The present study deals with boundary layer flows of buoyancy-driven magnetohydrodynamic, chemical-radiative, and temperature-sensitive Casson hybrid nanofluid over diverging channel. Copper (Cu) and aluminum oxide (Al<sub>2</sub>O<sub>3</sub>) nanoparticles are suspended upon ethylene glycol-based non-Newtonian Casson fluid. The proposed model is applicable in power transmission systems the design of nuclear reactors where a moving plate is used as a control rod, and the design of compression molding processes. The boundary layer governing equations undergo nonsimilar transformations followed by a quasilinearization technique and an implicit finite difference scheme. Varga's algorithm is applied on the obtained block tri-diagonal system of equations. The study pertinent to dimensionless parameters like Reynolds number, Eckert number, Casson parameter, and Richardson's number on velocity, temperature, drag coefficient, and heat transfer profiles. Also surface plots are plotted for varied values of Casson parameter and magnetic parameter on skin friction and heat transfer coefficients. It is to be noted that for enhanced values of Casson parameter β, the velocity profile is augmented, and the temperature profile is declined. It is observed that the temperature profile is enhanced at the center of the channel for enhanced values of viscous dissipation parameter Ec.