Using a numerical technique, this study explores the flow and thermal aspects of a Maxwell hybrid nanofluid across an exponentially stretched sheet. The analysis incorporates the effects of thermal radiation, viscous dissipation, Joule heating, and chemical reaction. We use the in-built MATLAB function bvp4c to successfully solve the governing equations after we convert them to ordinary differential equations. The key novelty of this work lies in employing the Maxwell hybrid nanofluid, a more complex fluid than traditional nanofluids or regular Maxwell fluids and conducting a multifaceted analysis that considers factors like couple stress, chemical reaction, and entropy generation optimization alongside flow and heat transfer. The findings demonstrate that the Maxwell parameter and the magnetic field parameter both reduce fluid velocity due to opposing forces and enhanced elasticity, respectively. The temperature profile exhibits a rise with increasing thermal radiation, volume fraction of nanoparticles, and Eckert number due to enhanced radiative absorption, improved heat transfer, and internal heat generation respectively. As the Brinkman number and volume percentage of copper nanoparticles increase, the entropy generation becomes more intense and the Bejan number decreases as a result of enhanced viscous dissipation and friction. Between the values of 0.1 and 0.7 for Maxwell parameter, the friction factor exhibits a decrement of 0.1077. The Nusselt number, signifying heat transfer efficiency, reduces with the Eckert number but increases with the radiation parameter and volume fraction of nanoparticles. Between the values of 0.1 and 0.7 for Eckert number, the friction factor exhibits a decrement of 0.1077. Lastly, a steeper concentration gradient causes the Sherwood number, which is an indication of the mass transmission rate, to rise with the Schmidt number. it is detected that the rate of heat transfer increases at a rate of 0.0721 when chemical reaction values lie between 0 and 1.8.
