　the　Rayleigh　number　(Ra),　nanoparticle　volume　fraction,　Darcy　effects,　Hartmann　number　(Ha)　and　effects　of　magnetic　inclination,　are　analyzed　for　their　impact　on　the　flow　behavior　and　temperature　distribution.Design/methodology/approachThe　finite　element　method　(FEM)　is　employed　for　simulating　variations　in　flow　and　temperature　after　validating　the　results.　Solving　the　non-linear　partial　differential　equations　while　incorporating　the　modified　Darcy　number　(10-3　＜=　Da　＜=　10-1),　Ra　(103　＜=　Ra　＜=　105)　and　Ha　(0　＜=　Ha　＜=　100)　as　the　dimensionless　operational　parameters.FindingsThis　study　demonstrates　that　in　enclosures　with　dynamically　positioned　bulges　filled　with　Cu-water　nanofluid,　heat　transfer　is　significantly　influenced　by　the　bulge　location　and　nanoparticle　volume　fraction,　which　alter　flow　and　heat　patterns.　The　varying　impact　of　magnetic　fields　on　heat　transfer　depends　on　the　Rayleigh　and　Has.Practical　implicationsThe　geometry　configurations　employed　in　this　research　have　broad　applications　in　various　engineering　disciplines,　including　heat　exchangers,　energy　storage,　biomedical　systems　and　food　processing.Originality/valueThis　research　provides　insights　into　how　different　shapes　of　the　heated　bulging　area　impact　the　hydromagnetic　convection　of　Cu-water　nanofluid　flow　in　a　dynamically　bulging-shaped　porous　system,　encompassing　curved　surfaces　and　various　multi-physical　conditions.