Industrial and business environments may benefit profoundly from the heat transfers provided by magnetohydrodynamic nanofluid flow via cone, wedge, and plate. Conical geometries are frequently employed in the creation of fluid system nozzles and diffusers. Conical nozzles promote fluid flow whereas conical diffusers diminish it. These parts are employed in a variety of applications, including jet engines and HVAC systems. In industrial systems, wedges are employed in relief valves that release pressure to regulate the discharge of pressurised fluids or gases. Motivated by this, this study aims to simulate the flow and heat transfer attributes of a magnetised Casson hybrid nanofluid (GO-MoS2/sodium alginate) subject to quadratic thermal radiation and nonlinear convection through cone-, wedge-, and plate-shaped geometries. The Darcy-Forchheimer and Cattaneo-Christov models were utilised to investigate the flow across porous media and heat transfer attributes, respectively. The solution to the governing equations is attained using bvp4c solver, and the effects of parameters like thermal relaxation parameter, Casson factor, Grashof number, magnetic parameter, Eckert number, and wall temperature on flow velocity and temperature are illustrated through graphs and tables, as are their consequences on physical quantities. The study reports that fluid velocity decreases with an increase in magnetic parameter, wall temperature, and thermal relaxation parameter, and fluid temperature decreases with an increase in magnetic parameter, Grashof number, and Eckert number. Further, the wall temperature and thermal relaxation parameters increase the heat transfer rate and reduce the skin friction coefficient. Moreover, a comparison with earlier published work is also done to verify the accuracy of the applied method and is reported to be consistent with previous studies.