This research explores entropy generation in the two-dimensional flow of MHD (Al₂O₃–TiO₂/H₂O) hybrid nanofluid over an exponentially stretching sheet within a porous medium. The study incorporates chemical reaction, thermal radiation, and Joule heating into the concentration and energy equations, which are thoroughly analyzed. The governing PDEs are transformed into nonlinear ODEs using similarity solutions and solved numerically with the bvp4c solver in MATLAB. The study examines the effects on flow profiles and key engineering parameters. Results show that increasing Brinkman and Reynolds numbers produces contrasting trends in entropy generation and the Bejan number. A stronger magnetic field and porous medium increase skin friction by 2.18 % in hybrid nanofluids. An enhanced Eckert number combined with radiation raises heat transfer by 5 % compared to conventional TiO₂/H₂O. The mass transfer rate increases by over 1.5 % with a rising reaction factor in Al₂O₃–TiO₂/H₂O.