In　this　paper,　the　Casson　fluid　model　and　the　inclined　magnetic　field　are　used　to　analyse　mathematically　the　energy　transport　of　double　diffusive　natural　convection　(DDNC)　in　a　curvilinear　enclosure.　The　Galerkin　finite　element　method　(GFEM)　is　used　to　discretize　the　equations.　When　simulating　the　different　ranges　of　Rayleigh　numbers　(105　≤　Ra　≤　108)　and　the　heated　part,　we　adopt　isotherms　and　streamlines　to　visualize　the　thermal　and　flow　fields.　In　addition,　we　study　the　impact　of　the　Casson　parameter　on　the　Nusselt　number　along　the　cavity　wall.　The　results　show　that　the　lower　values　of　Casson　fluid　parameter　have　a　significant　effect　on　the　Nusselt　number　in　the　middle　of　the　cavity.　Finally,　the　results　are　verified　with　the　existing　studies,　and　various　parameters　such　as　streamline,　isotherm,　isoconcentration　contour　and　kinetic　energy　are　presented　in　the　form　of　graphs　and　tabular　formats.　©　Published　under　licence　by　IOP　Publishing　Ltd.