In　the　current　work,　the　steady　flow　of　magnetohydrodynamic　of　Cu　-Al2O3/water　hybrid　nanofluid　was　investigated　along　with　Joule　heating　and　viscous　dissipation　effect　across　a　porous　shrinking　sheet.　Using　an　appropriate　similarity　transformation,　the　governing　partial　differential　equations　(PDEs)　are　transformed　into　ordinary　differential　equations　(ODEs).　The　system　of　ODEs　is　solved　using　the　bvp4c　function　in　MATLAB.　The　present　findings　are　numerically　and　visually　compared　to　the　available　literature,　and　excellent　agreements　are　discovered.　The　impacts　of　several　new　physical　governing　factors　on　velocity　and　temperature　profiles,　while　the　variation　of　heat　transfer　and　skin　friction,　are　visually　shown　and　explicated　hypothetically.　In　addition,　the　findings　demonstrate　the　presence　of　duality　within　a　limited　range　of　suction　parameters.　Increasing　the　solid　volume　fraction　phi　Cu　increases　the　values　of　f　＇＇　(0)　for　an　initial　solution　and　reduces　them　for　an　unstable　solution.　The　investigation　of　the　temporal　stability　of　the　solutions　concludes　that　the　first　solution　is　stable　only.　The　values　of　smallest　eigenvalues　values　(gamma　＞　0)　are　positive　for　first　solution　indicated　the　stability　of　solution　while　the　values　of　smallest　eigenvalues　values　(gamma　＜　0)　are　negative　for　second　solution　indicates　the　instability　of　solution.　The　quantitative　outcomes　are　in　Table　4.　The　concentration　of　Al2O3　and　Cu　is　almost　20%　(0.01　＜　phi　Al2O3　＜　0.2　and　0.01　＜　phi　Cu　＜　0.2).