Hybrid　nanofluids　are　crucial　for　enhancing　thermal　management,　efficiency,　and　longevity　in　industrial　applications　such　as　heat　exchangers,　automotive　cooling,　and　advanced　manufacturing.　The　current　study　primarily　investigates　the　impact　of　viscous　and　Joule　dissipation　on　copper-alumina　hybrid　nanofluid　flow　over　a　stretching　surface,　with　a　particular　focus　on　magnetic　field　effects　resulting　in　a　strong　Lorentz　force　along　the　vertical　direction.　The　governing　equations　are　non-dimensionalized　using　similarity　transformations,　resulting　in　coupled,　highly　nonlinear　ordinary　differential　equations　(ODEs).　The　coupled　system　of　ODEs　is　solved　numerically　using　the　Shooting　technique　and　a　fourth-order　Runge-Kutta　scheme　in　MATLAB.　The　results　are　plotted　graphically.　The　outcomes　mainly　indicate　that　at　the　surface,　momentum　intensifies　with　increased　stretching　but　declines　significantly　under　a　stronger　magnetic　field,　while　reduced　permeability　slows　down　flow　momentum,　resulting　in　higher　temperature　elevations.　The　outcomes　revealed　that　copper-alumina　hybrid　nanofluids　with　lower　permeability　could　improve　the　performance　of　miniature　industrial　devices.