The unsteady stagnation-point mixed-convection flow of a Cu–Al$_2$O$_3$/water hybrid nanofluid past a stationary vertical Riga plate is analyzed in the presence of convective boundary heating and Rosseland thermal radiation. The wall-fixed configuration of Riga plate is modeled using periodic distribution of electrodes and magnets that yield a parallel wall Lorentz force via an exponentially decaying Grinberg term. The externally prescribed velocity is $u_e(x,t)=ax/(1-ct)$, while the convective wall heat flux specification involves the Biot number. The description of hybrid nanofluid includes uniform nanoparticle concentrations, $\phi_{\mathrm{Cu}}=\phi_{\mathrm{Al_2O_3}}=0.02$, where water acts as base fluid. With the aid of similarity transformations, the system of nonlinear partial differential equations is cast in the form of coupled nonlinear ordinary differential equations. The solution of nonlinear boundary value problem is obtained via a fourth-order collocation approach, whereas stability analysis using temporal eigenvalues differentiates between stable and unstable solutions. For the limit case of viscous fluid flow, $Re_x^{1/2}C_f=1.2325876$ and $Re_x^{-1/2}Nu_x=0.045466$, $0.083373$, and $0.142974$ for $Bi=0.05$, $0.10$, and $0.20$, respectively. The existence of dual branches is reported when the mixed convection is opposing while there is only a single branch when the mixed convection is assisting. The least negative eigenvalues confirm that the first branch is stable while the second one is unstable. Higher deceleration in the time-dependent unsteady motion leads to a lower wall shear and enhanced heat transfer rate. Larger electromagnetic parameters enhance heat transfer owing to electromagnetic acceleration while increasing skin friction due to Lorentz-force effect. Larger decay parameter leads to less Lorentz-force effect thereby reducing shear and heat transfer. The findings reveal the contributions of unsteadiness, buoyancy, convection, radiation, and localized electromagnetic force in ensuring the stable flow of Cu-Al$_2$O$_3$/Water hybrid nanofluid along the wall.

Cu--Al$_2$O$_3$/water hybrid nanofluid,Riga plate,mixed convection,Rosseland radiation,convective heating,dual solutions,temporal stability,wall heat transfer