To　date,　when　considering　the　dynamics　of　water　conveying　multi-walled　carbon　nanoparticles　(MWCNT)　through　a　vertical　Cleveland　Z-staggered　cavity　where　entropy　generation　plays　a　significant　role,　nothing　is　known　about　the　increasing　Reynold　number,　Hartmann　number,　and　Darcy　number　when　constant　conduction　occurs　at　both　sides,　but　at　different　temperatures.　The　system-governing　equations　were　solved　using　suitable　models　and　the　Galerkin　Finite　Element　Method　(GFEM).　Based　on　the　outcome　of　the　simulation,　it　is　worth　noting　that　increasing　the　Reynold　number　causes　the　inertial　force　to　be　enhanced.　The　velocity　of　incompressible　Darcy-Forchheimer　flow　at　the　middle　vertical　Cleveland　Z-staggered　cavity　declines　with　a　higher　Reynold　number.　Enhancement　in　the　Hartman　number　causes　the　velocity　at　the　center　of　the　vertical　Cleveland　Z-staggered　cavity　to　be　reduced　due　to　the　associated　Lorentz　force,　which　is　absent　when　H-a　=　0　and　highly　significant　when　H-a　=　30.　As　the　Reynold　number　grows,　the　Bejan　number　declines　at　various　levels　of　the　Hartmann　number,　but　increases　at　multiple　levels　of　the　Darcy　number.