Modern industrial buildings and solar panels are both reliant on thermal efficiency. The Casson nanofluids are a potential working fluid due to their excellent heat transfer properties and adjustable flow behavior. Due to such significant uses, we examine solar-driven magneto-Casson squeezing nanofluid flow over a linearly stretched surface in porous media while incorporating combining effects of Joule heating, internal heat generation as well as thermal radiation. Additionally, Newtonian heating is applied to the bottom surface to improve thermal transmission. Linear thermal stratification is inadequate for accurately capturing heat transport in industrial machineries, because they need large temperature differences. For a more realistic depiction, quadratic thermal stratification is thus used. The working nanofluid contains cobalt ferrite (COFe2O4) nanoparticles that are suspended in sodium alginate, while the Hamilton–Crosser model is used to examine the impact of different nanoparticle shapes on the system. After applying similarity transformation to reduce the governing equations to nonlinear ordinary differential equations, Mathematica's NDSolve is used to resolve the resulting equations numerically. A thorough analysis is conducted of the impacts of important physical factors on skin friction, flow, temperature fields, and Nusselt number. Results indicate that the squeezing constraint increases the flow velocity, whereas the flow velocity is reduced by high magnetic effects. Increasing the Newtonian heating parameter increases the temperature field. However, due to the effect of thermal stratification, this increase is reduced. Diverse morphologies of the particles exhibit varying thermal performance; platelets-like the highest temperature, cylinders exhibit the lowest, and bricks and blades provide modest results. The present results are in close agreement with the results from previous studies, thus confirming the effectiveness of the simulation methodology being used for this work. The findings provide important information for improving contemporary heat transfer technology and creating energy-efficient solar thermal power systems.