The current study explores the behavior of particle shape on the radiative flow of Casson hybrid nanofluid towards an expanding/contracting convective sheet. The nanofluid under onsideration is a water-based hybrid comprising carbon nanotubes (CNTs) with particle shapes. The particle shape factor is employed to determine its significance on the flow characteristic. The standard equations for the flow and thermal transportation are derived based on the conservation laws, including the simultaneous effects of viscous dissipation, thermal radiation, along with uniform heat source. The Casson based model is employed to pronounce the rheological characteristic of the nanofluid, taking into account the non-Newtonian nature of the fluid. To further explore the system, the influence of multiple slip effects and an inclined magnetic field is considered. Multiple slip effects occur due to the simultaneous presence of velocity, thermal, and concentration slips at the solid-fluid interface. The inclined magnetic field is introduced to investigate the magnetohydrodynamic (MHD) effects on the flow characteristics. Numerical simulations are performed using appropriate numerical techniques to solve the resulting system of equations. The effects of various parameters, such as particle shape, slip parameters, magnetic field inclination, and thermal radiation, are thoroughly analyzed. The main findings of this works are; the interaction of CNTs that enhances the thermal conductivity of the nanofluid boost up the heat transfer rate further, and the particle concentrations enhance the fluid temperature significantly. The observation indicates that the increasing slip enhances both the velocity and temperature distribution.