This　paper　includes　a　numerical　investigation　of　a　hybrid　fluid　containing　4%　of　Al2O3-Cu　nanoparticles　in　a　lid-driven　container.　The　upper　wall　of　the　container　has　a　high　temperature　and　is　movable.　The　lower　wall　is　cool　and　wavy.　An　obstacle　is　set　in　the　middle　of　the　container　for　its　effect　on　thermal　activity.　The　medium　is　permeable　to　the　fluid,　and　the　entire　system　is　immersed　in　a　fixed-effect　magnetic　field.　The　digital　simulation　is　achieved　using　the　technique　of　Galerkin　finite　element　(GFEM)　which　solves　the　differential　equations.　This　investigation　aims　to　know　the　pattern　of　heat　transfer　between　the　lateral　walls　and　the　lower　wall　of　the　container　through　the　intervention　of　a　set　of　conditions　and　criteria,　namely:　the　strength　of　the　magnetic　field　changes　in　the　range　of　(Ha　=　0　to　100);　the　chamber　porosity　varies　in　the　range　of　(Da　=　10(-5)　to　10(-2));　the　strength　of　buoyancy　force　is　varied　according　to　the　Grashof　number　(Gr　=　10(2)　to　10(4));　the　cross-section　of　the　baffle　includes　the　following　shapes-elliptical,　square,　triangular　and　circular;　the　surface　of　the　lower　wall　contains　waves;　and　the　number　changes　(N　=　2　to　8).　Through　this　research,　it　was　concluded　that　the　triangular　shape　of　the　baffle　is　the　best　in　terms　of　thermal　activity.　Also,　increasing　the　number　of　lower-wall　waves　reduces　thermal　activity.　For　example,　the　change　in　the　shape　of　the　obstacle　from　the　elliptical　to　triangular　raises　the　value　of　Nu　number　at　a　rate　of　15.54%　for　Ha　=　0,　N　=　8,　and　Gr　=　10(4).